200324

Python


A140517等

Graphillion を使って計算してみた。

from graphillion import GraphSet
import graphillion.tutorial as tl

def A(points, n):
    if n == 1: return 1
    universe = tl.grid(n - 1, n - 1)
    GraphSet.set_universe(universe)
    cycles = GraphSet.cycles()
    for i in points:
        cycles = cycles.including(i)
    return cycles.len()

print([A([                            ], n) for n in range(2, 10)])

print([A([1                           ], n) for n in range(2, 10)])

print([A([1, n                        ], n) for n in range(2, 10)])
print([A([1,    n * (n - 1) + 1       ], n) for n in range(2, 10)])
print([A([1,                     n * n], n) for n in range(2, 10)])

print([A([1, n, n * (n - 1) + 1       ], n) for n in range(2, 10)])

print([A([1, n, n * (n - 1) + 1, n * n], n) for n in range(2, 10)])

出力結果
[1, 13, 213, 9349, 1222363, 487150371, 603841648931, 2318527339461265]
[1, 7, 97, 4111, 532269, 212372937, 263708907211, 1013068026356375]
[1, 4, 47, 1843, 232905, 92729439, 115234959344, 442748883422394]
[1, 4, 47, 1843, 232905, 92729439, 115234959344, 442748883422394]
[1, 3, 42, 1799, 232094, 92617031, 115156685746, 442641690778179]
[1, 2, 22, 822, 102052, 40504068, 50350960560, 193492369367420]
[1, 1, 11, 373, 44930, 17720400, 22013629316, 84579095455492]

200323(2)

Python


A003763(2)

paths を使うよりcycles を使う方が楽に書ける。

from graphillion import GraphSet
import graphillion.tutorial as tl

def A(n):
    universe = tl.grid(n - 1, n - 1)
    GraphSet.set_universe(universe)
    cycles = GraphSet.cycles(is_hamilton=True)
    return cycles.len()

def A003763(n):
    return A(2 * n)

print([A003763(n) for n in range(1, 5)])

出力結果
[1, 6, 1072, 4638576]

200323

Python


A003763(1)

Graphillion を使って計算してみた。

from graphillion import GraphSet
import graphillion.tutorial as tl

def A(n):
    universe = tl.grid(n - 1, n - 1)
    GraphSet.set_universe(universe)
    start, goal = 1, 2
    paths = GraphSet.paths(start, goal)
    for i in range(3, n * n + 1):
        paths = paths.including(i)
    return paths.len()

def A003763(n):
    return A(2 * n)

print([A003763(n) for n in range(1, 5)])

出力結果
[1, 6, 1072, 4638576]

200322

Python


A333439等

Graphillion を使って計算してみた。

from graphillion import GraphSet
import graphillion.tutorial as tl

def A(start, goal, n):
    if n == 1: return 1
    universe = tl.grid(n - 1, n - 1)
    GraphSet.set_universe(universe)
    paths = GraphSet.paths(start, goal)
    return paths.len()

print([A(1,     2, n) for n in range(2, 10)])
print([A(1, n + 1, n) for n in range(2, 10)])
print([A(1,     n, n) for n in range(1, 10)])
print([A(1, n * n, n) for n in range(1, 10)])

出力結果
[2, 8, 98, 4112, 532270, 212372938, 263708907212, 1013068026356376]
[2, 8, 98, 4112, 532270, 212372938, 263708907212, 1013068026356376]
[1, 2, 11, 178, 8590, 1246850, 550254085, 741333619848, 3046540983075504]
[1, 2, 12, 184, 8512, 1262816, 575780564, 789360053252, 3266598486981642]

200316

Crystal


A332954(3)

https://math.stackexchange.com/questions/3572301/why-are-the-numbers-of-two-different-permutations-the-same
上記の回答にあるように、a からb への全単射が存在する。

このことを確認してみた。

def a(k, m, n)
  a = (m..m + n - 1).map{|i| [i]}
  len = 1
  while len < n
    b = Array(Array(Int32)).new
    a.each{|c|
      (m..m + n - 1).each{|num|
        if !c.includes?(num)
          i = c.clone + [num]
          if (i[-2] * (len + k + 1)) > (i[-1] * (len + k))
            b << i
          end
        end
      }
    }
    a = b
    len += 1
  end
  a
end

def b(k, m, n)
  a = (m..m + n - 1).map{|i| [i]}
  len = 1
  while len < n
    b = Array(Array(Int32)).new
    a.each{|c|
      (m..m + n - 1).each{|num|
        if !c.includes?(num)
          i = c.clone + [num]
          if (i[-2] * (len + k + 1)) >= (i[-1] * (len + k))
            b << i
          end
        end
      }
    }
    a = b
    len += 1
  end
  # bijection
  a.map{|c| c.map{|i| i + 1} + [m]}
end

# 具体例も出力
(0..5).each{|i|
  (0..i + 1).each{|j|
    p a = (2..5).map{|k| a(i, j, k)}
    p b = (1..4).map{|k| b(i, j, k)}
    p [i, j, a == b]
  }
}

(0..13).each{|i|
  (0..i + 1).each{|j|
    a = (2..16).map{|k| a(i, j, k)}
    b = (1..15).map{|k| b(i, j, k)}
    p [i, j, a == b]
  }
}

出力結果
[[[1, 0]], [[2, 1, 0]], [[2, 3, 1, 0], [3, 2, 1, 0]], [[2, 3, 4, 1, 0], [3, 4, 2, 1, 0], [4, 3, 2, 1, 0]]]
[[[1, 0]], [[2, 1, 0]], [[2, 3, 1, 0], [3, 2, 1, 0]], [[2, 3, 4, 1, 0], [3, 4, 2, 1, 0], [4, 3, 2, 1, 0]]]
[0, 0, true]
[[[2, 1]], [[2, 3, 1], [3, 2, 1]], [[2, 3, 4, 1], [3, 4, 2, 1], [4, 3, 2, 1]], [[2, 3, 4, 5, 1], [3, 4, 5, 2, 1], [3, 5, 4, 2, 1], [4, 5, 3, 2, 1], [5, 3, 4, 2, 1], [5, 4, 3, 2, 1]]]
[[[2, 1]], [[2, 3, 1], [3, 2, 1]], [[2, 3, 4, 1], [3, 4, 2, 1], [4, 3, 2, 1]], [[2, 3, 4, 5, 1], [3, 4, 5, 2, 1], [3, 5, 4, 2, 1], [4, 5, 3, 2, 1], [5, 3, 4, 2, 1], [5, 4, 3, 2, 1]]]
[0, 1, true]
[[[1, 0]], [[2, 1, 0]], [[3, 2, 1, 0]], [[3, 4, 2, 1, 0], [4, 3, 2, 1, 0]]]
[[[1, 0]], [[2, 1, 0]], [[3, 2, 1, 0]], [[3, 4, 2, 1, 0], [4, 3, 2, 1, 0]]]
[1, 0, true]
[[[2, 1]], [[3, 2, 1]], [[3, 4, 2, 1], [4, 3, 2, 1]], [[3, 4, 5, 2, 1], [4, 5, 3, 2, 1], [5, 4, 3, 2, 1]]]
[[[2, 1]], [[3, 2, 1]], [[3, 4, 2, 1], [4, 3, 2, 1]], [[3, 4, 5, 2, 1], [4, 5, 3, 2, 1], [5, 4, 3, 2, 1]]]
[1, 1, true]
[[[3, 2]], [[3, 4, 2], [4, 3, 2]], [[3, 4, 5, 2], [4, 5, 3, 2], [5, 4, 3, 2]], [[3, 4, 5, 6, 2], [4, 5, 6, 3, 2], [5, 6, 4, 3, 2], [6, 4, 5, 3, 2], [6, 5, 4, 3, 2]]]
[[[3, 2]], [[3, 4, 2], [4, 3, 2]], [[3, 4, 5, 2], [4, 5, 3, 2], [5, 4, 3, 2]], [[3, 4, 5, 6, 2], [4, 5, 6, 3, 2], [5, 6, 4, 3, 2], [6, 4, 5, 3, 2], [6, 5, 4, 3, 2]]]
[1, 2, true]
[[[1, 0]], [[2, 1, 0]], [[3, 2, 1, 0]], [[4, 3, 2, 1, 0]]]
[[[1, 0]], [[2, 1, 0]], [[3, 2, 1, 0]], [[4, 3, 2, 1, 0]]]
[2, 0, true]
[[[2, 1]], [[3, 2, 1]], [[4, 3, 2, 1]], [[4, 5, 3, 2, 1], [5, 4, 3, 2, 1]]]
[[[2, 1]], [[3, 2, 1]], [[4, 3, 2, 1]], [[4, 5, 3, 2, 1], [5, 4, 3, 2, 1]]]
[2, 1, true]
[[[3, 2]], [[4, 3, 2]], [[4, 5, 3, 2], [5, 4, 3, 2]], [[4, 5, 6, 3, 2], [5, 6, 4, 3, 2], [6, 5, 4, 3, 2]]]
[[[3, 2]], [[4, 3, 2]], [[4, 5, 3, 2], [5, 4, 3, 2]], [[4, 5, 6, 3, 2], [5, 6, 4, 3, 2], [6, 5, 4, 3, 2]]]
[2, 2, true]
[[[4, 3]], [[4, 5, 3], [5, 4, 3]], [[4, 5, 6, 3], [5, 6, 4, 3], [6, 5, 4, 3]], [[4, 5, 6, 7, 3], [5, 6, 7, 4, 3], [6, 7, 5, 4, 3], [7, 5, 6, 4, 3], [7, 6, 5, 4, 3]]]
[[[4, 3]], [[4, 5, 3], [5, 4, 3]], [[4, 5, 6, 3], [5, 6, 4, 3], [6, 5, 4, 3]], [[4, 5, 6, 7, 3], [5, 6, 7, 4, 3], [6, 7, 5, 4, 3], [7, 5, 6, 4, 3], [7, 6, 5, 4, 3]]]
[2, 3, true]
[[[1, 0]], [[2, 1, 0]], [[3, 2, 1, 0]], [[4, 3, 2, 1, 0]]]
[[[1, 0]], [[2, 1, 0]], [[3, 2, 1, 0]], [[4, 3, 2, 1, 0]]]
[3, 0, true]
[[[2, 1]], [[3, 2, 1]], [[4, 3, 2, 1]], [[5, 4, 3, 2, 1]]]
[[[2, 1]], [[3, 2, 1]], [[4, 3, 2, 1]], [[5, 4, 3, 2, 1]]]
[3, 1, true]
[[[3, 2]], [[4, 3, 2]], [[5, 4, 3, 2]], [[5, 6, 4, 3, 2], [6, 5, 4, 3, 2]]]
[[[3, 2]], [[4, 3, 2]], [[5, 4, 3, 2]], [[5, 6, 4, 3, 2], [6, 5, 4, 3, 2]]]
[3, 2, true]
[[[4, 3]], [[5, 4, 3]], [[5, 6, 4, 3], [6, 5, 4, 3]], [[5, 6, 7, 4, 3], [6, 7, 5, 4, 3], [7, 6, 5, 4, 3]]]
[[[4, 3]], [[5, 4, 3]], [[5, 6, 4, 3], [6, 5, 4, 3]], [[5, 6, 7, 4, 3], [6, 7, 5, 4, 3], [7, 6, 5, 4, 3]]]
[3, 3, true]
[[[5, 4]], [[5, 6, 4], [6, 5, 4]], [[5, 6, 7, 4], [6, 7, 5, 4], [7, 6, 5, 4]], [[5, 6, 7, 8, 4], [6, 7, 8, 5, 4], [7, 8, 6, 5, 4], [8, 6, 7, 5, 4], [8, 7, 6, 5, 4]]]
[[[5, 4]], [[5, 6, 4], [6, 5, 4]], [[5, 6, 7, 4], [6, 7, 5, 4], [7, 6, 5, 4]], [[5, 6, 7, 8, 4], [6, 7, 8, 5, 4], [7, 8, 6, 5, 4], [8, 6, 7, 5, 4], [8, 7, 6, 5, 4]]]
[3, 4, true]
[[[1, 0]], [[2, 1, 0]], [[3, 2, 1, 0]], [[4, 3, 2, 1, 0]]]
[[[1, 0]], [[2, 1, 0]], [[3, 2, 1, 0]], [[4, 3, 2, 1, 0]]]
[4, 0, true]
[[[2, 1]], [[3, 2, 1]], [[4, 3, 2, 1]], [[5, 4, 3, 2, 1]]]
[[[2, 1]], [[3, 2, 1]], [[4, 3, 2, 1]], [[5, 4, 3, 2, 1]]]
[4, 1, true]
[[[3, 2]], [[4, 3, 2]], [[5, 4, 3, 2]], [[6, 5, 4, 3, 2]]]
[[[3, 2]], [[4, 3, 2]], [[5, 4, 3, 2]], [[6, 5, 4, 3, 2]]]
[4, 2, true]
[[[4, 3]], [[5, 4, 3]], [[6, 5, 4, 3]], [[6, 7, 5, 4, 3], [7, 6, 5, 4, 3]]]
[[[4, 3]], [[5, 4, 3]], [[6, 5, 4, 3]], [[6, 7, 5, 4, 3], [7, 6, 5, 4, 3]]]
[4, 3, true]
[[[5, 4]], [[6, 5, 4]], [[6, 7, 5, 4], [7, 6, 5, 4]], [[6, 7, 8, 5, 4], [7, 8, 6, 5, 4], [8, 7, 6, 5, 4]]]
[[[5, 4]], [[6, 5, 4]], [[6, 7, 5, 4], [7, 6, 5, 4]], [[6, 7, 8, 5, 4], [7, 8, 6, 5, 4], [8, 7, 6, 5, 4]]]
[4, 4, true]
[[[6, 5]], [[6, 7, 5], [7, 6, 5]], [[6, 7, 8, 5], [7, 8, 6, 5], [8, 7, 6, 5]], [[6, 7, 8, 9, 5], [7, 8, 9, 6, 5], [8, 9, 7, 6, 5], [9, 7, 8, 6, 5], [9, 8, 7, 6, 5]]]
[[[6, 5]], [[6, 7, 5], [7, 6, 5]], [[6, 7, 8, 5], [7, 8, 6, 5], [8, 7, 6, 5]], [[6, 7, 8, 9, 5], [7, 8, 9, 6, 5], [8, 9, 7, 6, 5], [9, 7, 8, 6, 5], [9, 8, 7, 6, 5]]]
[4, 5, true]
[[[1, 0]], [[2, 1, 0]], [[3, 2, 1, 0]], [[4, 3, 2, 1, 0]]]
[[[1, 0]], [[2, 1, 0]], [[3, 2, 1, 0]], [[4, 3, 2, 1, 0]]]
[5, 0, true]
[[[2, 1]], [[3, 2, 1]], [[4, 3, 2, 1]], [[5, 4, 3, 2, 1]]]
[[[2, 1]], [[3, 2, 1]], [[4, 3, 2, 1]], [[5, 4, 3, 2, 1]]]
[5, 1, true]
[[[3, 2]], [[4, 3, 2]], [[5, 4, 3, 2]], [[6, 5, 4, 3, 2]]]
[[[3, 2]], [[4, 3, 2]], [[5, 4, 3, 2]], [[6, 5, 4, 3, 2]]]
[5, 2, true]
[[[4, 3]], [[5, 4, 3]], [[6, 5, 4, 3]], [[7, 6, 5, 4, 3]]]
[[[4, 3]], [[5, 4, 3]], [[6, 5, 4, 3]], [[7, 6, 5, 4, 3]]]
[5, 3, true]
[[[5, 4]], [[6, 5, 4]], [[7, 6, 5, 4]], [[7, 8, 6, 5, 4], [8, 7, 6, 5, 4]]]
[[[5, 4]], [[6, 5, 4]], [[7, 6, 5, 4]], [[7, 8, 6, 5, 4], [8, 7, 6, 5, 4]]]
[5, 4, true]
[[[6, 5]], [[7, 6, 5]], [[7, 8, 6, 5], [8, 7, 6, 5]], [[7, 8, 9, 6, 5], [8, 9, 7, 6, 5], [9, 8, 7, 6, 5]]]
[[[6, 5]], [[7, 6, 5]], [[7, 8, 6, 5], [8, 7, 6, 5]], [[7, 8, 9, 6, 5], [8, 9, 7, 6, 5], [9, 8, 7, 6, 5]]]
[5, 5, true]
[[[7, 6]], [[7, 8, 6], [8, 7, 6]], [[7, 8, 9, 6], [8, 9, 7, 6], [9, 8, 7, 6]], [[7, 8, 9, 10, 6], [8, 9, 10, 7, 6], [9, 10, 8, 7, 6], [10, 8, 9, 7, 6], [10, 9, 8, 7, 6]]]
[[[7, 6]], [[7, 8, 6], [8, 7, 6]], [[7, 8, 9, 6], [8, 9, 7, 6], [9, 8, 7, 6]], [[7, 8, 9, 10, 6], [8, 9, 10, 7, 6], [9, 10, 8, 7, 6], [10, 8, 9, 7, 6], [10, 9, 8, 7, 6]]]
[5, 6, true]
[0, 0, true]
[0, 1, true]
[1, 0, true]
[1, 1, true]
[1, 2, true]
[2, 0, true]
[2, 1, true]
[2, 2, true]
[2, 3, true]
[3, 0, true]
[3, 1, true]
[3, 2, true]
[3, 3, true]
[3, 4, true]
[4, 0, true]
[4, 1, true]
[4, 2, true]
[4, 3, true]
[4, 4, true]
[4, 5, true]
[5, 0, true]
[5, 1, true]
[5, 2, true]
[5, 3, true]
[5, 4, true]
[5, 5, true]
[5, 6, true]
[6, 0, true]
[6, 1, true]
[6, 2, true]
[6, 3, true]
[6, 4, true]
[6, 5, true]
[6, 6, true]
[6, 7, true]
[7, 0, true]
[7, 1, true]
[7, 2, true]
[7, 3, true]
[7, 4, true]
[7, 5, true]
[7, 6, true]
[7, 7, true]
[7, 8, true]
[8, 0, true]
[8, 1, true]
[8, 2, true]
[8, 3, true]
[8, 4, true]
[8, 5, true]
[8, 6, true]
[8, 7, true]
[8, 8, true]
[8, 9, true]
[9, 0, true]
[9, 1, true]
[9, 2, true]
[9, 3, true]
[9, 4, true]
[9, 5, true]
[9, 6, true]
[9, 7, true]
[9, 8, true]
[9, 9, true]
[9, 10, true]
[10, 0, true]
[10, 1, true]
[10, 2, true]
[10, 3, true]
[10, 4, true]
[10, 5, true]
[10, 6, true]
[10, 7, true]
[10, 8, true]
[10, 9, true]
[10, 10, true]
[10, 11, true]
[11, 0, true]
[11, 1, true]
[11, 2, true]
[11, 3, true]
[11, 4, true]
[11, 5, true]
[11, 6, true]
[11, 7, true]
[11, 8, true]
[11, 9, true]
[11, 10, true]
[11, 11, true]
[11, 12, true]
[12, 0, true]
[12, 1, true]
[12, 2, true]
[12, 3, true]
[12, 4, true]
[12, 5, true]
[12, 6, true]
[12, 7, true]
[12, 8, true]
[12, 9, true]
[12, 10, true]
[12, 11, true]
[12, 12, true]
[12, 13, true]
[13, 0, true]
[13, 1, true]
[13, 2, true]
[13, 3, true]
[13, 4, true]
[13, 5, true]
[13, 6, true]
[13, 7, true]
[13, 8, true]
[13, 9, true]
[13, 10, true]
[13, 11, true]
[13, 12, true]
[13, 13, true]
[13, 14, true]

200315

Crystal


A332954(2)

sigma(1) の値で中身を分類してみても、同じになるようだ。

def a(k, m, n)
  a = (m..m + n - 1).map{|i| [i]}
  len = 1
  while len < n
    b = Array(Array(Int32)).new
    a.each{|c|
      (m..m + n - 1).each{|num|
        if !c.includes?(num)
          i = c.clone + [num]
          if (i[-2] * (len + k + 1)) > (i[-1] * (len + k))
            b << i
          end
        end
      }
    }
    a = b
    len += 1
  end
  ary = Array.new(n, 0)
  a.each{|c| ary[c[0] - m] += 1}
  ary[1..-1]
end

def b(k, m, n)
  a = (m..m + n - 1).map{|i| [i]}
  len = 1
  while len < n
    b = Array(Array(Int32)).new
    a.each{|c|
      (m..m + n - 1).each{|num|
        if !c.includes?(num)
          i = c.clone + [num]
          if (i[-2] * (len + k + 1)) >= (i[-1] * (len + k))
            b << i
          end
        end
      }
    }
    a = b
    len += 1
  end
  ary = Array.new(n, 0)
  a.each{|c| ary[c[0] - m] += 1}
  ary
end

(0..13).each{|i|
  (0..i + 1).each{|j|
    p a = (1..16).map{|k| a(i, j, k)}
    p b = (0..15).map{|k| b(i, j, k)}
    p [i, j, a == b]
  }
}

出力結果
[[], [1], [0, 1], [0, 1, 1], [0, 1, 1, 1], [0, 1, 2, 1, 2], [0, 1, 2, 2, 1, 3], [0, 1, 3, 5, 2, 3, 5], [0, 1, 3, 6, 5, 3, 4, 8], [0, 1, 4, 8, 12, 8, 5, 9, 13], [0, 1, 4, 12, 20, 18, 8, 11, 13, 21], [0, 1, 5, 18, 29, 42, 21, 22, 19, 27, 38], [0, 1, 5, 23, 44, 69, 48, 33, 30, 33, 38, 64], [0, 1, 6, 40, 77, 120, 128, 86, 69, 70, 66, 95, 116], [0, 1, 6, 41, 107, 196, 247, 188, 113, 116, 113, 124, 133, 216], [0, 1, 7, 61, 182, 302, 396, 451, 263, 246, 219, 239, 189, 283, 405]]
[[], [1], [0, 1], [0, 1, 1], [0, 1, 1, 1], [0, 1, 2, 1, 2], [0, 1, 2, 2, 1, 3], [0, 1, 3, 5, 2, 3, 5], [0, 1, 3, 6, 5, 3, 4, 8], [0, 1, 4, 8, 12, 8, 5, 9, 13], [0, 1, 4, 12, 20, 18, 8, 11, 13, 21], [0, 1, 5, 18, 29, 42, 21, 22, 19, 27, 38], [0, 1, 5, 23, 44, 69, 48, 33, 30, 33, 38, 64], [0, 1, 6, 40, 77, 120, 128, 86, 69, 70, 66, 95, 116], [0, 1, 6, 41, 107, 196, 247, 188, 113, 116, 113, 124, 133, 216], [0, 1, 7, 61, 182, 302, 396, 451, 263, 246, 219, 239, 189, 283, 405]]
[0, 0, true]
[[], [1], [1, 1], [1, 1, 1], [1, 2, 1, 2], [1, 2, 2, 1, 3], [1, 3, 5, 2, 3, 5], [1, 3, 6, 5, 3, 4, 8], [1, 4, 8, 12, 8, 5, 9, 13], [1, 4, 12, 20, 18, 8, 11, 13, 21], [1, 5, 18, 29, 42, 21, 22, 19, 27, 38], [1, 5, 23, 44, 69, 48, 33, 30, 33, 38, 64], [1, 6, 40, 77, 120, 128, 86, 69, 70, 66, 95, 116], [1, 6, 41, 107, 196, 247, 188, 113, 116, 113, 124, 133, 216], [1, 7, 61, 182, 302, 396, 451, 263, 246, 219, 239, 189, 283, 405], [1, 7, 79, 279, 512, 752, 932, 649, 393, 420, 470, 326, 403, 500, 714]]
[[], [1], [1, 1], [1, 1, 1], [1, 2, 1, 2], [1, 2, 2, 1, 3], [1, 3, 5, 2, 3, 5], [1, 3, 6, 5, 3, 4, 8], [1, 4, 8, 12, 8, 5, 9, 13], [1, 4, 12, 20, 18, 8, 11, 13, 21], [1, 5, 18, 29, 42, 21, 22, 19, 27, 38], [1, 5, 23, 44, 69, 48, 33, 30, 33, 38, 64], [1, 6, 40, 77, 120, 128, 86, 69, 70, 66, 95, 116], [1, 6, 41, 107, 196, 247, 188, 113, 116, 113, 124, 133, 216], [1, 7, 61, 182, 302, 396, 451, 263, 246, 219, 239, 189, 283, 405], [1, 7, 79, 279, 512, 752, 932, 649, 393, 420, 470, 326, 403, 500, 714]]
[0, 1, true]
[[], [1], [0, 1], [0, 0, 1], [0, 0, 1, 1], [0, 0, 1, 1, 1], [0, 0, 1, 1, 1, 2], [0, 0, 1, 1, 2, 1, 3], [0, 0, 1, 1, 2, 2, 2, 5], [0, 0, 1, 1, 3, 3, 2, 4, 7], [0, 0, 1, 1, 3, 4, 5, 5, 7, 12], [0, 0, 1, 1, 4, 6, 8, 8, 7, 12, 17], [0, 0, 1, 1, 4, 7, 12, 11, 14, 16, 19, 31], [0, 0, 1, 1, 5, 10, 25, 21, 21, 26, 25, 35, 46], [0, 0, 1, 1, 5, 11, 25, 35, 36, 50, 46, 50, 56, 89], [0, 0, 1, 1, 6, 15, 40, 59, 68, 53, 77, 86, 67, 100, 141]]
[[], [1], [0, 1], [0, 0, 1], [0, 0, 1, 1], [0, 0, 1, 1, 1], [0, 0, 1, 1, 1, 2], [0, 0, 1, 1, 2, 1, 3], [0, 0, 1, 1, 2, 2, 2, 5], [0, 0, 1, 1, 3, 3, 2, 4, 7], [0, 0, 1, 1, 3, 4, 5, 5, 7, 12], [0, 0, 1, 1, 4, 6, 8, 8, 7, 12, 17], [0, 0, 1, 1, 4, 7, 12, 11, 14, 16, 19, 31], [0, 0, 1, 1, 5, 10, 25, 21, 21, 26, 25, 35, 46], [0, 0, 1, 1, 5, 11, 25, 35, 36, 50, 46, 50, 56, 89], [0, 0, 1, 1, 6, 15, 40, 59, 68, 53, 77, 86, 67, 100, 141]]
[1, 0, true]
[[], [1], [0, 1], [0, 1, 1], [0, 1, 1, 1], [0, 1, 1, 1, 2], [0, 1, 1, 2, 1, 3], [0, 1, 1, 2, 2, 2, 5], [0, 1, 1, 3, 3, 2, 4, 7], [0, 1, 1, 3, 4, 5, 5, 7, 12], [0, 1, 1, 4, 6, 8, 8, 7, 12, 17], [0, 1, 1, 4, 7, 12, 11, 14, 16, 19, 31], [0, 1, 1, 5, 10, 25, 21, 21, 26, 25, 35, 46], [0, 1, 1, 5, 11, 25, 35, 36, 50, 46, 50, 56, 89], [0, 1, 1, 6, 15, 40, 59, 68, 53, 77, 86, 67, 100, 141], [0, 1, 1, 6, 16, 57, 75, 131, 93, 151, 174, 132, 151, 186, 270]]
[[], [1], [0, 1], [0, 1, 1], [0, 1, 1, 1], [0, 1, 1, 1, 2], [0, 1, 1, 2, 1, 3], [0, 1, 1, 2, 2, 2, 5], [0, 1, 1, 3, 3, 2, 4, 7], [0, 1, 1, 3, 4, 5, 5, 7, 12], [0, 1, 1, 4, 6, 8, 8, 7, 12, 17], [0, 1, 1, 4, 7, 12, 11, 14, 16, 19, 31], [0, 1, 1, 5, 10, 25, 21, 21, 26, 25, 35, 46], [0, 1, 1, 5, 11, 25, 35, 36, 50, 46, 50, 56, 89], [0, 1, 1, 6, 15, 40, 59, 68, 53, 77, 86, 67, 100, 141], [0, 1, 1, 6, 16, 57, 75, 131, 93, 151, 174, 132, 151, 186, 270]]
[1, 1, true]
[[], [1], [1, 1], [1, 1, 1], [1, 1, 1, 2], [1, 1, 2, 1, 3], [1, 1, 2, 2, 2, 5], [1, 1, 3, 3, 2, 4, 7], [1, 1, 3, 4, 5, 5, 7, 12], [1, 1, 4, 6, 8, 8, 7, 12, 17], [1, 1, 4, 7, 12, 11, 14, 16, 19, 31], [1, 1, 5, 10, 25, 21, 21, 26, 25, 35, 46], [1, 1, 5, 11, 25, 35, 36, 50, 46, 50, 56, 89], [1, 1, 6, 15, 40, 59, 68, 53, 77, 86, 67, 100, 141], [1, 1, 6, 16, 57, 75, 131, 93, 151, 174, 132, 151, 186, 270], [1, 1, 7, 21, 90, 129, 277, 205, 176, 317, 245, 266, 242, 333, 449]]
[[], [1], [1, 1], [1, 1, 1], [1, 1, 1, 2], [1, 1, 2, 1, 3], [1, 1, 2, 2, 2, 5], [1, 1, 3, 3, 2, 4, 7], [1, 1, 3, 4, 5, 5, 7, 12], [1, 1, 4, 6, 8, 8, 7, 12, 17], [1, 1, 4, 7, 12, 11, 14, 16, 19, 31], [1, 1, 5, 10, 25, 21, 21, 26, 25, 35, 46], [1, 1, 5, 11, 25, 35, 36, 50, 46, 50, 56, 89], [1, 1, 6, 15, 40, 59, 68, 53, 77, 86, 67, 100, 141], [1, 1, 6, 16, 57, 75, 131, 93, 151, 174, 132, 151, 186, 270], [1, 1, 7, 21, 90, 129, 277, 205, 176, 317, 245, 266, 242, 333, 449]]
[1, 2, true]
[[], [1], [0, 1], [0, 0, 1], [0, 0, 0, 1], [0, 0, 0, 1, 1], [0, 0, 0, 1, 1, 1], [0, 0, 0, 1, 1, 1, 2], [0, 0, 0, 1, 1, 1, 1, 3], [0, 0, 0, 1, 1, 1, 2, 2, 5], [0, 0, 0, 1, 1, 1, 2, 2, 3, 7], [0, 0, 0, 1, 1, 1, 3, 3, 4, 7, 11], [0, 0, 0, 1, 1, 1, 3, 4, 3, 7, 10, 16], [0, 0, 0, 1, 1, 1, 4, 6, 5, 14, 12, 19, 26], [0, 0, 0, 1, 1, 1, 4, 7, 7, 11, 20, 22, 26, 41], [0, 0, 0, 1, 1, 1, 5, 10, 11, 19, 25, 42, 35, 50, 70]]
[[], [1], [0, 1], [0, 0, 1], [0, 0, 0, 1], [0, 0, 0, 1, 1], [0, 0, 0, 1, 1, 1], [0, 0, 0, 1, 1, 1, 2], [0, 0, 0, 1, 1, 1, 1, 3], [0, 0, 0, 1, 1, 1, 2, 2, 5], [0, 0, 0, 1, 1, 1, 2, 2, 3, 7], [0, 0, 0, 1, 1, 1, 3, 3, 4, 7, 11], [0, 0, 0, 1, 1, 1, 3, 4, 3, 7, 10, 16], [0, 0, 0, 1, 1, 1, 4, 6, 5, 14, 12, 19, 26], [0, 0, 0, 1, 1, 1, 4, 7, 7, 11, 20, 22, 26, 41], [0, 0, 0, 1, 1, 1, 5, 10, 11, 19, 25, 42, 35, 50, 70]]
[2, 0, true]
[[], [1], [0, 1], [0, 0, 1], [0, 0, 1, 1], [0, 0, 1, 1, 1], [0, 0, 1, 1, 1, 2], [0, 0, 1, 1, 1, 1, 3], [0, 0, 1, 1, 1, 2, 2, 5], [0, 0, 1, 1, 1, 2, 2, 3, 7], [0, 0, 1, 1, 1, 3, 3, 4, 7, 11], [0, 0, 1, 1, 1, 3, 4, 3, 7, 10, 16], [0, 0, 1, 1, 1, 4, 6, 5, 14, 12, 19, 26], [0, 0, 1, 1, 1, 4, 7, 7, 11, 20, 22, 26, 41], [0, 0, 1, 1, 1, 5, 10, 11, 19, 25, 42, 35, 50, 70], [0, 0, 1, 1, 1, 5, 11, 14, 32, 25, 50, 58, 64, 76, 111]]
[[], [1], [0, 1], [0, 0, 1], [0, 0, 1, 1], [0, 0, 1, 1, 1], [0, 0, 1, 1, 1, 2], [0, 0, 1, 1, 1, 1, 3], [0, 0, 1, 1, 1, 2, 2, 5], [0, 0, 1, 1, 1, 2, 2, 3, 7], [0, 0, 1, 1, 1, 3, 3, 4, 7, 11], [0, 0, 1, 1, 1, 3, 4, 3, 7, 10, 16], [0, 0, 1, 1, 1, 4, 6, 5, 14, 12, 19, 26], [0, 0, 1, 1, 1, 4, 7, 7, 11, 20, 22, 26, 41], [0, 0, 1, 1, 1, 5, 10, 11, 19, 25, 42, 35, 50, 70], [0, 0, 1, 1, 1, 5, 11, 14, 32, 25, 50, 58, 64, 76, 111]]
[2, 1, true]
[[], [1], [0, 1], [0, 1, 1], [0, 1, 1, 1], [0, 1, 1, 1, 2], [0, 1, 1, 1, 1, 3], [0, 1, 1, 1, 2, 2, 5], [0, 1, 1, 1, 2, 2, 3, 7], [0, 1, 1, 1, 3, 3, 4, 7, 11], [0, 1, 1, 1, 3, 4, 3, 7, 10, 16], [0, 1, 1, 1, 4, 6, 5, 14, 12, 19, 26], [0, 1, 1, 1, 4, 7, 7, 11, 20, 22, 26, 41], [0, 1, 1, 1, 5, 10, 11, 19, 25, 42, 35, 50, 70], [0, 1, 1, 1, 5, 11, 14, 32, 25, 50, 58, 64, 76, 111], [0, 1, 1, 1, 6, 15, 21, 54, 49, 69, 122, 128, 105, 150, 209]]
[[], [1], [0, 1], [0, 1, 1], [0, 1, 1, 1], [0, 1, 1, 1, 2], [0, 1, 1, 1, 1, 3], [0, 1, 1, 1, 2, 2, 5], [0, 1, 1, 1, 2, 2, 3, 7], [0, 1, 1, 1, 3, 3, 4, 7, 11], [0, 1, 1, 1, 3, 4, 3, 7, 10, 16], [0, 1, 1, 1, 4, 6, 5, 14, 12, 19, 26], [0, 1, 1, 1, 4, 7, 7, 11, 20, 22, 26, 41], [0, 1, 1, 1, 5, 10, 11, 19, 25, 42, 35, 50, 70], [0, 1, 1, 1, 5, 11, 14, 32, 25, 50, 58, 64, 76, 111], [0, 1, 1, 1, 6, 15, 21, 54, 49, 69, 122, 128, 105, 150, 209]]
[2, 2, true]
[[], [1], [1, 1], [1, 1, 1], [1, 1, 1, 2], [1, 1, 1, 1, 3], [1, 1, 1, 2, 2, 5], [1, 1, 1, 2, 2, 3, 7], [1, 1, 1, 3, 3, 4, 7, 11], [1, 1, 1, 3, 4, 3, 7, 10, 16], [1, 1, 1, 4, 6, 5, 14, 12, 19, 26], [1, 1, 1, 4, 7, 7, 11, 20, 22, 26, 41], [1, 1, 1, 5, 10, 11, 19, 25, 42, 35, 50, 70], [1, 1, 1, 5, 11, 14, 32, 25, 50, 58, 64, 76, 111], [1, 1, 1, 6, 15, 21, 54, 49, 69, 122, 128, 105, 150, 209], [1, 1, 1, 6, 16, 25, 78, 75, 68, 141, 210, 178, 171, 220, 348]]
[[], [1], [1, 1], [1, 1, 1], [1, 1, 1, 2], [1, 1, 1, 1, 3], [1, 1, 1, 2, 2, 5], [1, 1, 1, 2, 2, 3, 7], [1, 1, 1, 3, 3, 4, 7, 11], [1, 1, 1, 3, 4, 3, 7, 10, 16], [1, 1, 1, 4, 6, 5, 14, 12, 19, 26], [1, 1, 1, 4, 7, 7, 11, 20, 22, 26, 41], [1, 1, 1, 5, 10, 11, 19, 25, 42, 35, 50, 70], [1, 1, 1, 5, 11, 14, 32, 25, 50, 58, 64, 76, 111], [1, 1, 1, 6, 15, 21, 54, 49, 69, 122, 128, 105, 150, 209], [1, 1, 1, 6, 16, 25, 78, 75, 68, 141, 210, 178, 171, 220, 348]]
[2, 3, true]
[[], [1], [0, 1], [0, 0, 1], [0, 0, 0, 1], [0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 1], [0, 0, 0, 0, 1, 1, 1], [0, 0, 0, 0, 1, 1, 1, 2], [0, 0, 0, 0, 1, 1, 1, 1, 3], [0, 0, 0, 0, 1, 1, 1, 1, 2, 5], [0, 0, 0, 0, 1, 1, 1, 1, 2, 3, 7], [0, 0, 0, 0, 1, 1, 1, 1, 2, 4, 5, 11], [0, 0, 0, 0, 1, 1, 1, 1, 3, 3, 6, 10, 15], [0, 0, 0, 0, 1, 1, 1, 1, 3, 4, 6, 12, 16, 25], [0, 0, 0, 0, 1, 1, 1, 1, 4, 6, 5, 14, 17, 26, 35]]
[[], [1], [0, 1], [0, 0, 1], [0, 0, 0, 1], [0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 1], [0, 0, 0, 0, 1, 1, 1], [0, 0, 0, 0, 1, 1, 1, 2], [0, 0, 0, 0, 1, 1, 1, 1, 3], [0, 0, 0, 0, 1, 1, 1, 1, 2, 5], [0, 0, 0, 0, 1, 1, 1, 1, 2, 3, 7], [0, 0, 0, 0, 1, 1, 1, 1, 2, 4, 5, 11], [0, 0, 0, 0, 1, 1, 1, 1, 3, 3, 6, 10, 15], [0, 0, 0, 0, 1, 1, 1, 1, 3, 4, 6, 12, 16, 25], [0, 0, 0, 0, 1, 1, 1, 1, 4, 6, 5, 14, 17, 26, 35]]
[3, 0, true]
[[], [1], [0, 1], [0, 0, 1], [0, 0, 0, 1], [0, 0, 0, 1, 1], [0, 0, 0, 1, 1, 1], [0, 0, 0, 1, 1, 1, 2], [0, 0, 0, 1, 1, 1, 1, 3], [0, 0, 0, 1, 1, 1, 1, 2, 5], [0, 0, 0, 1, 1, 1, 1, 2, 3, 7], [0, 0, 0, 1, 1, 1, 1, 2, 4, 5, 11], [0, 0, 0, 1, 1, 1, 1, 3, 3, 6, 10, 15], [0, 0, 0, 1, 1, 1, 1, 3, 4, 6, 12, 16, 25], [0, 0, 0, 1, 1, 1, 1, 4, 6, 5, 14, 17, 26, 35], [0, 0, 0, 1, 1, 1, 1, 4, 7, 7, 14, 34, 35, 41, 63]]
[[], [1], [0, 1], [0, 0, 1], [0, 0, 0, 1], [0, 0, 0, 1, 1], [0, 0, 0, 1, 1, 1], [0, 0, 0, 1, 1, 1, 2], [0, 0, 0, 1, 1, 1, 1, 3], [0, 0, 0, 1, 1, 1, 1, 2, 5], [0, 0, 0, 1, 1, 1, 1, 2, 3, 7], [0, 0, 0, 1, 1, 1, 1, 2, 4, 5, 11], [0, 0, 0, 1, 1, 1, 1, 3, 3, 6, 10, 15], [0, 0, 0, 1, 1, 1, 1, 3, 4, 6, 12, 16, 25], [0, 0, 0, 1, 1, 1, 1, 4, 6, 5, 14, 17, 26, 35], [0, 0, 0, 1, 1, 1, 1, 4, 7, 7, 14, 34, 35, 41, 63]]
[3, 1, true]
[[], [1], [0, 1], [0, 0, 1], [0, 0, 1, 1], [0, 0, 1, 1, 1], [0, 0, 1, 1, 1, 2], [0, 0, 1, 1, 1, 1, 3], [0, 0, 1, 1, 1, 1, 2, 5], [0, 0, 1, 1, 1, 1, 2, 3, 7], [0, 0, 1, 1, 1, 1, 2, 4, 5, 11], [0, 0, 1, 1, 1, 1, 3, 3, 6, 10, 15], [0, 0, 1, 1, 1, 1, 3, 4, 6, 12, 16, 25], [0, 0, 1, 1, 1, 1, 4, 6, 5, 14, 17, 26, 35], [0, 0, 1, 1, 1, 1, 4, 7, 7, 14, 34, 35, 41, 63], [0, 0, 1, 1, 1, 1, 5, 10, 11, 14, 36, 58, 48, 68, 94]]
[[], [1], [0, 1], [0, 0, 1], [0, 0, 1, 1], [0, 0, 1, 1, 1], [0, 0, 1, 1, 1, 2], [0, 0, 1, 1, 1, 1, 3], [0, 0, 1, 1, 1, 1, 2, 5], [0, 0, 1, 1, 1, 1, 2, 3, 7], [0, 0, 1, 1, 1, 1, 2, 4, 5, 11], [0, 0, 1, 1, 1, 1, 3, 3, 6, 10, 15], [0, 0, 1, 1, 1, 1, 3, 4, 6, 12, 16, 25], [0, 0, 1, 1, 1, 1, 4, 6, 5, 14, 17, 26, 35], [0, 0, 1, 1, 1, 1, 4, 7, 7, 14, 34, 35, 41, 63], [0, 0, 1, 1, 1, 1, 5, 10, 11, 14, 36, 58, 48, 68, 94]]
[3, 2, true]
[[], [1], [0, 1], [0, 1, 1], [0, 1, 1, 1], [0, 1, 1, 1, 2], [0, 1, 1, 1, 1, 3], [0, 1, 1, 1, 1, 2, 5], [0, 1, 1, 1, 1, 2, 3, 7], [0, 1, 1, 1, 1, 2, 4, 5, 11], [0, 1, 1, 1, 1, 3, 3, 6, 10, 15], [0, 1, 1, 1, 1, 3, 4, 6, 12, 16, 25], [0, 1, 1, 1, 1, 4, 6, 5, 14, 17, 26, 35], [0, 1, 1, 1, 1, 4, 7, 7, 14, 34, 35, 41, 63], [0, 1, 1, 1, 1, 5, 10, 11, 14, 36, 58, 48, 68, 94], [0, 1, 1, 1, 1, 5, 11, 14, 18, 42, 72, 92, 89, 108, 171]]
[[], [1], [0, 1], [0, 1, 1], [0, 1, 1, 1], [0, 1, 1, 1, 2], [0, 1, 1, 1, 1, 3], [0, 1, 1, 1, 1, 2, 5], [0, 1, 1, 1, 1, 2, 3, 7], [0, 1, 1, 1, 1, 2, 4, 5, 11], [0, 1, 1, 1, 1, 3, 3, 6, 10, 15], [0, 1, 1, 1, 1, 3, 4, 6, 12, 16, 25], [0, 1, 1, 1, 1, 4, 6, 5, 14, 17, 26, 35], [0, 1, 1, 1, 1, 4, 7, 7, 14, 34, 35, 41, 63], [0, 1, 1, 1, 1, 5, 10, 11, 14, 36, 58, 48, 68, 94], [0, 1, 1, 1, 1, 5, 11, 14, 18, 42, 72, 92, 89, 108, 171]]
[3, 3, true]
[[], [1], [1, 1], [1, 1, 1], [1, 1, 1, 2], [1, 1, 1, 1, 3], [1, 1, 1, 1, 2, 5], [1, 1, 1, 1, 2, 3, 7], [1, 1, 1, 1, 2, 4, 5, 11], [1, 1, 1, 1, 3, 3, 6, 10, 15], [1, 1, 1, 1, 3, 4, 6, 12, 16, 25], [1, 1, 1, 1, 4, 6, 5, 14, 17, 26, 35], [1, 1, 1, 1, 4, 7, 7, 14, 34, 35, 41, 63], [1, 1, 1, 1, 5, 10, 11, 14, 36, 58, 48, 68, 94], [1, 1, 1, 1, 5, 11, 14, 18, 42, 72, 92, 89, 108, 171], [1, 1, 1, 1, 6, 15, 21, 29, 45, 85, 122, 158, 136, 202, 266]]

[[], [1], [1, 1], [1, 1, 1], [1, 1, 1, 2], [1, 1, 1, 1, 3], [1, 1, 1, 1, 2, 5], [1, 1, 1, 1, 2, 3, 7], [1, 1, 1, 1, 2, 4, 5, 11], [1, 1, 1, 1, 3, 3, 6, 10, 15], [1, 1, 1, 1, 3, 4, 6, 12, 16, 25], [1, 1, 1, 1, 4, 6, 5, 14, 17, 26, 35], [1, 1, 1, 1, 4, 7, 7, 14, 34, 35, 41, 63], [1, 1, 1, 1, 5, 10, 11, 14, 36, 58, 48, 68, 94], [1, 1, 1, 1, 5, 11, 14, 18, 42, 72, 92, 89, 108, 171], [1, 1, 1, 1, 6, 15, 21, 29, 45, 85, 122, 158, 136, 202, 266]]
[3, 4, true]
[[], [1], [0, 1], [0, 0, 1], [0, 0, 0, 1], [0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 1, 1], [0, 0, 0, 0, 0, 1, 1, 1], [0, 0, 0, 0, 0, 1, 1, 1, 2], [0, 0, 0, 0, 0, 1, 1, 1, 1, 3], [0, 0, 0, 0, 0, 1, 1, 1, 1, 2, 5], [0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 3, 7], [0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 4, 5, 11], [0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 2, 6, 7, 15], [0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 3, 6, 10, 16, 23]]
[[], [1], [0, 1], [0, 0, 1], [0, 0, 0, 1], [0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 1, 1], [0, 0, 0, 0, 0, 1, 1, 1], [0, 0, 0, 0, 0, 1, 1, 1, 2], [0, 0, 0, 0, 0, 1, 1, 1, 1, 3], [0, 0, 0, 0, 0, 1, 1, 1, 1, 2, 5], [0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 3, 7], [0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 4, 5, 11], [0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 2, 6, 7, 15], [0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 3, 6, 10, 16, 23]]
[4, 0, true]
[[], [1], [0, 1], [0, 0, 1], [0, 0, 0, 1], [0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 1], [0, 0, 0, 0, 1, 1, 1], [0, 0, 0, 0, 1, 1, 1, 2], [0, 0, 0, 0, 1, 1, 1, 1, 3], [0, 0, 0, 0, 1, 1, 1, 1, 2, 5], [0, 0, 0, 0, 1, 1, 1, 1, 1, 3, 7], [0, 0, 0, 0, 1, 1, 1, 1, 1, 4, 5, 11], [0, 0, 0, 0, 1, 1, 1, 1, 1, 2, 6, 7, 15], [0, 0, 0, 0, 1, 1, 1, 1, 1, 3, 6, 10, 16, 23], [0, 0, 0, 0, 1, 1, 1, 1, 1, 3, 4, 9, 17, 22, 34]]
[[], [1], [0, 1], [0, 0, 1], [0, 0, 0, 1], [0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 1], [0, 0, 0, 0, 1, 1, 1], [0, 0, 0, 0, 1, 1, 1, 2], [0, 0, 0, 0, 1, 1, 1, 1, 3], [0, 0, 0, 0, 1, 1, 1, 1, 2, 5], [0, 0, 0, 0, 1, 1, 1, 1, 1, 3, 7], [0, 0, 0, 0, 1, 1, 1, 1, 1, 4, 5, 11], [0, 0, 0, 0, 1, 1, 1, 1, 1, 2, 6, 7, 15], [0, 0, 0, 0, 1, 1, 1, 1, 1, 3, 6, 10, 16, 23], [0, 0, 0, 0, 1, 1, 1, 1, 1, 3, 4, 9, 17, 22, 34]]
[4, 1, true]
[[], [1], [0, 1], [0, 0, 1], [0, 0, 0, 1], [0, 0, 0, 1, 1], [0, 0, 0, 1, 1, 1], [0, 0, 0, 1, 1, 1, 2], [0, 0, 0, 1, 1, 1, 1, 3], [0, 0, 0, 1, 1, 1, 1, 2, 5], [0, 0, 0, 1, 1, 1, 1, 1, 3, 7], [0, 0, 0, 1, 1, 1, 1, 1, 4, 5, 11], [0, 0, 0, 1, 1, 1, 1, 1, 2, 6, 7, 15], [0, 0, 0, 1, 1, 1, 1, 1, 3, 6, 10, 16, 23], [0, 0, 0, 1, 1, 1, 1, 1, 3, 4, 9, 17, 22, 34], [0, 0, 0, 1, 1, 1, 1, 1, 4, 6, 10, 24, 27, 41, 54]]
[[], [1], [0, 1], [0, 0, 1], [0, 0, 0, 1], [0, 0, 0, 1, 1], [0, 0, 0, 1, 1, 1], [0, 0, 0, 1, 1, 1, 2], [0, 0, 0, 1, 1, 1, 1, 3], [0, 0, 0, 1, 1, 1, 1, 2, 5], [0, 0, 0, 1, 1, 1, 1, 1, 3, 7], [0, 0, 0, 1, 1, 1, 1, 1, 4, 5, 11], [0, 0, 0, 1, 1, 1, 1, 1, 2, 6, 7, 15], [0, 0, 0, 1, 1, 1, 1, 1, 3, 6, 10, 16, 23], [0, 0, 0, 1, 1, 1, 1, 1, 3, 4, 9, 17, 22, 34], [0, 0, 0, 1, 1, 1, 1, 1, 4, 6, 10, 24, 27, 41, 54]]
[4, 2, true]
[[], [1], [0, 1], [0, 0, 1], [0, 0, 1, 1], [0, 0, 1, 1, 1], [0, 0, 1, 1, 1, 2], [0, 0, 1, 1, 1, 1, 3], [0, 0, 1, 1, 1, 1, 2, 5], [0, 0, 1, 1, 1, 1, 1, 3, 7], [0, 0, 1, 1, 1, 1, 1, 4, 5, 11], [0, 0, 1, 1, 1, 1, 1, 2, 6, 7, 15], [0, 0, 1, 1, 1, 1, 1, 3, 6, 10, 16, 23], [0, 0, 1, 1, 1, 1, 1, 3, 4, 9, 17, 22, 34], [0, 0, 1, 1, 1, 1, 1, 4, 6, 10, 24, 27, 41, 54], [0, 0, 1, 1, 1, 1, 1, 4, 7, 7, 20, 34, 48, 56, 85]]
[[], [1], [0, 1], [0, 0, 1], [0, 0, 1, 1], [0, 0, 1, 1, 1], [0, 0, 1, 1, 1, 2], [0, 0, 1, 1, 1, 1, 3], [0, 0, 1, 1, 1, 1, 2, 5], [0, 0, 1, 1, 1, 1, 1, 3, 7], [0, 0, 1, 1, 1, 1, 1, 4, 5, 11], [0, 0, 1, 1, 1, 1, 1, 2, 6, 7, 15], [0, 0, 1, 1, 1, 1, 1, 3, 6, 10, 16, 23], [0, 0, 1, 1, 1, 1, 1, 3, 4, 9, 17, 22, 34], [0, 0, 1, 1, 1, 1, 1, 4, 6, 10, 24, 27, 41, 54], [0, 0, 1, 1, 1, 1, 1, 4, 7, 7, 20, 34, 48, 56, 85]]
[4, 3, true]
[[], [1], [0, 1], [0, 1, 1], [0, 1, 1, 1], [0, 1, 1, 1, 2], [0, 1, 1, 1, 1, 3], [0, 1, 1, 1, 1, 2, 5], [0, 1, 1, 1, 1, 1, 3, 7], [0, 1, 1, 1, 1, 1, 4, 5, 11], [0, 1, 1, 1, 1, 1, 2, 6, 7, 15], [0, 1, 1, 1, 1, 1, 3, 6, 10, 16, 23], [0, 1, 1, 1, 1, 1, 3, 4, 9, 17, 22, 34], [0, 1, 1, 1, 1, 1, 4, 6, 10, 24, 27, 41, 54], [0, 1, 1, 1, 1, 1, 4, 7, 7, 20, 34, 48, 56, 85], [0, 1, 1, 1, 1, 1, 5, 10, 11, 25, 41, 92, 75, 106, 145]]
[[], [1], [0, 1], [0, 1, 1], [0, 1, 1, 1], [0, 1, 1, 1, 2], [0, 1, 1, 1, 1, 3], [0, 1, 1, 1, 1, 2, 5], [0, 1, 1, 1, 1, 1, 3, 7], [0, 1, 1, 1, 1, 1, 4, 5, 11], [0, 1, 1, 1, 1, 1, 2, 6, 7, 15], [0, 1, 1, 1, 1, 1, 3, 6, 10, 16, 23], [0, 1, 1, 1, 1, 1, 3, 4, 9, 17, 22, 34], [0, 1, 1, 1, 1, 1, 4, 6, 10, 24, 27, 41, 54], [0, 1, 1, 1, 1, 1, 4, 7, 7, 20, 34, 48, 56, 85], [0, 1, 1, 1, 1, 1, 5, 10, 11, 25, 41, 92, 75, 106, 145]]
[4, 4, true]
[[], [1], [1, 1], [1, 1, 1], [1, 1, 1, 2], [1, 1, 1, 1, 3], [1, 1, 1, 1, 2, 5], [1, 1, 1, 1, 1, 3, 7], [1, 1, 1, 1, 1, 4, 5, 11], [1, 1, 1, 1, 1, 2, 6, 7, 15], [1, 1, 1, 1, 1, 3, 6, 10, 16, 23], [1, 1, 1, 1, 1, 3, 4, 9, 17, 22, 34], [1, 1, 1, 1, 1, 4, 6, 10, 24, 27, 41, 54], [1, 1, 1, 1, 1, 4, 7, 7, 20, 34, 48, 56, 85], [1, 1, 1, 1, 1, 5, 10, 11, 25, 41, 92, 75, 106, 145], [1, 1, 1, 1, 1, 5, 11, 14, 18, 40, 100, 126, 121, 147, 231]]
[[], [1], [1, 1], [1, 1, 1], [1, 1, 1, 2], [1, 1, 1, 1, 3], [1, 1, 1, 1, 2, 5], [1, 1, 1, 1, 1, 3, 7], [1, 1, 1, 1, 1, 4, 5, 11], [1, 1, 1, 1, 1, 2, 6, 7, 15], [1, 1, 1, 1, 1, 3, 6, 10, 16, 23], [1, 1, 1, 1, 1, 3, 4, 9, 17, 22, 34], [1, 1, 1, 1, 1, 4, 6, 10, 24, 27, 41, 54], [1, 1, 1, 1, 1, 4, 7, 7, 20, 34, 48, 56, 85], [1, 1, 1, 1, 1, 5, 10, 11, 25, 41, 92, 75, 106, 145], [1, 1, 1, 1, 1, 5, 11, 14, 18, 40, 100, 126, 121, 147, 231]]
[4, 5, true]
[[], [1], [0, 1], [0, 0, 1], [0, 0, 0, 1], [0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 1, 1], [0, 0, 0, 0, 0, 0, 1, 1, 1], [0, 0, 0, 0, 0, 0, 1, 1, 1, 2], [0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 3], [0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 2, 5], [0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 3, 7], [0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 2, 5, 11], [0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 6, 7, 15]]
[[], [1], [0, 1], [0, 0, 1], [0, 0, 0, 1], [0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 1, 1], [0, 0, 0, 0, 0, 0, 1, 1, 1], [0, 0, 0, 0, 0, 0, 1, 1, 1, 2], [0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 3], [0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 2, 5], [0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 3, 7], [0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 2, 5, 11], [0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 6, 7, 15]]
[5, 0, true]
[[], [1], [0, 1], [0, 0, 1], [0, 0, 0, 1], [0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 1, 1], [0, 0, 0, 0, 0, 1, 1, 1], [0, 0, 0, 0, 0, 1, 1, 1, 2], [0, 0, 0, 0, 0, 1, 1, 1, 1, 3], [0, 0, 0, 0, 0, 1, 1, 1, 1, 2, 5], [0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 3, 7], [0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 2, 5, 11], [0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 6, 7, 15], [0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 4, 10, 11, 23]]
[[], [1], [0, 1], [0, 0, 1], [0, 0, 0, 1], [0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 1, 1], [0, 0, 0, 0, 0, 1, 1, 1], [0, 0, 0, 0, 0, 1, 1, 1, 2], [0, 0, 0, 0, 0, 1, 1, 1, 1, 3], [0, 0, 0, 0, 0, 1, 1, 1, 1, 2, 5], [0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 3, 7], [0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 2, 5, 11], [0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 6, 7, 15], [0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 4, 10, 11, 23]]
[5, 1, true]
[[], [1], [0, 1], [0, 0, 1], [0, 0, 0, 1], [0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 1], [0, 0, 0, 0, 1, 1, 1], [0, 0, 0, 0, 1, 1, 1, 2], [0, 0, 0, 0, 1, 1, 1, 1, 3], [0, 0, 0, 0, 1, 1, 1, 1, 2, 5], [0, 0, 0, 0, 1, 1, 1, 1, 1, 3, 7], [0, 0, 0, 0, 1, 1, 1, 1, 1, 2, 5, 11], [0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 6, 7, 15], [0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 4, 10, 11, 23], [0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 3, 9, 14, 22, 31]]
[[], [1], [0, 1], [0, 0, 1], [0, 0, 0, 1], [0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 1], [0, 0, 0, 0, 1, 1, 1], [0, 0, 0, 0, 1, 1, 1, 2], [0, 0, 0, 0, 1, 1, 1, 1, 3], [0, 0, 0, 0, 1, 1, 1, 1, 2, 5], [0, 0, 0, 0, 1, 1, 1, 1, 1, 3, 7], [0, 0, 0, 0, 1, 1, 1, 1, 1, 2, 5, 11], [0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 6, 7, 15], [0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 4, 10, 11, 23], [0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 3, 9, 14, 22, 31]]
[5, 2, true]
[[], [1], [0, 1], [0, 0, 1], [0, 0, 0, 1], [0, 0, 0, 1, 1], [0, 0, 0, 1, 1, 1], [0, 0, 0, 1, 1, 1, 2], [0, 0, 0, 1, 1, 1, 1, 3], [0, 0, 0, 1, 1, 1, 1, 2, 5], [0, 0, 0, 1, 1, 1, 1, 1, 3, 7], [0, 0, 0, 1, 1, 1, 1, 1, 2, 5, 11], [0, 0, 0, 1, 1, 1, 1, 1, 1, 6, 7, 15], [0, 0, 0, 1, 1, 1, 1, 1, 1, 4, 10, 11, 23], [0, 0, 0, 1, 1, 1, 1, 1, 1, 3, 9, 14, 22, 31], [0, 0, 0, 1, 1, 1, 1, 1, 1, 3, 8, 15, 27, 34, 52]]
[[], [1], [0, 1], [0, 0, 1], [0, 0, 0, 1], [0, 0, 0, 1, 1], [0, 0, 0, 1, 1, 1], [0, 0, 0, 1, 1, 1, 2], [0, 0, 0, 1, 1, 1, 1, 3], [0, 0, 0, 1, 1, 1, 1, 2, 5], [0, 0, 0, 1, 1, 1, 1, 1, 3, 7], [0, 0, 0, 1, 1, 1, 1, 1, 2, 5, 11], [0, 0, 0, 1, 1, 1, 1, 1, 1, 6, 7, 15], [0, 0, 0, 1, 1, 1, 1, 1, 1, 4, 10, 11, 23], [0, 0, 0, 1, 1, 1, 1, 1, 1, 3, 9, 14, 22, 31], [0, 0, 0, 1, 1, 1, 1, 1, 1, 3, 8, 15, 27, 34, 52]]
[5, 3, true]
[[], [1], [0, 1], [0, 0, 1], [0, 0, 1, 1], [0, 0, 1, 1, 1], [0, 0, 1, 1, 1, 2], [0, 0, 1, 1, 1, 1, 3], [0, 0, 1, 1, 1, 1, 2, 5], [0, 0, 1, 1, 1, 1, 1, 3, 7], [0, 0, 1, 1, 1, 1, 1, 2, 5, 11], [0, 0, 1, 1, 1, 1, 1, 1, 6, 7, 15], [0, 0, 1, 1, 1, 1, 1, 1, 4, 10, 11, 23], [0, 0, 1, 1, 1, 1, 1, 1, 3, 9, 14, 22, 31], [0, 0, 1, 1, 1, 1, 1, 1, 3, 8, 15, 27, 34, 52], [0, 0, 1, 1, 1, 1, 1, 1, 4, 6, 15, 34, 37, 56, 73]]
[[], [1], [0, 1], [0, 0, 1], [0, 0, 1, 1], [0, 0, 1, 1, 1], [0, 0, 1, 1, 1, 2], [0, 0, 1, 1, 1, 1, 3], [0, 0, 1, 1, 1, 1, 2, 5], [0, 0, 1, 1, 1, 1, 1, 3, 7], [0, 0, 1, 1, 1, 1, 1, 2, 5, 11], [0, 0, 1, 1, 1, 1, 1, 1, 6, 7, 15], [0, 0, 1, 1, 1, 1, 1, 1, 4, 10, 11, 23], [0, 0, 1, 1, 1, 1, 1, 1, 3, 9, 14, 22, 31], [0, 0, 1, 1, 1, 1, 1, 1, 3, 8, 15, 27, 34, 52], [0, 0, 1, 1, 1, 1, 1, 1, 4, 6, 15, 34, 37, 56, 73]]
[5, 4, true]
[[], [1], [0, 1], [0, 1, 1], [0, 1, 1, 1], [0, 1, 1, 1, 2], [0, 1, 1, 1, 1, 3], [0, 1, 1, 1, 1, 2, 5], [0, 1, 1, 1, 1, 1, 3, 7], [0, 1, 1, 1, 1, 1, 2, 5, 11], [0, 1, 1, 1, 1, 1, 1, 6, 7, 15], [0, 1, 1, 1, 1, 1, 1, 4, 10, 11, 23], [0, 1, 1, 1, 1, 1, 1, 3, 9, 14, 22, 31], [0, 1, 1, 1, 1, 1, 1, 3, 8, 15, 27, 34, 52], [0, 1, 1, 1, 1, 1, 1, 4, 6, 15, 34, 37, 56, 73], [0, 1, 1, 1, 1, 1, 1, 4, 7, 14, 34, 54, 75, 86, 131]]
[[], [1], [0, 1], [0, 1, 1], [0, 1, 1, 1], [0, 1, 1, 1, 2], [0, 1, 1, 1, 1, 3], [0, 1, 1, 1, 1, 2, 5], [0, 1, 1, 1, 1, 1, 3, 7], [0, 1, 1, 1, 1, 1, 2, 5, 11], [0, 1, 1, 1, 1, 1, 1, 6, 7, 15], [0, 1, 1, 1, 1, 1, 1, 4, 10, 11, 23], [0, 1, 1, 1, 1, 1, 1, 3, 9, 14, 22, 31], [0, 1, 1, 1, 1, 1, 1, 3, 8, 15, 27, 34, 52], [0, 1, 1, 1, 1, 1, 1, 4, 6, 15, 34, 37, 56, 73], [0, 1, 1, 1, 1, 1, 1, 4, 7, 14, 34, 54, 75, 86, 131]]
[5, 5, true]
[[], [1], [1, 1], [1, 1, 1], [1, 1, 1, 2], [1, 1, 1, 1, 3], [1, 1, 1, 1, 2, 5], [1, 1, 1, 1, 1, 3, 7], [1, 1, 1, 1, 1, 2, 5, 11], [1, 1, 1, 1, 1, 1, 6, 7, 15], [1, 1, 1, 1, 1, 1, 4, 10, 11, 23], [1, 1, 1, 1, 1, 1, 3, 9, 14, 22, 31], [1, 1, 1, 1, 1, 1, 3, 8, 15, 27, 34, 52], [1, 1, 1, 1, 1, 1, 4, 6, 15, 34, 37, 56, 73], [1, 1, 1, 1, 1, 1, 4, 7, 14, 34, 54, 75, 86, 131], [1, 1, 1, 1, 1, 1, 5, 10, 11, 36, 58, 89, 102, 144, 196]]
[[], [1], [1, 1], [1, 1, 1], [1, 1, 1, 2], [1, 1, 1, 1, 3], [1, 1, 1, 1, 2, 5], [1, 1, 1, 1, 1, 3, 7], [1, 1, 1, 1, 1, 2, 5, 11], [1, 1, 1, 1, 1, 1, 6, 7, 15], [1, 1, 1, 1, 1, 1, 4, 10, 11, 23], [1, 1, 1, 1, 1, 1, 3, 9, 14, 22, 31], [1, 1, 1, 1, 1, 1, 3, 8, 15, 27, 34, 52], [1, 1, 1, 1, 1, 1, 4, 6, 15, 34, 37, 56, 73], [1, 1, 1, 1, 1, 1, 4, 7, 14, 34, 54, 75, 86, 131], [1, 1, 1, 1, 1, 1, 5, 10, 11, 36, 58, 89, 102, 144, 196]]
[5, 6, true]
[[], [1], [0, 1], [0, 0, 1], [0, 0, 0, 1], [0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 1, 1], [0, 0, 0, 0, 0, 0, 0, 1, 1, 1], [0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 2], [0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 3], [0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 2, 5], [0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 3, 7], [0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 2, 5, 11]]
[[], [1], [0, 1], [0, 0, 1], [0, 0, 0, 1], [0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 1, 1], [0, 0, 0, 0, 0, 0, 0, 1, 1, 1], [0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 2], [0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 3], [0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 2, 5], [0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 3, 7], [0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 2, 5, 11]]
[6, 0, true]
[[], [1], [0, 1], [0, 0, 1], [0, 0, 0, 1], [0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 1, 1], [0, 0, 0, 0, 0, 0, 1, 1, 1], [0, 0, 0, 0, 0, 0, 1, 1, 1, 2], [0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 3], [0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 2, 5], [0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 3, 7], [0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 2, 5, 11], [0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 3, 7, 15]]
[[], [1], [0, 1], [0, 0, 1], [0, 0, 0, 1], [0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 1, 1], [0, 0, 0, 0, 0, 0, 1, 1, 1], [0, 0, 0, 0, 0, 0, 1, 1, 1, 2], [0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 3], [0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 2, 5], [0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 3, 7], [0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 2, 5, 11], [0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 3, 7, 15]]
[6, 1, true]
[[], [1], [0, 1], [0, 0, 1], [0, 0, 0, 1], [0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 1, 1], [0, 0, 0, 0, 0, 1, 1, 1], [0, 0, 0, 0, 0, 1, 1, 1, 2], [0, 0, 0, 0, 0, 1, 1, 1, 1, 3], [0, 0, 0, 0, 0, 1, 1, 1, 1, 2, 5], [0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 3, 7], [0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 2, 5, 11], [0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 3, 7, 15], [0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 2, 10, 11, 23]]
[[], [1], [0, 1], [0, 0, 1], [0, 0, 0, 1], [0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 1, 1], [0, 0, 0, 0, 0, 1, 1, 1], [0, 0, 0, 0, 0, 1, 1, 1, 2], [0, 0, 0, 0, 0, 1, 1, 1, 1, 3], [0, 0, 0, 0, 0, 1, 1, 1, 1, 2, 5], [0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 3, 7], [0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 2, 5, 11], [0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 3, 7, 15], [0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 2, 10, 11, 23]]
[6, 2, true]
[[], [1], [0, 1], [0, 0, 1], [0, 0, 0, 1], [0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 1], [0, 0, 0, 0, 1, 1, 1], [0, 0, 0, 0, 1, 1, 1, 2], [0, 0, 0, 0, 1, 1, 1, 1, 3], [0, 0, 0, 0, 1, 1, 1, 1, 2, 5], [0, 0, 0, 0, 1, 1, 1, 1, 1, 3, 7], [0, 0, 0, 0, 1, 1, 1, 1, 1, 2, 5, 11], [0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 3, 7, 15], [0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 2, 10, 11, 23], [0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 6, 14, 15, 31]]
[[], [1], [0, 1], [0, 0, 1], [0, 0, 0, 1], [0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 1], [0, 0, 0, 0, 1, 1, 1], [0, 0, 0, 0, 1, 1, 1, 2], [0, 0, 0, 0, 1, 1, 1, 1, 3], [0, 0, 0, 0, 1, 1, 1, 1, 2, 5], [0, 0, 0, 0, 1, 1, 1, 1, 1, 3, 7], [0, 0, 0, 0, 1, 1, 1, 1, 1, 2, 5, 11], [0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 3, 7, 15], [0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 2, 10, 11, 23], [0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 6, 14, 15, 31]]
[6, 3, true]
[[], [1], [0, 1], [0, 0, 1], [0, 0, 0, 1], [0, 0, 0, 1, 1], [0, 0, 0, 1, 1, 1], [0, 0, 0, 1, 1, 1, 2], [0, 0, 0, 1, 1, 1, 1, 3], [0, 0, 0, 1, 1, 1, 1, 2, 5], [0, 0, 0, 1, 1, 1, 1, 1, 3, 7], [0, 0, 0, 1, 1, 1, 1, 1, 2, 5, 11], [0, 0, 0, 1, 1, 1, 1, 1, 1, 3, 7, 15], [0, 0, 0, 1, 1, 1, 1, 1, 1, 2, 10, 11, 23], [0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 6, 14, 15, 31], [0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 6, 15, 22, 34, 47]]
[[], [1], [0, 1], [0, 0, 1], [0, 0, 0, 1], [0, 0, 0, 1, 1], [0, 0, 0, 1, 1, 1], [0, 0, 0, 1, 1, 1, 2], [0, 0, 0, 1, 1, 1, 1, 3], [0, 0, 0, 1, 1, 1, 1, 2, 5], [0, 0, 0, 1, 1, 1, 1, 1, 3, 7], [0, 0, 0, 1, 1, 1, 1, 1, 2, 5, 11], [0, 0, 0, 1, 1, 1, 1, 1, 1, 3, 7, 15], [0, 0, 0, 1, 1, 1, 1, 1, 1, 2, 10, 11, 23], [0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 6, 14, 15, 31], [0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 6, 15, 22, 34, 47]]
[6, 4, true]
[[], [1], [0, 1], [0, 0, 1], [0, 0, 1, 1], [0, 0, 1, 1, 1], [0, 0, 1, 1, 1, 2], [0, 0, 1, 1, 1, 1, 3], [0, 0, 1, 1, 1, 1, 2, 5], [0, 0, 1, 1, 1, 1, 1, 3, 7], [0, 0, 1, 1, 1, 1, 1, 2, 5, 11], [0, 0, 1, 1, 1, 1, 1, 1, 3, 7, 15], [0, 0, 1, 1, 1, 1, 1, 1, 2, 10, 11, 23], [0, 0, 1, 1, 1, 1, 1, 1, 1, 6, 14, 15, 31], [0, 0, 1, 1, 1, 1, 1, 1, 1, 6, 15, 22, 34, 47], [0, 0, 1, 1, 1, 1, 1, 1, 1, 3, 12, 21, 37, 46, 70]]
[[], [1], [0, 1], [0, 0, 1], [0, 0, 1, 1], [0, 0, 1, 1, 1], [0, 0, 1, 1, 1, 2], [0, 0, 1, 1, 1, 1, 3], [0, 0, 1, 1, 1, 1, 2, 5], [0, 0, 1, 1, 1, 1, 1, 3, 7], [0, 0, 1, 1, 1, 1, 1, 2, 5, 11], [0, 0, 1, 1, 1, 1, 1, 1, 3, 7, 15], [0, 0, 1, 1, 1, 1, 1, 1, 2, 10, 11, 23], [0, 0, 1, 1, 1, 1, 1, 1, 1, 6, 14, 15, 31], [0, 0, 1, 1, 1, 1, 1, 1, 1, 6, 15, 22, 34, 47], [0, 0, 1, 1, 1, 1, 1, 1, 1, 3, 12, 21, 37, 46, 70]]
[6, 5, true]
[[], [1], [0, 1], [0, 1, 1], [0, 1, 1, 1], [0, 1, 1, 1, 2], [0, 1, 1, 1, 1, 3], [0, 1, 1, 1, 1, 2, 5], [0, 1, 1, 1, 1, 1, 3, 7], [0, 1, 1, 1, 1, 1, 2, 5, 11], [0, 1, 1, 1, 1, 1, 1, 3, 7, 15], [0, 1, 1, 1, 1, 1, 1, 2, 10, 11, 23], [0, 1, 1, 1, 1, 1, 1, 1, 6, 14, 15, 31], [0, 1, 1, 1, 1, 1, 1, 1, 6, 15, 22, 34, 47], [0, 1, 1, 1, 1, 1, 1, 1, 3, 12, 21, 37, 46, 70], [0, 1, 1, 1, 1, 1, 1, 1, 4, 12, 25, 54, 57, 86, 111]]
[[], [1], [0, 1], [0, 1, 1], [0, 1, 1, 1], [0, 1, 1, 1, 2], [0, 1, 1, 1, 1, 3], [0, 1, 1, 1, 1, 2, 5], [0, 1, 1, 1, 1, 1, 3, 7], [0, 1, 1, 1, 1, 1, 2, 5, 11], [0, 1, 1, 1, 1, 1, 1, 3, 7, 15], [0, 1, 1, 1, 1, 1, 1, 2, 10, 11, 23], [0, 1, 1, 1, 1, 1, 1, 1, 6, 14, 15, 31], [0, 1, 1, 1, 1, 1, 1, 1, 6, 15, 22, 34, 47], [0, 1, 1, 1, 1, 1, 1, 1, 3, 12, 21, 37, 46, 70], [0, 1, 1, 1, 1, 1, 1, 1, 4, 12, 25, 54, 57, 86, 111]]
[6, 6, true]
[[], [1], [1, 1], [1, 1, 1], [1, 1, 1, 2], [1, 1, 1, 1, 3], [1, 1, 1, 1, 2, 5], [1, 1, 1, 1, 1, 3, 7], [1, 1, 1, 1, 1, 2, 5, 11], [1, 1, 1, 1, 1, 1, 3, 7, 15], [1, 1, 1, 1, 1, 1, 2, 10, 11, 23], [1, 1, 1, 1, 1, 1, 1, 6, 14, 15, 31], [1, 1, 1, 1, 1, 1, 1, 6, 15, 22, 34, 47], [1, 1, 1, 1, 1, 1, 1, 3, 12, 21, 37, 46, 70], [1, 1, 1, 1, 1, 1, 1, 4, 12, 25, 54, 57, 86, 111], [1, 1, 1, 1, 1, 1, 1, 4, 7, 21, 48, 74, 102, 116, 177]]
[[], [1], [1, 1], [1, 1, 1], [1, 1, 1, 2], [1, 1, 1, 1, 3], [1, 1, 1, 1, 2, 5], [1, 1, 1, 1, 1, 3, 7], [1, 1, 1, 1, 1, 2, 5, 11], [1, 1, 1, 1, 1, 1, 3, 7, 15], [1, 1, 1, 1, 1, 1, 2, 10, 11, 23], [1, 1, 1, 1, 1, 1, 1, 6, 14, 15, 31], [1, 1, 1, 1, 1, 1, 1, 6, 15, 22, 34, 47], [1, 1, 1, 1, 1, 1, 1, 3, 12, 21, 37, 46, 70], [1, 1, 1, 1, 1, 1, 1, 4, 12, 25, 54, 57, 86, 111], [1, 1, 1, 1, 1, 1, 1, 4, 7, 21, 48, 74, 102, 116, 177]]
[6, 7, true]
[[], [1], [0, 1], [0, 0, 1], [0, 0, 0, 1], [0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 1, 1], [0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1], [0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 2], [0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 3], [0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 2, 5], [0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 3, 7]]
[[], [1], [0, 1], [0, 0, 1], [0, 0, 0, 1], [0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 1, 1], [0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1], [0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 2], [0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 3], [0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 2, 5], [0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 3, 7]]
[7, 0, true]
[[], [1], [0, 1], [0, 0, 1], [0, 0, 0, 1], [0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 1, 1], [0, 0, 0, 0, 0, 0, 0, 1, 1, 1], [0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 2], [0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 3], [0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 2, 5], [0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 3, 7], [0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 2, 5, 11]]
[[], [1], [0, 1], [0, 0, 1], [0, 0, 0, 1], [0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 1, 1], [0, 0, 0, 0, 0, 0, 0, 1, 1, 1], [0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 2], [0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 3], [0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 2, 5], [0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 3, 7], [0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 2, 5, 11]]
[7, 1, true]
[[], [1], [0, 1], [0, 0, 1], [0, 0, 0, 1], [0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 1, 1], [0, 0, 0, 0, 0, 0, 1, 1, 1], [0, 0, 0, 0, 0, 0, 1, 1, 1, 2], [0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 3], [0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 2, 5], [0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 3, 7], [0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 2, 5, 11], [0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 3, 7, 15]]
[[], [1], [0, 1], [0, 0, 1], [0, 0, 0, 1], [0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 1, 1], [0, 0, 0, 0, 0, 0, 1, 1, 1], [0, 0, 0, 0, 0, 0, 1, 1, 1, 2], [0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 3], [0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 2, 5], [0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 3, 7], [0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 2, 5, 11], [0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 3, 7, 15]]
[7, 2, true]
[[], [1], [0, 1], [0, 0, 1], [0, 0, 0, 1], [0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 1, 1], [0, 0, 0, 0, 0, 1, 1, 1], [0, 0, 0, 0, 0, 1, 1, 1, 2], [0, 0, 0, 0, 0, 1, 1, 1, 1, 3], [0, 0, 0, 0, 0, 1, 1, 1, 1, 2, 5], [0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 3, 7], [0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 2, 5, 11], [0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 3, 7, 15], [0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 2, 5, 11, 23]]
[[], [1], [0, 1], [0, 0, 1], [0, 0, 0, 1], [0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 1, 1], [0, 0, 0, 0, 0, 1, 1, 1], [0, 0, 0, 0, 0, 1, 1, 1, 2], [0, 0, 0, 0, 0, 1, 1, 1, 1, 3], [0, 0, 0, 0, 0, 1, 1, 1, 1, 2, 5], [0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 3, 7], [0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 2, 5, 11], [0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 3, 7, 15], [0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 2, 5, 11, 23]]
[7, 3, true]
[[], [1], [0, 1], [0, 0, 1], [0, 0, 0, 1], [0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 1], [0, 0, 0, 0, 1, 1, 1], [0, 0, 0, 0, 1, 1, 1, 2], [0, 0, 0, 0, 1, 1, 1, 1, 3], [0, 0, 0, 0, 1, 1, 1, 1, 2, 5], [0, 0, 0, 0, 1, 1, 1, 1, 1, 3, 7], [0, 0, 0, 0, 1, 1, 1, 1, 1, 2, 5, 11], [0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 3, 7, 15], [0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 2, 5, 11, 23], [0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 3, 14, 15, 31]]
[[], [1], [0, 1], [0, 0, 1], [0, 0, 0, 1], [0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 1], [0, 0, 0, 0, 1, 1, 1], [0, 0, 0, 0, 1, 1, 1, 2], [0, 0, 0, 0, 1, 1, 1, 1, 3], [0, 0, 0, 0, 1, 1, 1, 1, 2, 5], [0, 0, 0, 0, 1, 1, 1, 1, 1, 3, 7], [0, 0, 0, 0, 1, 1, 1, 1, 1, 2, 5, 11], [0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 3, 7, 15], [0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 2, 5, 11, 23], [0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 3, 14, 15, 31]]
[7, 4, true]
[[], [1], [0, 1], [0, 0, 1], [0, 0, 0, 1], [0, 0, 0, 1, 1], [0, 0, 0, 1, 1, 1], [0, 0, 0, 1, 1, 1, 2], [0, 0, 0, 1, 1, 1, 1, 3], [0, 0, 0, 1, 1, 1, 1, 2, 5], [0, 0, 0, 1, 1, 1, 1, 1, 3, 7], [0, 0, 0, 1, 1, 1, 1, 1, 2, 5, 11], [0, 0, 0, 1, 1, 1, 1, 1, 1, 3, 7, 15], [0, 0, 0, 1, 1, 1, 1, 1, 1, 2, 5, 11, 23], [0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 3, 14, 15, 31], [0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 2, 10, 22, 23, 47]]
[[], [1], [0, 1], [0, 0, 1], [0, 0, 0, 1], [0, 0, 0, 1, 1], [0, 0, 0, 1, 1, 1], [0, 0, 0, 1, 1, 1, 2], [0, 0, 0, 1, 1, 1, 1, 3], [0, 0, 0, 1, 1, 1, 1, 2, 5], [0, 0, 0, 1, 1, 1, 1, 1, 3, 7], [0, 0, 0, 1, 1, 1, 1, 1, 2, 5, 11], [0, 0, 0, 1, 1, 1, 1, 1, 1, 3, 7, 15], [0, 0, 0, 1, 1, 1, 1, 1, 1, 2, 5, 11, 23], [0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 3, 14, 15, 31], [0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 2, 10, 22, 23, 47]]
[7, 5, true]
[[], [1], [0, 1], [0, 0, 1], [0, 0, 1, 1], [0, 0, 1, 1, 1], [0, 0, 1, 1, 1, 2], [0, 0, 1, 1, 1, 1, 3], [0, 0, 1, 1, 1, 1, 2, 5], [0, 0, 1, 1, 1, 1, 1, 3, 7], [0, 0, 1, 1, 1, 1, 1, 2, 5, 11], [0, 0, 1, 1, 1, 1, 1, 1, 3, 7, 15], [0, 0, 1, 1, 1, 1, 1, 1, 2, 5, 11, 23], [0, 0, 1, 1, 1, 1, 1, 1, 1, 3, 14, 15, 31], [0, 0, 1, 1, 1, 1, 1, 1, 1, 2, 10, 22, 23, 47], [0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 9, 21, 30, 46, 63]]
[[], [1], [0, 1], [0, 0, 1], [0, 0, 1, 1], [0, 0, 1, 1, 1], [0, 0, 1, 1, 1, 2], [0, 0, 1, 1, 1, 1, 3], [0, 0, 1, 1, 1, 1, 2, 5], [0, 0, 1, 1, 1, 1, 1, 3, 7], [0, 0, 1, 1, 1, 1, 1, 2, 5, 11], [0, 0, 1, 1, 1, 1, 1, 1, 3, 7, 15], [0, 0, 1, 1, 1, 1, 1, 1, 2, 5, 11, 23], [0, 0, 1, 1, 1, 1, 1, 1, 1, 3, 14, 15, 31], [0, 0, 1, 1, 1, 1, 1, 1, 1, 2, 10, 22, 23, 47], [0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 9, 21, 30, 46, 63]]
[7, 6, true]
[[], [1], [0, 1], [0, 1, 1], [0, 1, 1, 1], [0, 1, 1, 1, 2], [0, 1, 1, 1, 1, 3], [0, 1, 1, 1, 1, 2, 5], [0, 1, 1, 1, 1, 1, 3, 7], [0, 1, 1, 1, 1, 1, 2, 5, 11], [0, 1, 1, 1, 1, 1, 1, 3, 7, 15], [0, 1, 1, 1, 1, 1, 1, 2, 5, 11, 23], [0, 1, 1, 1, 1, 1, 1, 1, 3, 14, 15, 31], [0, 1, 1, 1, 1, 1, 1, 1, 2, 10, 22, 23, 47], [0, 1, 1, 1, 1, 1, 1, 1, 1, 9, 21, 30, 46, 63], [0, 1, 1, 1, 1, 1, 1, 1, 1, 6, 20, 33, 57, 70, 106]]
[[], [1], [0, 1], [0, 1, 1], [0, 1, 1, 1], [0, 1, 1, 1, 2], [0, 1, 1, 1, 1, 3], [0, 1, 1, 1, 1, 2, 5], [0, 1, 1, 1, 1, 1, 3, 7], [0, 1, 1, 1, 1, 1, 2, 5, 11], [0, 1, 1, 1, 1, 1, 1, 3, 7, 15], [0, 1, 1, 1, 1, 1, 1, 2, 5, 11, 23], [0, 1, 1, 1, 1, 1, 1, 1, 3, 14, 15, 31], [0, 1, 1, 1, 1, 1, 1, 1, 2, 10, 22, 23, 47], [0, 1, 1, 1, 1, 1, 1, 1, 1, 9, 21, 30, 46, 63], [0, 1, 1, 1, 1, 1, 1, 1, 1, 6, 20, 33, 57, 70, 106]]
[7, 7, true]
[[], [1], [1, 1], [1, 1, 1], [1, 1, 1, 2], [1, 1, 1, 1, 3], [1, 1, 1, 1, 2, 5], [1, 1, 1, 1, 1, 3, 7], [1, 1, 1, 1, 1, 2, 5, 11], [1, 1, 1, 1, 1, 1, 3, 7, 15], [1, 1, 1, 1, 1, 1, 2, 5, 11, 23], [1, 1, 1, 1, 1, 1, 1, 3, 14, 15, 31], [1, 1, 1, 1, 1, 1, 1, 2, 10, 22, 23, 47], [1, 1, 1, 1, 1, 1, 1, 1, 9, 21, 30, 46, 63], [1, 1, 1, 1, 1, 1, 1, 1, 6, 20, 33, 57, 70, 106], [1, 1, 1, 1, 1, 1, 1, 1, 4, 18, 35, 74, 77, 116, 149]]
[[], [1], [1, 1], [1, 1, 1], [1, 1, 1, 2], [1, 1, 1, 1, 3], [1, 1, 1, 1, 2, 5], [1, 1, 1, 1, 1, 3, 7], [1, 1, 1, 1, 1, 2, 5, 11], [1, 1, 1, 1, 1, 1, 3, 7, 15], [1, 1, 1, 1, 1, 1, 2, 5, 11, 23], [1, 1, 1, 1, 1, 1, 1, 3, 14, 15, 31], [1, 1, 1, 1, 1, 1, 1, 2, 10, 22, 23, 47], [1, 1, 1, 1, 1, 1, 1, 1, 9, 21, 30, 46, 63], [1, 1, 1, 1, 1, 1, 1, 1, 6, 20, 33, 57, 70, 106], [1, 1, 1, 1, 1, 1, 1, 1, 4, 18, 35, 74, 77, 116, 149]]
[7, 8, true]
[[], [1], [0, 1], [0, 0, 1], [0, 0, 0, 1], [0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 2], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 3], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 2, 5]]
[[], [1], [0, 1], [0, 0, 1], [0, 0, 0, 1], [0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 2], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 3], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 2, 5]]
[8, 0, true]
[[], [1], [0, 1], [0, 0, 1], [0, 0, 0, 1], [0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 1, 1], [0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1], [0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 2], [0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 3], [0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 2, 5], [0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 3, 7]]
[[], [1], [0, 1], [0, 0, 1], [0, 0, 0, 1], [0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 1, 1], [0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1], [0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 2], [0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 3], [0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 2, 5], [0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 3, 7]]
[8, 1, true]
[[], [1], [0, 1], [0, 0, 1], [0, 0, 0, 1], [0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 1, 1], [0, 0, 0, 0, 0, 0, 0, 1, 1, 1], [0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 2], [0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 3], [0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 2, 5], [0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 3, 7], [0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 2, 5, 11]]
[[], [1], [0, 1], [0, 0, 1], [0, 0, 0, 1], [0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 1, 1], [0, 0, 0, 0, 0, 0, 0, 1, 1, 1], [0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 2], [0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 3], [0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 2, 5], [0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 3, 7], [0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 2, 5, 11]]
[8, 2, true]
[[], [1], [0, 1], [0, 0, 1], [0, 0, 0, 1], [0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 1, 1], [0, 0, 0, 0, 0, 0, 1, 1, 1], [0, 0, 0, 0, 0, 0, 1, 1, 1, 2], [0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 3], [0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 2, 5], [0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 3, 7], [0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 2, 5, 11], [0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 3, 7, 15]]
[[], [1], [0, 1], [0, 0, 1], [0, 0, 0, 1], [0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 1, 1], [0, 0, 0, 0, 0, 0, 1, 1, 1], [0, 0, 0, 0, 0, 0, 1, 1, 1, 2], [0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 3], [0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 2, 5], [0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 3, 7], [0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 2, 5, 11], [0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 3, 7, 15]]
[8, 3, true]
[[], [1], [0, 1], [0, 0, 1], [0, 0, 0, 1], [0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 1, 1], [0, 0, 0, 0, 0, 1, 1, 1], [0, 0, 0, 0, 0, 1, 1, 1, 2], [0, 0, 0, 0, 0, 1, 1, 1, 1, 3], [0, 0, 0, 0, 0, 1, 1, 1, 1, 2, 5], [0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 3, 7], [0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 2, 5, 11], [0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 3, 7, 15], [0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 2, 5, 11, 23]]
[[], [1], [0, 1], [0, 0, 1], [0, 0, 0, 1], [0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 1, 1], [0, 0, 0, 0, 0, 1, 1, 1], [0, 0, 0, 0, 0, 1, 1, 1, 2], [0, 0, 0, 0, 0, 1, 1, 1, 1, 3], [0, 0, 0, 0, 0, 1, 1, 1, 1, 2, 5], [0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 3, 7], [0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 2, 5, 11], [0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 3, 7, 15], [0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 2, 5, 11, 23]]
[8, 4, true]
[[], [1], [0, 1], [0, 0, 1], [0, 0, 0, 1], [0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 1], [0, 0, 0, 0, 1, 1, 1], [0, 0, 0, 0, 1, 1, 1, 2], [0, 0, 0, 0, 1, 1, 1, 1, 3], [0, 0, 0, 0, 1, 1, 1, 1, 2, 5], [0, 0, 0, 0, 1, 1, 1, 1, 1, 3, 7], [0, 0, 0, 0, 1, 1, 1, 1, 1, 2, 5, 11], [0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 3, 7, 15], [0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 2, 5, 11, 23], [0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 3, 7, 15, 31]]
[[], [1], [0, 1], [0, 0, 1], [0, 0, 0, 1], [0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 1], [0, 0, 0, 0, 1, 1, 1], [0, 0, 0, 0, 1, 1, 1, 2], [0, 0, 0, 0, 1, 1, 1, 1, 3], [0, 0, 0, 0, 1, 1, 1, 1, 2, 5], [0, 0, 0, 0, 1, 1, 1, 1, 1, 3, 7], [0, 0, 0, 0, 1, 1, 1, 1, 1, 2, 5, 11], [0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 3, 7, 15], [0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 2, 5, 11, 23], [0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 3, 7, 15, 31]]
[8, 5, true]
[[], [1], [0, 1], [0, 0, 1], [0, 0, 0, 1], [0, 0, 0, 1, 1], [0, 0, 0, 1, 1, 1], [0, 0, 0, 1, 1, 1, 2], [0, 0, 0, 1, 1, 1, 1, 3], [0, 0, 0, 1, 1, 1, 1, 2, 5], [0, 0, 0, 1, 1, 1, 1, 1, 3, 7], [0, 0, 0, 1, 1, 1, 1, 1, 2, 5, 11], [0, 0, 0, 1, 1, 1, 1, 1, 1, 3, 7, 15], [0, 0, 0, 1, 1, 1, 1, 1, 1, 2, 5, 11, 23], [0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 3, 7, 15, 31], [0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 2, 5, 22, 23, 47]]
[[], [1], [0, 1], [0, 0, 1], [0, 0, 0, 1], [0, 0, 0, 1, 1], [0, 0, 0, 1, 1, 1], [0, 0, 0, 1, 1, 1, 2], [0, 0, 0, 1, 1, 1, 1, 3], [0, 0, 0, 1, 1, 1, 1, 2, 5], [0, 0, 0, 1, 1, 1, 1, 1, 3, 7], [0, 0, 0, 1, 1, 1, 1, 1, 2, 5, 11], [0, 0, 0, 1, 1, 1, 1, 1, 1, 3, 7, 15], [0, 0, 0, 1, 1, 1, 1, 1, 1, 2, 5, 11, 23], [0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 3, 7, 15, 31], [0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 2, 5, 22, 23, 47]]
[8, 6, true]
[[], [1], [0, 1], [0, 0, 1], [0, 0, 1, 1], [0, 0, 1, 1, 1], [0, 0, 1, 1, 1, 2], [0, 0, 1, 1, 1, 1, 3], [0, 0, 1, 1, 1, 1, 2, 5], [0, 0, 1, 1, 1, 1, 1, 3, 7], [0, 0, 1, 1, 1, 1, 1, 2, 5, 11], [0, 0, 1, 1, 1, 1, 1, 1, 3, 7, 15], [0, 0, 1, 1, 1, 1, 1, 1, 2, 5, 11, 23], [0, 0, 1, 1, 1, 1, 1, 1, 1, 3, 7, 15, 31], [0, 0, 1, 1, 1, 1, 1, 1, 1, 2, 5, 22, 23, 47], [0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 3, 14, 30, 31, 63]]
[[], [1], [0, 1], [0, 0, 1], [0, 0, 1, 1], [0, 0, 1, 1, 1], [0, 0, 1, 1, 1, 2], [0, 0, 1, 1, 1, 1, 3], [0, 0, 1, 1, 1, 1, 2, 5], [0, 0, 1, 1, 1, 1, 1, 3, 7], [0, 0, 1, 1, 1, 1, 1, 2, 5, 11], [0, 0, 1, 1, 1, 1, 1, 1, 3, 7, 15], [0, 0, 1, 1, 1, 1, 1, 1, 2, 5, 11, 23], [0, 0, 1, 1, 1, 1, 1, 1, 1, 3, 7, 15, 31], [0, 0, 1, 1, 1, 1, 1, 1, 1, 2, 5, 22, 23, 47], [0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 3, 14, 30, 31, 63]]
[8, 7, true]
[[], [1], [0, 1], [0, 1, 1], [0, 1, 1, 1], [0, 1, 1, 1, 2], [0, 1, 1, 1, 1, 3], [0, 1, 1, 1, 1, 2, 5], [0, 1, 1, 1, 1, 1, 3, 7], [0, 1, 1, 1, 1, 1, 2, 5, 11], [0, 1, 1, 1, 1, 1, 1, 3, 7, 15], [0, 1, 1, 1, 1, 1, 1, 2, 5, 11, 23], [0, 1, 1, 1, 1, 1, 1, 1, 3, 7, 15, 31], [0, 1, 1, 1, 1, 1, 1, 1, 2, 5, 22, 23, 47], [0, 1, 1, 1, 1, 1, 1, 1, 1, 3, 14, 30, 31, 63], [0, 1, 1, 1, 1, 1, 1, 1, 1, 2, 15, 33, 46, 70, 95]]
[[], [1], [0, 1], [0, 1, 1], [0, 1, 1, 1], [0, 1, 1, 1, 2], [0, 1, 1, 1, 1, 3], [0, 1, 1, 1, 1, 2, 5], [0, 1, 1, 1, 1, 1, 3, 7], [0, 1, 1, 1, 1, 1, 2, 5, 11], [0, 1, 1, 1, 1, 1, 1, 3, 7, 15], [0, 1, 1, 1, 1, 1, 1, 2, 5, 11, 23], [0, 1, 1, 1, 1, 1, 1, 1, 3, 7, 15, 31], [0, 1, 1, 1, 1, 1, 1, 1, 2, 5, 22, 23, 47], [0, 1, 1, 1, 1, 1, 1, 1, 1, 3, 14, 30, 31, 63], [0, 1, 1, 1, 1, 1, 1, 1, 1, 2, 15, 33, 46, 70, 95]]
[8, 8, true]
[[], [1], [1, 1], [1, 1, 1], [1, 1, 1, 2], [1, 1, 1, 1, 3], [1, 1, 1, 1, 2, 5], [1, 1, 1, 1, 1, 3, 7], [1, 1, 1, 1, 1, 2, 5, 11], [1, 1, 1, 1, 1, 1, 3, 7, 15], [1, 1, 1, 1, 1, 1, 2, 5, 11, 23], [1, 1, 1, 1, 1, 1, 1, 3, 7, 15, 31], [1, 1, 1, 1, 1, 1, 1, 2, 5, 22, 23, 47], [1, 1, 1, 1, 1, 1, 1, 1, 3, 14, 30, 31, 63], [1, 1, 1, 1, 1, 1, 1, 1, 2, 15, 33, 46, 70, 95], [1, 1, 1, 1, 1, 1, 1, 1, 1, 9, 28, 45, 77, 94, 142]]
[[], [1], [1, 1], [1, 1, 1], [1, 1, 1, 2], [1, 1, 1, 1, 3], [1, 1, 1, 1, 2, 5], [1, 1, 1, 1, 1, 3, 7], [1, 1, 1, 1, 1, 2, 5, 11], [1, 1, 1, 1, 1, 1, 3, 7, 15], [1, 1, 1, 1, 1, 1, 2, 5, 11, 23], [1, 1, 1, 1, 1, 1, 1, 3, 7, 15, 31], [1, 1, 1, 1, 1, 1, 1, 2, 5, 22, 23, 47], [1, 1, 1, 1, 1, 1, 1, 1, 3, 14, 30, 31, 63], [1, 1, 1, 1, 1, 1, 1, 1, 2, 15, 33, 46, 70, 95], [1, 1, 1, 1, 1, 1, 1, 1, 1, 9, 28, 45, 77, 94, 142]]
[8, 9, true]
[[], [1], [0, 1], [0, 0, 1], [0, 0, 0, 1], [0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 2], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 3]]
[[], [1], [0, 1], [0, 0, 1], [0, 0, 0, 1], [0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 2], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 3]]
[9, 0, true]
[[], [1], [0, 1], [0, 0, 1], [0, 0, 0, 1], [0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 2], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 3], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 2, 5]]
[[], [1], [0, 1], [0, 0, 1], [0, 0, 0, 1], [0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 2], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 3], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 2, 5]]
[9, 1, true]
[[], [1], [0, 1], [0, 0, 1], [0, 0, 0, 1], [0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 1, 1], [0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1], [0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 2], [0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 3], [0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 2, 5], [0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 3, 7]]
[[], [1], [0, 1], [0, 0, 1], [0, 0, 0, 1], [0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 1, 1], [0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1], [0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 2], [0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 3], [0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 2, 5], [0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 3, 7]]
[9, 2, true]
[[], [1], [0, 1], [0, 0, 1], [0, 0, 0, 1], [0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 1, 1], [0, 0, 0, 0, 0, 0, 0, 1, 1, 1], [0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 2], [0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 3], [0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 2, 5], [0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 3, 7], [0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 2, 5, 11]]
[[], [1], [0, 1], [0, 0, 1], [0, 0, 0, 1], [0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 1, 1], [0, 0, 0, 0, 0, 0, 0, 1, 1, 1], [0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 2], [0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 3], [0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 2, 5], [0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 3, 7], [0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 2, 5, 11]]
[9, 3, true]
[[], [1], [0, 1], [0, 0, 1], [0, 0, 0, 1], [0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 1, 1], [0, 0, 0, 0, 0, 0, 1, 1, 1], [0, 0, 0, 0, 0, 0, 1, 1, 1, 2], [0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 3], [0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 2, 5], [0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 3, 7], [0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 2, 5, 11], [0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 3, 7, 15]]
[[], [1], [0, 1], [0, 0, 1], [0, 0, 0, 1], [0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 1, 1], [0, 0, 0, 0, 0, 0, 1, 1, 1], [0, 0, 0, 0, 0, 0, 1, 1, 1, 2], [0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 3], [0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 2, 5], [0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 3, 7], [0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 2, 5, 11], [0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 3, 7, 15]]
[9, 4, true]
[[], [1], [0, 1], [0, 0, 1], [0, 0, 0, 1], [0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 1, 1], [0, 0, 0, 0, 0, 1, 1, 1], [0, 0, 0, 0, 0, 1, 1, 1, 2], [0, 0, 0, 0, 0, 1, 1, 1, 1, 3], [0, 0, 0, 0, 0, 1, 1, 1, 1, 2, 5], [0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 3, 7], [0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 2, 5, 11], [0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 3, 7, 15], [0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 2, 5, 11, 23]]
[[], [1], [0, 1], [0, 0, 1], [0, 0, 0, 1], [0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 1, 1], [0, 0, 0, 0, 0, 1, 1, 1], [0, 0, 0, 0, 0, 1, 1, 1, 2], [0, 0, 0, 0, 0, 1, 1, 1, 1, 3], [0, 0, 0, 0, 0, 1, 1, 1, 1, 2, 5], [0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 3, 7], [0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 2, 5, 11], [0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 3, 7, 15], [0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 2, 5, 11, 23]]
[9, 5, true]
[[], [1], [0, 1], [0, 0, 1], [0, 0, 0, 1], [0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 1], [0, 0, 0, 0, 1, 1, 1], [0, 0, 0, 0, 1, 1, 1, 2], [0, 0, 0, 0, 1, 1, 1, 1, 3], [0, 0, 0, 0, 1, 1, 1, 1, 2, 5], [0, 0, 0, 0, 1, 1, 1, 1, 1, 3, 7], [0, 0, 0, 0, 1, 1, 1, 1, 1, 2, 5, 11], [0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 3, 7, 15], [0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 2, 5, 11, 23], [0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 3, 7, 15, 31]]
[[], [1], [0, 1], [0, 0, 1], [0, 0, 0, 1], [0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 1], [0, 0, 0, 0, 1, 1, 1], [0, 0, 0, 0, 1, 1, 1, 2], [0, 0, 0, 0, 1, 1, 1, 1, 3], [0, 0, 0, 0, 1, 1, 1, 1, 2, 5], [0, 0, 0, 0, 1, 1, 1, 1, 1, 3, 7], [0, 0, 0, 0, 1, 1, 1, 1, 1, 2, 5, 11], [0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 3, 7, 15], [0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 2, 5, 11, 23], [0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 3, 7, 15, 31]]
[9, 6, true]
[[], [1], [0, 1], [0, 0, 1], [0, 0, 0, 1], [0, 0, 0, 1, 1], [0, 0, 0, 1, 1, 1], [0, 0, 0, 1, 1, 1, 2], [0, 0, 0, 1, 1, 1, 1, 3], [0, 0, 0, 1, 1, 1, 1, 2, 5], [0, 0, 0, 1, 1, 1, 1, 1, 3, 7], [0, 0, 0, 1, 1, 1, 1, 1, 2, 5, 11], [0, 0, 0, 1, 1, 1, 1, 1, 1, 3, 7, 15], [0, 0, 0, 1, 1, 1, 1, 1, 1, 2, 5, 11, 23], [0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 3, 7, 15, 31], [0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 2, 5, 11, 23, 47]]
[[], [1], [0, 1], [0, 0, 1], [0, 0, 0, 1], [0, 0, 0, 1, 1], [0, 0, 0, 1, 1, 1], [0, 0, 0, 1, 1, 1, 2], [0, 0, 0, 1, 1, 1, 1, 3], [0, 0, 0, 1, 1, 1, 1, 2, 5], [0, 0, 0, 1, 1, 1, 1, 1, 3, 7], [0, 0, 0, 1, 1, 1, 1, 1, 2, 5, 11], [0, 0, 0, 1, 1, 1, 1, 1, 1, 3, 7, 15], [0, 0, 0, 1, 1, 1, 1, 1, 1, 2, 5, 11, 23], [0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 3, 7, 15, 31], [0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 2, 5, 11, 23, 47]]
[9, 7, true]
[[], [1], [0, 1], [0, 0, 1], [0, 0, 1, 1], [0, 0, 1, 1, 1], [0, 0, 1, 1, 1, 2], [0, 0, 1, 1, 1, 1, 3], [0, 0, 1, 1, 1, 1, 2, 5], [0, 0, 1, 1, 1, 1, 1, 3, 7], [0, 0, 1, 1, 1, 1, 1, 2, 5, 11], [0, 0, 1, 1, 1, 1, 1, 1, 3, 7, 15], [0, 0, 1, 1, 1, 1, 1, 1, 2, 5, 11, 23], [0, 0, 1, 1, 1, 1, 1, 1, 1, 3, 7, 15, 31], [0, 0, 1, 1, 1, 1, 1, 1, 1, 2, 5, 11, 23, 47], [0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 3, 7, 30, 31, 63]]
[[], [1], [0, 1], [0, 0, 1], [0, 0, 1, 1], [0, 0, 1, 1, 1], [0, 0, 1, 1, 1, 2], [0, 0, 1, 1, 1, 1, 3], [0, 0, 1, 1, 1, 1, 2, 5], [0, 0, 1, 1, 1, 1, 1, 3, 7], [0, 0, 1, 1, 1, 1, 1, 2, 5, 11], [0, 0, 1, 1, 1, 1, 1, 1, 3, 7, 15], [0, 0, 1, 1, 1, 1, 1, 1, 2, 5, 11, 23], [0, 0, 1, 1, 1, 1, 1, 1, 1, 3, 7, 15, 31], [0, 0, 1, 1, 1, 1, 1, 1, 1, 2, 5, 11, 23, 47], [0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 3, 7, 30, 31, 63]]
[9, 8, true]
[[], [1], [0, 1], [0, 1, 1], [0, 1, 1, 1], [0, 1, 1, 1, 2], [0, 1, 1, 1, 1, 3], [0, 1, 1, 1, 1, 2, 5], [0, 1, 1, 1, 1, 1, 3, 7], [0, 1, 1, 1, 1, 1, 2, 5, 11], [0, 1, 1, 1, 1, 1, 1, 3, 7, 15], [0, 1, 1, 1, 1, 1, 1, 2, 5, 11, 23], [0, 1, 1, 1, 1, 1, 1, 1, 3, 7, 15, 31], [0, 1, 1, 1, 1, 1, 1, 1, 2, 5, 11, 23, 47], [0, 1, 1, 1, 1, 1, 1, 1, 1, 3, 7, 30, 31, 63], [0, 1, 1, 1, 1, 1, 1, 1, 1, 2, 5, 22, 46, 47, 95]]
[[], [1], [0, 1], [0, 1, 1], [0, 1, 1, 1], [0, 1, 1, 1, 2], [0, 1, 1, 1, 1, 3], [0, 1, 1, 1, 1, 2, 5], [0, 1, 1, 1, 1, 1, 3, 7], [0, 1, 1, 1, 1, 1, 2, 5, 11], [0, 1, 1, 1, 1, 1, 1, 3, 7, 15], [0, 1, 1, 1, 1, 1, 1, 2, 5, 11, 23], [0, 1, 1, 1, 1, 1, 1, 1, 3, 7, 15, 31], [0, 1, 1, 1, 1, 1, 1, 1, 2, 5, 11, 23, 47], [0, 1, 1, 1, 1, 1, 1, 1, 1, 3, 7, 30, 31, 63], [0, 1, 1, 1, 1, 1, 1, 1, 1, 2, 5, 22, 46, 47, 95]]
[9, 9, true]
[[], [1], [1, 1], [1, 1, 1], [1, 1, 1, 2], [1, 1, 1, 1, 3], [1, 1, 1, 1, 2, 5], [1, 1, 1, 1, 1, 3, 7], [1, 1, 1, 1, 1, 2, 5, 11], [1, 1, 1, 1, 1, 1, 3, 7, 15], [1, 1, 1, 1, 1, 1, 2, 5, 11, 23], [1, 1, 1, 1, 1, 1, 1, 3, 7, 15, 31], [1, 1, 1, 1, 1, 1, 1, 2, 5, 11, 23, 47], [1, 1, 1, 1, 1, 1, 1, 1, 3, 7, 30, 31, 63], [1, 1, 1, 1, 1, 1, 1, 1, 2, 5, 22, 46, 47, 95], [1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 21, 45, 62, 94, 127]]
[[], [1], [1, 1], [1, 1, 1], [1, 1, 1, 2], [1, 1, 1, 1, 3], [1, 1, 1, 1, 2, 5], [1, 1, 1, 1, 1, 3, 7], [1, 1, 1, 1, 1, 2, 5, 11], [1, 1, 1, 1, 1, 1, 3, 7, 15], [1, 1, 1, 1, 1, 1, 2, 5, 11, 23], [1, 1, 1, 1, 1, 1, 1, 3, 7, 15, 31], [1, 1, 1, 1, 1, 1, 1, 2, 5, 11, 23, 47], [1, 1, 1, 1, 1, 1, 1, 1, 3, 7, 30, 31, 63], [1, 1, 1, 1, 1, 1, 1, 1, 2, 5, 22, 46, 47, 95], [1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 21, 45, 62, 94, 127]]
[9, 10, true]
[[], [1], [0, 1], [0, 0, 1], [0, 0, 0, 1], [0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 2]]
[[], [1], [0, 1], [0, 0, 1], [0, 0, 0, 1], [0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 2]]
[10, 0, true]
[[], [1], [0, 1], [0, 0, 1], [0, 0, 0, 1], [0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 2], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 3]]
[[], [1], [0, 1], [0, 0, 1], [0, 0, 0, 1], [0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 2], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 3]]
[10, 1, true]
[[], [1], [0, 1], [0, 0, 1], [0, 0, 0, 1], [0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 2], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 3], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 2, 5]]
[[], [1], [0, 1], [0, 0, 1], [0, 0, 0, 1], [0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 2], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 3], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 2, 5]]
[10, 2, true]
[[], [1], [0, 1], [0, 0, 1], [0, 0, 0, 1], [0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 1, 1], [0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1], [0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 2], [0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 3], [0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 2, 5], [0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 3, 7]]
[[], [1], [0, 1], [0, 0, 1], [0, 0, 0, 1], [0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 1, 1], [0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1], [0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 2], [0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 3], [0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 2, 5], [0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 3, 7]]
[10, 3, true]
[[], [1], [0, 1], [0, 0, 1], [0, 0, 0, 1], [0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 1, 1], [0, 0, 0, 0, 0, 0, 0, 1, 1, 1], [0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 2], [0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 3], [0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 2, 5], [0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 3, 7], [0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 2, 5, 11]]
[[], [1], [0, 1], [0, 0, 1], [0, 0, 0, 1], [0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 1, 1], [0, 0, 0, 0, 0, 0, 0, 1, 1, 1], [0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 2], [0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 3], [0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 2, 5], [0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 3, 7], [0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 2, 5, 11]]
[10, 4, true]
[[], [1], [0, 1], [0, 0, 1], [0, 0, 0, 1], [0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 1, 1], [0, 0, 0, 0, 0, 0, 1, 1, 1], [0, 0, 0, 0, 0, 0, 1, 1, 1, 2], [0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 3], [0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 2, 5], [0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 3, 7], [0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 2, 5, 11], [0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 3, 7, 15]]
[[], [1], [0, 1], [0, 0, 1], [0, 0, 0, 1], [0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 1, 1], [0, 0, 0, 0, 0, 0, 1, 1, 1], [0, 0, 0, 0, 0, 0, 1, 1, 1, 2], [0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 3], [0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 2, 5], [0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 3, 7], [0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 2, 5, 11], [0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 3, 7, 15]]
[10, 5, true]
[[], [1], [0, 1], [0, 0, 1], [0, 0, 0, 1], [0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 1, 1], [0, 0, 0, 0, 0, 1, 1, 1], [0, 0, 0, 0, 0, 1, 1, 1, 2], [0, 0, 0, 0, 0, 1, 1, 1, 1, 3], [0, 0, 0, 0, 0, 1, 1, 1, 1, 2, 5], [0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 3, 7], [0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 2, 5, 11], [0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 3, 7, 15], [0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 2, 5, 11, 23]]
[[], [1], [0, 1], [0, 0, 1], [0, 0, 0, 1], [0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 1, 1], [0, 0, 0, 0, 0, 1, 1, 1], [0, 0, 0, 0, 0, 1, 1, 1, 2], [0, 0, 0, 0, 0, 1, 1, 1, 1, 3], [0, 0, 0, 0, 0, 1, 1, 1, 1, 2, 5], [0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 3, 7], [0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 2, 5, 11], [0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 3, 7, 15], [0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 2, 5, 11, 23]]
[10, 6, true]
[[], [1], [0, 1], [0, 0, 1], [0, 0, 0, 1], [0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 1], [0, 0, 0, 0, 1, 1, 1], [0, 0, 0, 0, 1, 1, 1, 2], [0, 0, 0, 0, 1, 1, 1, 1, 3], [0, 0, 0, 0, 1, 1, 1, 1, 2, 5], [0, 0, 0, 0, 1, 1, 1, 1, 1, 3, 7], [0, 0, 0, 0, 1, 1, 1, 1, 1, 2, 5, 11], [0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 3, 7, 15], [0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 2, 5, 11, 23], [0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 3, 7, 15, 31]]
[[], [1], [0, 1], [0, 0, 1], [0, 0, 0, 1], [0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 1], [0, 0, 0, 0, 1, 1, 1], [0, 0, 0, 0, 1, 1, 1, 2], [0, 0, 0, 0, 1, 1, 1, 1, 3], [0, 0, 0, 0, 1, 1, 1, 1, 2, 5], [0, 0, 0, 0, 1, 1, 1, 1, 1, 3, 7], [0, 0, 0, 0, 1, 1, 1, 1, 1, 2, 5, 11], [0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 3, 7, 15], [0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 2, 5, 11, 23], [0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 3, 7, 15, 31]]
[10, 7, true]
[[], [1], [0, 1], [0, 0, 1], [0, 0, 0, 1], [0, 0, 0, 1, 1], [0, 0, 0, 1, 1, 1], [0, 0, 0, 1, 1, 1, 2], [0, 0, 0, 1, 1, 1, 1, 3], [0, 0, 0, 1, 1, 1, 1, 2, 5], [0, 0, 0, 1, 1, 1, 1, 1, 3, 7], [0, 0, 0, 1, 1, 1, 1, 1, 2, 5, 11], [0, 0, 0, 1, 1, 1, 1, 1, 1, 3, 7, 15], [0, 0, 0, 1, 1, 1, 1, 1, 1, 2, 5, 11, 23], [0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 3, 7, 15, 31], [0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 2, 5, 11, 23, 47]]
[[], [1], [0, 1], [0, 0, 1], [0, 0, 0, 1], [0, 0, 0, 1, 1], [0, 0, 0, 1, 1, 1], [0, 0, 0, 1, 1, 1, 2], [0, 0, 0, 1, 1, 1, 1, 3], [0, 0, 0, 1, 1, 1, 1, 2, 5], [0, 0, 0, 1, 1, 1, 1, 1, 3, 7], [0, 0, 0, 1, 1, 1, 1, 1, 2, 5, 11], [0, 0, 0, 1, 1, 1, 1, 1, 1, 3, 7, 15], [0, 0, 0, 1, 1, 1, 1, 1, 1, 2, 5, 11, 23], [0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 3, 7, 15, 31], [0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 2, 5, 11, 23, 47]]
[10, 8, true]
[[], [1], [0, 1], [0, 0, 1], [0, 0, 1, 1], [0, 0, 1, 1, 1], [0, 0, 1, 1, 1, 2], [0, 0, 1, 1, 1, 1, 3], [0, 0, 1, 1, 1, 1, 2, 5], [0, 0, 1, 1, 1, 1, 1, 3, 7], [0, 0, 1, 1, 1, 1, 1, 2, 5, 11], [0, 0, 1, 1, 1, 1, 1, 1, 3, 7, 15], [0, 0, 1, 1, 1, 1, 1, 1, 2, 5, 11, 23], [0, 0, 1, 1, 1, 1, 1, 1, 1, 3, 7, 15, 31], [0, 0, 1, 1, 1, 1, 1, 1, 1, 2, 5, 11, 23, 47], [0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 3, 7, 15, 31, 63]]
[[], [1], [0, 1], [0, 0, 1], [0, 0, 1, 1], [0, 0, 1, 1, 1], [0, 0, 1, 1, 1, 2], [0, 0, 1, 1, 1, 1, 3], [0, 0, 1, 1, 1, 1, 2, 5], [0, 0, 1, 1, 1, 1, 1, 3, 7], [0, 0, 1, 1, 1, 1, 1, 2, 5, 11], [0, 0, 1, 1, 1, 1, 1, 1, 3, 7, 15], [0, 0, 1, 1, 1, 1, 1, 1, 2, 5, 11, 23], [0, 0, 1, 1, 1, 1, 1, 1, 1, 3, 7, 15, 31], [0, 0, 1, 1, 1, 1, 1, 1, 1, 2, 5, 11, 23, 47], [0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 3, 7, 15, 31, 63]]
[10, 9, true]
[[], [1], [0, 1], [0, 1, 1], [0, 1, 1, 1], [0, 1, 1, 1, 2], [0, 1, 1, 1, 1, 3], [0, 1, 1, 1, 1, 2, 5], [0, 1, 1, 1, 1, 1, 3, 7], [0, 1, 1, 1, 1, 1, 2, 5, 11], [0, 1, 1, 1, 1, 1, 1, 3, 7, 15], [0, 1, 1, 1, 1, 1, 1, 2, 5, 11, 23], [0, 1, 1, 1, 1, 1, 1, 1, 3, 7, 15, 31], [0, 1, 1, 1, 1, 1, 1, 1, 2, 5, 11, 23, 47], [0, 1, 1, 1, 1, 1, 1, 1, 1, 3, 7, 15, 31, 63], [0, 1, 1, 1, 1, 1, 1, 1, 1, 2, 5, 11, 46, 47, 95]]
[[], [1], [0, 1], [0, 1, 1], [0, 1, 1, 1], [0, 1, 1, 1, 2], [0, 1, 1, 1, 1, 3], [0, 1, 1, 1, 1, 2, 5], [0, 1, 1, 1, 1, 1, 3, 7], [0, 1, 1, 1, 1, 1, 2, 5, 11], [0, 1, 1, 1, 1, 1, 1, 3, 7, 15], [0, 1, 1, 1, 1, 1, 1, 2, 5, 11, 23], [0, 1, 1, 1, 1, 1, 1, 1, 3, 7, 15, 31], [0, 1, 1, 1, 1, 1, 1, 1, 2, 5, 11, 23, 47], [0, 1, 1, 1, 1, 1, 1, 1, 1, 3, 7, 15, 31, 63], [0, 1, 1, 1, 1, 1, 1, 1, 1, 2, 5, 11, 46, 47, 95]]
[10, 10, true]
[[], [1], [1, 1], [1, 1, 1], [1, 1, 1, 2], [1, 1, 1, 1, 3], [1, 1, 1, 1, 2, 5], [1, 1, 1, 1, 1, 3, 7], [1, 1, 1, 1, 1, 2, 5, 11], [1, 1, 1, 1, 1, 1, 3, 7, 15], [1, 1, 1, 1, 1, 1, 2, 5, 11, 23], [1, 1, 1, 1, 1, 1, 1, 3, 7, 15, 31], [1, 1, 1, 1, 1, 1, 1, 2, 5, 11, 23, 47], [1, 1, 1, 1, 1, 1, 1, 1, 3, 7, 15, 31, 63], [1, 1, 1, 1, 1, 1, 1, 1, 2, 5, 11, 46, 47, 95], [1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 7, 30, 62, 63, 127]]
[[], [1], [1, 1], [1, 1, 1], [1, 1, 1, 2], [1, 1, 1, 1, 3], [1, 1, 1, 1, 2, 5], [1, 1, 1, 1, 1, 3, 7], [1, 1, 1, 1, 1, 2, 5, 11], [1, 1, 1, 1, 1, 1, 3, 7, 15], [1, 1, 1, 1, 1, 1, 2, 5, 11, 23], [1, 1, 1, 1, 1, 1, 1, 3, 7, 15, 31], [1, 1, 1, 1, 1, 1, 1, 2, 5, 11, 23, 47], [1, 1, 1, 1, 1, 1, 1, 1, 3, 7, 15, 31, 63], [1, 1, 1, 1, 1, 1, 1, 1, 2, 5, 11, 46, 47, 95], [1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 7, 30, 62, 63, 127]]
[10, 11, true]
[[], [1], [0, 1], [0, 0, 1], [0, 0, 0, 1], [0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1]]
[[], [1], [0, 1], [0, 0, 1], [0, 0, 0, 1], [0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1]]
[11, 0, true]
[[], [1], [0, 1], [0, 0, 1], [0, 0, 0, 1], [0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 2]]
[[], [1], [0, 1], [0, 0, 1], [0, 0, 0, 1], [0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 2]]
[11, 1, true]
[[], [1], [0, 1], [0, 0, 1], [0, 0, 0, 1], [0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 2], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 3]]
[[], [1], [0, 1], [0, 0, 1], [0, 0, 0, 1], [0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 2], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 3]]
[11, 2, true]
[[], [1], [0, 1], [0, 0, 1], [0, 0, 0, 1], [0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 2], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 3], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 2, 5]]
[[], [1], [0, 1], [0, 0, 1], [0, 0, 0, 1], [0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 2], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 3], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 2, 5]]
[11, 3, true]
[[], [1], [0, 1], [0, 0, 1], [0, 0, 0, 1], [0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 1, 1], [0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1], [0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 2], [0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 3], [0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 2, 5], [0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 3, 7]]
[[], [1], [0, 1], [0, 0, 1], [0, 0, 0, 1], [0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 1, 1], [0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1], [0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 2], [0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 3], [0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 2, 5], [0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 3, 7]]
[11, 4, true]
[[], [1], [0, 1], [0, 0, 1], [0, 0, 0, 1], [0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 1, 1], [0, 0, 0, 0, 0, 0, 0, 1, 1, 1], [0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 2], [0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 3], [0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 2, 5], [0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 3, 7], [0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 2, 5, 11]]
[[], [1], [0, 1], [0, 0, 1], [0, 0, 0, 1], [0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 1, 1], [0, 0, 0, 0, 0, 0, 0, 1, 1, 1], [0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 2], [0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 3], [0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 2, 5], [0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 3, 7], [0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 2, 5, 11]]
[11, 5, true]
[[], [1], [0, 1], [0, 0, 1], [0, 0, 0, 1], [0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 1, 1], [0, 0, 0, 0, 0, 0, 1, 1, 1], [0, 0, 0, 0, 0, 0, 1, 1, 1, 2], [0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 3], [0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 2, 5], [0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 3, 7], [0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 2, 5, 11], [0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 3, 7, 15]]
[[], [1], [0, 1], [0, 0, 1], [0, 0, 0, 1], [0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 1, 1], [0, 0, 0, 0, 0, 0, 1, 1, 1], [0, 0, 0, 0, 0, 0, 1, 1, 1, 2], [0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 3], [0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 2, 5], [0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 3, 7], [0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 2, 5, 11], [0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 3, 7, 15]]
[11, 6, true]
[[], [1], [0, 1], [0, 0, 1], [0, 0, 0, 1], [0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 1, 1], [0, 0, 0, 0, 0, 1, 1, 1], [0, 0, 0, 0, 0, 1, 1, 1, 2], [0, 0, 0, 0, 0, 1, 1, 1, 1, 3], [0, 0, 0, 0, 0, 1, 1, 1, 1, 2, 5], [0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 3, 7], [0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 2, 5, 11], [0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 3, 7, 15], [0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 2, 5, 11, 23]]
[[], [1], [0, 1], [0, 0, 1], [0, 0, 0, 1], [0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 1, 1], [0, 0, 0, 0, 0, 1, 1, 1], [0, 0, 0, 0, 0, 1, 1, 1, 2], [0, 0, 0, 0, 0, 1, 1, 1, 1, 3], [0, 0, 0, 0, 0, 1, 1, 1, 1, 2, 5], [0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 3, 7], [0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 2, 5, 11], [0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 3, 7, 15], [0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 2, 5, 11, 23]]
[11, 7, true]
[[], [1], [0, 1], [0, 0, 1], [0, 0, 0, 1], [0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 1], [0, 0, 0, 0, 1, 1, 1], [0, 0, 0, 0, 1, 1, 1, 2], [0, 0, 0, 0, 1, 1, 1, 1, 3], [0, 0, 0, 0, 1, 1, 1, 1, 2, 5], [0, 0, 0, 0, 1, 1, 1, 1, 1, 3, 7], [0, 0, 0, 0, 1, 1, 1, 1, 1, 2, 5, 11], [0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 3, 7, 15], [0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 2, 5, 11, 23], [0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 3, 7, 15, 31]]
[[], [1], [0, 1], [0, 0, 1], [0, 0, 0, 1], [0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 1], [0, 0, 0, 0, 1, 1, 1], [0, 0, 0, 0, 1, 1, 1, 2], [0, 0, 0, 0, 1, 1, 1, 1, 3], [0, 0, 0, 0, 1, 1, 1, 1, 2, 5], [0, 0, 0, 0, 1, 1, 1, 1, 1, 3, 7], [0, 0, 0, 0, 1, 1, 1, 1, 1, 2, 5, 11], [0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 3, 7, 15], [0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 2, 5, 11, 23], [0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 3, 7, 15, 31]]
[11, 8, true]
[[], [1], [0, 1], [0, 0, 1], [0, 0, 0, 1], [0, 0, 0, 1, 1], [0, 0, 0, 1, 1, 1], [0, 0, 0, 1, 1, 1, 2], [0, 0, 0, 1, 1, 1, 1, 3], [0, 0, 0, 1, 1, 1, 1, 2, 5], [0, 0, 0, 1, 1, 1, 1, 1, 3, 7], [0, 0, 0, 1, 1, 1, 1, 1, 2, 5, 11], [0, 0, 0, 1, 1, 1, 1, 1, 1, 3, 7, 15], [0, 0, 0, 1, 1, 1, 1, 1, 1, 2, 5, 11, 23], [0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 3, 7, 15, 31], [0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 2, 5, 11, 23, 47]]
[[], [1], [0, 1], [0, 0, 1], [0, 0, 0, 1], [0, 0, 0, 1, 1], [0, 0, 0, 1, 1, 1], [0, 0, 0, 1, 1, 1, 2], [0, 0, 0, 1, 1, 1, 1, 3], [0, 0, 0, 1, 1, 1, 1, 2, 5], [0, 0, 0, 1, 1, 1, 1, 1, 3, 7], [0, 0, 0, 1, 1, 1, 1, 1, 2, 5, 11], [0, 0, 0, 1, 1, 1, 1, 1, 1, 3, 7, 15], [0, 0, 0, 1, 1, 1, 1, 1, 1, 2, 5, 11, 23], [0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 3, 7, 15, 31], [0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 2, 5, 11, 23, 47]]
[11, 9, true]
[[], [1], [0, 1], [0, 0, 1], [0, 0, 1, 1], [0, 0, 1, 1, 1], [0, 0, 1, 1, 1, 2], [0, 0, 1, 1, 1, 1, 3], [0, 0, 1, 1, 1, 1, 2, 5], [0, 0, 1, 1, 1, 1, 1, 3, 7], [0, 0, 1, 1, 1, 1, 1, 2, 5, 11], [0, 0, 1, 1, 1, 1, 1, 1, 3, 7, 15], [0, 0, 1, 1, 1, 1, 1, 1, 2, 5, 11, 23], [0, 0, 1, 1, 1, 1, 1, 1, 1, 3, 7, 15, 31], [0, 0, 1, 1, 1, 1, 1, 1, 1, 2, 5, 11, 23, 47], [0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 3, 7, 15, 31, 63]]
[[], [1], [0, 1], [0, 0, 1], [0, 0, 1, 1], [0, 0, 1, 1, 1], [0, 0, 1, 1, 1, 2], [0, 0, 1, 1, 1, 1, 3], [0, 0, 1, 1, 1, 1, 2, 5], [0, 0, 1, 1, 1, 1, 1, 3, 7], [0, 0, 1, 1, 1, 1, 1, 2, 5, 11], [0, 0, 1, 1, 1, 1, 1, 1, 3, 7, 15], [0, 0, 1, 1, 1, 1, 1, 1, 2, 5, 11, 23], [0, 0, 1, 1, 1, 1, 1, 1, 1, 3, 7, 15, 31], [0, 0, 1, 1, 1, 1, 1, 1, 1, 2, 5, 11, 23, 47], [0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 3, 7, 15, 31, 63]]
[11, 10, true]
[[], [1], [0, 1], [0, 1, 1], [0, 1, 1, 1], [0, 1, 1, 1, 2], [0, 1, 1, 1, 1, 3], [0, 1, 1, 1, 1, 2, 5], [0, 1, 1, 1, 1, 1, 3, 7], [0, 1, 1, 1, 1, 1, 2, 5, 11], [0, 1, 1, 1, 1, 1, 1, 3, 7, 15], [0, 1, 1, 1, 1, 1, 1, 2, 5, 11, 23], [0, 1, 1, 1, 1, 1, 1, 1, 3, 7, 15, 31], [0, 1, 1, 1, 1, 1, 1, 1, 2, 5, 11, 23, 47], [0, 1, 1, 1, 1, 1, 1, 1, 1, 3, 7, 15, 31, 63], [0, 1, 1, 1, 1, 1, 1, 1, 1, 2, 5, 11, 23, 47, 95]]
[[], [1], [0, 1], [0, 1, 1], [0, 1, 1, 1], [0, 1, 1, 1, 2], [0, 1, 1, 1, 1, 3], [0, 1, 1, 1, 1, 2, 5], [0, 1, 1, 1, 1, 1, 3, 7], [0, 1, 1, 1, 1, 1, 2, 5, 11], [0, 1, 1, 1, 1, 1, 1, 3, 7, 15], [0, 1, 1, 1, 1, 1, 1, 2, 5, 11, 23], [0, 1, 1, 1, 1, 1, 1, 1, 3, 7, 15, 31], [0, 1, 1, 1, 1, 1, 1, 1, 2, 5, 11, 23, 47], [0, 1, 1, 1, 1, 1, 1, 1, 1, 3, 7, 15, 31, 63], [0, 1, 1, 1, 1, 1, 1, 1, 1, 2, 5, 11, 23, 47, 95]]
[11, 11, true]
[[], [1], [1, 1], [1, 1, 1], [1, 1, 1, 2], [1, 1, 1, 1, 3], [1, 1, 1, 1, 2, 5], [1, 1, 1, 1, 1, 3, 7], [1, 1, 1, 1, 1, 2, 5, 11], [1, 1, 1, 1, 1, 1, 3, 7, 15], [1, 1, 1, 1, 1, 1, 2, 5, 11, 23], [1, 1, 1, 1, 1, 1, 1, 3, 7, 15, 31], [1, 1, 1, 1, 1, 1, 1, 2, 5, 11, 23, 47], [1, 1, 1, 1, 1, 1, 1, 1, 3, 7, 15, 31, 63], [1, 1, 1, 1, 1, 1, 1, 1, 2, 5, 11, 23, 47, 95], [1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 7, 15, 62, 63, 127]]
[[], [1], [1, 1], [1, 1, 1], [1, 1, 1, 2], [1, 1, 1, 1, 3], [1, 1, 1, 1, 2, 5], [1, 1, 1, 1, 1, 3, 7], [1, 1, 1, 1, 1, 2, 5, 11], [1, 1, 1, 1, 1, 1, 3, 7, 15], [1, 1, 1, 1, 1, 1, 2, 5, 11, 23], [1, 1, 1, 1, 1, 1, 1, 3, 7, 15, 31], [1, 1, 1, 1, 1, 1, 1, 2, 5, 11, 23, 47], [1, 1, 1, 1, 1, 1, 1, 1, 3, 7, 15, 31, 63], [1, 1, 1, 1, 1, 1, 1, 1, 2, 5, 11, 23, 47, 95], [1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 7, 15, 62, 63, 127]]
[11, 12, true]
[[], [1], [0, 1], [0, 0, 1], [0, 0, 0, 1], [0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1]]
[[], [1], [0, 1], [0, 0, 1], [0, 0, 0, 1], [0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1]]
[12, 0, true]
[[], [1], [0, 1], [0, 0, 1], [0, 0, 0, 1], [0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1]]
[[], [1], [0, 1], [0, 0, 1], [0, 0, 0, 1], [0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1]]
[12, 1, true]
[[], [1], [0, 1], [0, 0, 1], [0, 0, 0, 1], [0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 2]]
[[], [1], [0, 1], [0, 0, 1], [0, 0, 0, 1], [0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 2]]
[12, 2, true]
[[], [1], [0, 1], [0, 0, 1], [0, 0, 0, 1], [0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 2], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 3]]
[[], [1], [0, 1], [0, 0, 1], [0, 0, 0, 1], [0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 2], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 3]]
[12, 3, true]
[[], [1], [0, 1], [0, 0, 1], [0, 0, 0, 1], [0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 2], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 3], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 2, 5]]
[[], [1], [0, 1], [0, 0, 1], [0, 0, 0, 1], [0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 2], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 3], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 2, 5]]
[12, 4, true]
[[], [1], [0, 1], [0, 0, 1], [0, 0, 0, 1], [0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 1, 1], [0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1], [0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 2], [0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 3], [0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 2, 5], [0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 3, 7]]
[[], [1], [0, 1], [0, 0, 1], [0, 0, 0, 1], [0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 1, 1], [0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1], [0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 2], [0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 3], [0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 2, 5], [0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 3, 7]]
[12, 5, true]
[[], [1], [0, 1], [0, 0, 1], [0, 0, 0, 1], [0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 1, 1], [0, 0, 0, 0, 0, 0, 0, 1, 1, 1], [0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 2], [0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 3], [0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 2, 5], [0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 3, 7], [0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 2, 5, 11]]
[[], [1], [0, 1], [0, 0, 1], [0, 0, 0, 1], [0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 1, 1], [0, 0, 0, 0, 0, 0, 0, 1, 1, 1], [0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 2], [0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 3], [0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 2, 5], [0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 3, 7], [0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 2, 5, 11]]
[12, 6, true]
[[], [1], [0, 1], [0, 0, 1], [0, 0, 0, 1], [0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 1, 1], [0, 0, 0, 0, 0, 0, 1, 1, 1], [0, 0, 0, 0, 0, 0, 1, 1, 1, 2], [0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 3], [0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 2, 5], [0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 3, 7], [0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 2, 5, 11], [0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 3, 7, 15]]
[[], [1], [0, 1], [0, 0, 1], [0, 0, 0, 1], [0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 1, 1], [0, 0, 0, 0, 0, 0, 1, 1, 1], [0, 0, 0, 0, 0, 0, 1, 1, 1, 2], [0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 3], [0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 2, 5], [0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 3, 7], [0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 2, 5, 11], [0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 3, 7, 15]]
[12, 7, true]
[[], [1], [0, 1], [0, 0, 1], [0, 0, 0, 1], [0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 1, 1], [0, 0, 0, 0, 0, 1, 1, 1], [0, 0, 0, 0, 0, 1, 1, 1, 2], [0, 0, 0, 0, 0, 1, 1, 1, 1, 3], [0, 0, 0, 0, 0, 1, 1, 1, 1, 2, 5], [0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 3, 7], [0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 2, 5, 11], [0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 3, 7, 15], [0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 2, 5, 11, 23]]
[[], [1], [0, 1], [0, 0, 1], [0, 0, 0, 1], [0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 1, 1], [0, 0, 0, 0, 0, 1, 1, 1], [0, 0, 0, 0, 0, 1, 1, 1, 2], [0, 0, 0, 0, 0, 1, 1, 1, 1, 3], [0, 0, 0, 0, 0, 1, 1, 1, 1, 2, 5], [0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 3, 7], [0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 2, 5, 11], [0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 3, 7, 15], [0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 2, 5, 11, 23]]
[12, 8, true]
[[], [1], [0, 1], [0, 0, 1], [0, 0, 0, 1], [0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 1], [0, 0, 0, 0, 1, 1, 1], [0, 0, 0, 0, 1, 1, 1, 2], [0, 0, 0, 0, 1, 1, 1, 1, 3], [0, 0, 0, 0, 1, 1, 1, 1, 2, 5], [0, 0, 0, 0, 1, 1, 1, 1, 1, 3, 7], [0, 0, 0, 0, 1, 1, 1, 1, 1, 2, 5, 11], [0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 3, 7, 15], [0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 2, 5, 11, 23], [0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 3, 7, 15, 31]]
[[], [1], [0, 1], [0, 0, 1], [0, 0, 0, 1], [0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 1], [0, 0, 0, 0, 1, 1, 1], [0, 0, 0, 0, 1, 1, 1, 2], [0, 0, 0, 0, 1, 1, 1, 1, 3], [0, 0, 0, 0, 1, 1, 1, 1, 2, 5], [0, 0, 0, 0, 1, 1, 1, 1, 1, 3, 7], [0, 0, 0, 0, 1, 1, 1, 1, 1, 2, 5, 11], [0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 3, 7, 15], [0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 2, 5, 11, 23], [0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 3, 7, 15, 31]]
[12, 9, true]
[[], [1], [0, 1], [0, 0, 1], [0, 0, 0, 1], [0, 0, 0, 1, 1], [0, 0, 0, 1, 1, 1], [0, 0, 0, 1, 1, 1, 2], [0, 0, 0, 1, 1, 1, 1, 3], [0, 0, 0, 1, 1, 1, 1, 2, 5], [0, 0, 0, 1, 1, 1, 1, 1, 3, 7], [0, 0, 0, 1, 1, 1, 1, 1, 2, 5, 11], [0, 0, 0, 1, 1, 1, 1, 1, 1, 3, 7, 15], [0, 0, 0, 1, 1, 1, 1, 1, 1, 2, 5, 11, 23], [0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 3, 7, 15, 31], [0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 2, 5, 11, 23, 47]]
[[], [1], [0, 1], [0, 0, 1], [0, 0, 0, 1], [0, 0, 0, 1, 1], [0, 0, 0, 1, 1, 1], [0, 0, 0, 1, 1, 1, 2], [0, 0, 0, 1, 1, 1, 1, 3], [0, 0, 0, 1, 1, 1, 1, 2, 5], [0, 0, 0, 1, 1, 1, 1, 1, 3, 7], [0, 0, 0, 1, 1, 1, 1, 1, 2, 5, 11], [0, 0, 0, 1, 1, 1, 1, 1, 1, 3, 7, 15], [0, 0, 0, 1, 1, 1, 1, 1, 1, 2, 5, 11, 23], [0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 3, 7, 15, 31], [0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 2, 5, 11, 23, 47]]
[12, 10, true]
[[], [1], [0, 1], [0, 0, 1], [0, 0, 1, 1], [0, 0, 1, 1, 1], [0, 0, 1, 1, 1, 2], [0, 0, 1, 1, 1, 1, 3], [0, 0, 1, 1, 1, 1, 2, 5], [0, 0, 1, 1, 1, 1, 1, 3, 7], [0, 0, 1, 1, 1, 1, 1, 2, 5, 11], [0, 0, 1, 1, 1, 1, 1, 1, 3, 7, 15], [0, 0, 1, 1, 1, 1, 1, 1, 2, 5, 11, 23], [0, 0, 1, 1, 1, 1, 1, 1, 1, 3, 7, 15, 31], [0, 0, 1, 1, 1, 1, 1, 1, 1, 2, 5, 11, 23, 47], [0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 3, 7, 15, 31, 63]]
[[], [1], [0, 1], [0, 0, 1], [0, 0, 1, 1], [0, 0, 1, 1, 1], [0, 0, 1, 1, 1, 2], [0, 0, 1, 1, 1, 1, 3], [0, 0, 1, 1, 1, 1, 2, 5], [0, 0, 1, 1, 1, 1, 1, 3, 7], [0, 0, 1, 1, 1, 1, 1, 2, 5, 11], [0, 0, 1, 1, 1, 1, 1, 1, 3, 7, 15], [0, 0, 1, 1, 1, 1, 1, 1, 2, 5, 11, 23], [0, 0, 1, 1, 1, 1, 1, 1, 1, 3, 7, 15, 31], [0, 0, 1, 1, 1, 1, 1, 1, 1, 2, 5, 11, 23, 47], [0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 3, 7, 15, 31, 63]]
[12, 11, true]
[[], [1], [0, 1], [0, 1, 1], [0, 1, 1, 1], [0, 1, 1, 1, 2], [0, 1, 1, 1, 1, 3], [0, 1, 1, 1, 1, 2, 5], [0, 1, 1, 1, 1, 1, 3, 7], [0, 1, 1, 1, 1, 1, 2, 5, 11], [0, 1, 1, 1, 1, 1, 1, 3, 7, 15], [0, 1, 1, 1, 1, 1, 1, 2, 5, 11, 23], [0, 1, 1, 1, 1, 1, 1, 1, 3, 7, 15, 31], [0, 1, 1, 1, 1, 1, 1, 1, 2, 5, 11, 23, 47], [0, 1, 1, 1, 1, 1, 1, 1, 1, 3, 7, 15, 31, 63], [0, 1, 1, 1, 1, 1, 1, 1, 1, 2, 5, 11, 23, 47, 95]]
[[], [1], [0, 1], [0, 1, 1], [0, 1, 1, 1], [0, 1, 1, 1, 2], [0, 1, 1, 1, 1, 3], [0, 1, 1, 1, 1, 2, 5], [0, 1, 1, 1, 1, 1, 3, 7], [0, 1, 1, 1, 1, 1, 2, 5, 11], [0, 1, 1, 1, 1, 1, 1, 3, 7, 15], [0, 1, 1, 1, 1, 1, 1, 2, 5, 11, 23], [0, 1, 1, 1, 1, 1, 1, 1, 3, 7, 15, 31], [0, 1, 1, 1, 1, 1, 1, 1, 2, 5, 11, 23, 47], [0, 1, 1, 1, 1, 1, 1, 1, 1, 3, 7, 15, 31, 63], [0, 1, 1, 1, 1, 1, 1, 1, 1, 2, 5, 11, 23, 47, 95]]
[12, 12, true]
[[], [1], [1, 1], [1, 1, 1], [1, 1, 1, 2], [1, 1, 1, 1, 3], [1, 1, 1, 1, 2, 5], [1, 1, 1, 1, 1, 3, 7], [1, 1, 1, 1, 1, 2, 5, 11], [1, 1, 1, 1, 1, 1, 3, 7, 15], [1, 1, 1, 1, 1, 1, 2, 5, 11, 23], [1, 1, 1, 1, 1, 1, 1, 3, 7, 15, 31], [1, 1, 1, 1, 1, 1, 1, 2, 5, 11, 23, 47], [1, 1, 1, 1, 1, 1, 1, 1, 3, 7, 15, 31, 63], [1, 1, 1, 1, 1, 1, 1, 1, 2, 5, 11, 23, 47, 95], [1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 7, 15, 31, 63, 127]]
[[], [1], [1, 1], [1, 1, 1], [1, 1, 1, 2], [1, 1, 1, 1, 3], [1, 1, 1, 1, 2, 5], [1, 1, 1, 1, 1, 3, 7], [1, 1, 1, 1, 1, 2, 5, 11], [1, 1, 1, 1, 1, 1, 3, 7, 15], [1, 1, 1, 1, 1, 1, 2, 5, 11, 23], [1, 1, 1, 1, 1, 1, 1, 3, 7, 15, 31], [1, 1, 1, 1, 1, 1, 1, 2, 5, 11, 23, 47], [1, 1, 1, 1, 1, 1, 1, 1, 3, 7, 15, 31, 63], [1, 1, 1, 1, 1, 1, 1, 1, 2, 5, 11, 23, 47, 95], [1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 7, 15, 31, 63, 127]]
[12, 13, true]
[[], [1], [0, 1], [0, 0, 1], [0, 0, 0, 1], [0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1]]
[[], [1], [0, 1], [0, 0, 1], [0, 0, 0, 1], [0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1]]
[13, 0, true]
[[], [1], [0, 1], [0, 0, 1], [0, 0, 0, 1], [0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1]]
[[], [1], [0, 1], [0, 0, 1], [0, 0, 0, 1], [0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1]]
[13, 1, true]
[[], [1], [0, 1], [0, 0, 1], [0, 0, 0, 1], [0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1]]
[[], [1], [0, 1], [0, 0, 1], [0, 0, 0, 1], [0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1]]
[13, 2, true]
[[], [1], [0, 1], [0, 0, 1], [0, 0, 0, 1], [0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 2]]
[[], [1], [0, 1], [0, 0, 1], [0, 0, 0, 1], [0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 2]]
[13, 3, true]
[[], [1], [0, 1], [0, 0, 1], [0, 0, 0, 1], [0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 2], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 3]]
[[], [1], [0, 1], [0, 0, 1], [0, 0, 0, 1], [0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 2], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 3]]
[13, 4, true]
[[], [1], [0, 1], [0, 0, 1], [0, 0, 0, 1], [0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 2], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 3], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 2, 5]]
[[], [1], [0, 1], [0, 0, 1], [0, 0, 0, 1], [0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 2], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 3], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 2, 5]]
[13, 5, true]
[[], [1], [0, 1], [0, 0, 1], [0, 0, 0, 1], [0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 1, 1], [0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1], [0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 2], [0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 3], [0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 2, 5], [0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 3, 7]]
[[], [1], [0, 1], [0, 0, 1], [0, 0, 0, 1], [0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 1, 1], [0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1], [0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 2], [0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 3], [0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 2, 5], [0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 3, 7]]
[13, 6, true]
[[], [1], [0, 1], [0, 0, 1], [0, 0, 0, 1], [0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 1, 1], [0, 0, 0, 0, 0, 0, 0, 1, 1, 1], [0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 2], [0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 3], [0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 2, 5], [0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 3, 7], [0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 2, 5, 11]]
[[], [1], [0, 1], [0, 0, 1], [0, 0, 0, 1], [0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 1, 1], [0, 0, 0, 0, 0, 0, 0, 1, 1, 1], [0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 2], [0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 3], [0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 2, 5], [0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 3, 7], [0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 2, 5, 11]]
[13, 7, true]
[[], [1], [0, 1], [0, 0, 1], [0, 0, 0, 1], [0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 1, 1], [0, 0, 0, 0, 0, 0, 1, 1, 1], [0, 0, 0, 0, 0, 0, 1, 1, 1, 2], [0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 3], [0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 2, 5], [0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 3, 7], [0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 2, 5, 11], [0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 3, 7, 15]]
[[], [1], [0, 1], [0, 0, 1], [0, 0, 0, 1], [0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 1, 1], [0, 0, 0, 0, 0, 0, 1, 1, 1], [0, 0, 0, 0, 0, 0, 1, 1, 1, 2], [0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 3], [0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 2, 5], [0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 3, 7], [0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 2, 5, 11], [0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 3, 7, 15]]
[13, 8, true]
[[], [1], [0, 1], [0, 0, 1], [0, 0, 0, 1], [0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 1, 1], [0, 0, 0, 0, 0, 1, 1, 1], [0, 0, 0, 0, 0, 1, 1, 1, 2], [0, 0, 0, 0, 0, 1, 1, 1, 1, 3], [0, 0, 0, 0, 0, 1, 1, 1, 1, 2, 5], [0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 3, 7], [0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 2, 5, 11], [0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 3, 7, 15], [0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 2, 5, 11, 23]]
[[], [1], [0, 1], [0, 0, 1], [0, 0, 0, 1], [0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 1, 1], [0, 0, 0, 0, 0, 1, 1, 1], [0, 0, 0, 0, 0, 1, 1, 1, 2], [0, 0, 0, 0, 0, 1, 1, 1, 1, 3], [0, 0, 0, 0, 0, 1, 1, 1, 1, 2, 5], [0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 3, 7], [0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 2, 5, 11], [0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 3, 7, 15], [0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 2, 5, 11, 23]]
[13, 9, true]
[[], [1], [0, 1], [0, 0, 1], [0, 0, 0, 1], [0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 1], [0, 0, 0, 0, 1, 1, 1], [0, 0, 0, 0, 1, 1, 1, 2], [0, 0, 0, 0, 1, 1, 1, 1, 3], [0, 0, 0, 0, 1, 1, 1, 1, 2, 5], [0, 0, 0, 0, 1, 1, 1, 1, 1, 3, 7], [0, 0, 0, 0, 1, 1, 1, 1, 1, 2, 5, 11], [0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 3, 7, 15], [0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 2, 5, 11, 23], [0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 3, 7, 15, 31]]
[[], [1], [0, 1], [0, 0, 1], [0, 0, 0, 1], [0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 1], [0, 0, 0, 0, 1, 1, 1], [0, 0, 0, 0, 1, 1, 1, 2], [0, 0, 0, 0, 1, 1, 1, 1, 3], [0, 0, 0, 0, 1, 1, 1, 1, 2, 5], [0, 0, 0, 0, 1, 1, 1, 1, 1, 3, 7], [0, 0, 0, 0, 1, 1, 1, 1, 1, 2, 5, 11], [0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 3, 7, 15], [0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 2, 5, 11, 23], [0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 3, 7, 15, 31]]
[13, 10, true]
[[], [1], [0, 1], [0, 0, 1], [0, 0, 0, 1], [0, 0, 0, 1, 1], [0, 0, 0, 1, 1, 1], [0, 0, 0, 1, 1, 1, 2], [0, 0, 0, 1, 1, 1, 1, 3], [0, 0, 0, 1, 1, 1, 1, 2, 5], [0, 0, 0, 1, 1, 1, 1, 1, 3, 7], [0, 0, 0, 1, 1, 1, 1, 1, 2, 5, 11], [0, 0, 0, 1, 1, 1, 1, 1, 1, 3, 7, 15], [0, 0, 0, 1, 1, 1, 1, 1, 1, 2, 5, 11, 23], [0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 3, 7, 15, 31], [0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 2, 5, 11, 23, 47]]
[[], [1], [0, 1], [0, 0, 1], [0, 0, 0, 1], [0, 0, 0, 1, 1], [0, 0, 0, 1, 1, 1], [0, 0, 0, 1, 1, 1, 2], [0, 0, 0, 1, 1, 1, 1, 3], [0, 0, 0, 1, 1, 1, 1, 2, 5], [0, 0, 0, 1, 1, 1, 1, 1, 3, 7], [0, 0, 0, 1, 1, 1, 1, 1, 2, 5, 11], [0, 0, 0, 1, 1, 1, 1, 1, 1, 3, 7, 15], [0, 0, 0, 1, 1, 1, 1, 1, 1, 2, 5, 11, 23], [0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 3, 7, 15, 31], [0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 2, 5, 11, 23, 47]]
[13, 11, true]
[[], [1], [0, 1], [0, 0, 1], [0, 0, 1, 1], [0, 0, 1, 1, 1], [0, 0, 1, 1, 1, 2], [0, 0, 1, 1, 1, 1, 3], [0, 0, 1, 1, 1, 1, 2, 5], [0, 0, 1, 1, 1, 1, 1, 3, 7], [0, 0, 1, 1, 1, 1, 1, 2, 5, 11], [0, 0, 1, 1, 1, 1, 1, 1, 3, 7, 15], [0, 0, 1, 1, 1, 1, 1, 1, 2, 5, 11, 23], [0, 0, 1, 1, 1, 1, 1, 1, 1, 3, 7, 15, 31], [0, 0, 1, 1, 1, 1, 1, 1, 1, 2, 5, 11, 23, 47], [0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 3, 7, 15, 31, 63]]
[[], [1], [0, 1], [0, 0, 1], [0, 0, 1, 1], [0, 0, 1, 1, 1], [0, 0, 1, 1, 1, 2], [0, 0, 1, 1, 1, 1, 3], [0, 0, 1, 1, 1, 1, 2, 5], [0, 0, 1, 1, 1, 1, 1, 3, 7], [0, 0, 1, 1, 1, 1, 1, 2, 5, 11], [0, 0, 1, 1, 1, 1, 1, 1, 3, 7, 15], [0, 0, 1, 1, 1, 1, 1, 1, 2, 5, 11, 23], [0, 0, 1, 1, 1, 1, 1, 1, 1, 3, 7, 15, 31], [0, 0, 1, 1, 1, 1, 1, 1, 1, 2, 5, 11, 23, 47], [0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 3, 7, 15, 31, 63]]
[13, 12, true]
[[], [1], [0, 1], [0, 1, 1], [0, 1, 1, 1], [0, 1, 1, 1, 2], [0, 1, 1, 1, 1, 3], [0, 1, 1, 1, 1, 2, 5], [0, 1, 1, 1, 1, 1, 3, 7], [0, 1, 1, 1, 1, 1, 2, 5, 11], [0, 1, 1, 1, 1, 1, 1, 3, 7, 15], [0, 1, 1, 1, 1, 1, 1, 2, 5, 11, 23], [0, 1, 1, 1, 1, 1, 1, 1, 3, 7, 15, 31], [0, 1, 1, 1, 1, 1, 1, 1, 2, 5, 11, 23, 47], [0, 1, 1, 1, 1, 1, 1, 1, 1, 3, 7, 15, 31, 63], [0, 1, 1, 1, 1, 1, 1, 1, 1, 2, 5, 11, 23, 47, 95]]
[[], [1], [0, 1], [0, 1, 1], [0, 1, 1, 1], [0, 1, 1, 1, 2], [0, 1, 1, 1, 1, 3], [0, 1, 1, 1, 1, 2, 5], [0, 1, 1, 1, 1, 1, 3, 7], [0, 1, 1, 1, 1, 1, 2, 5, 11], [0, 1, 1, 1, 1, 1, 1, 3, 7, 15], [0, 1, 1, 1, 1, 1, 1, 2, 5, 11, 23], [0, 1, 1, 1, 1, 1, 1, 1, 3, 7, 15, 31], [0, 1, 1, 1, 1, 1, 1, 1, 2, 5, 11, 23, 47], [0, 1, 1, 1, 1, 1, 1, 1, 1, 3, 7, 15, 31, 63], [0, 1, 1, 1, 1, 1, 1, 1, 1, 2, 5, 11, 23, 47, 95]]
[13, 13, true]
[[], [1], [1, 1], [1, 1, 1], [1, 1, 1, 2], [1, 1, 1, 1, 3], [1, 1, 1, 1, 2, 5], [1, 1, 1, 1, 1, 3, 7], [1, 1, 1, 1, 1, 2, 5, 11], [1, 1, 1, 1, 1, 1, 3, 7, 15], [1, 1, 1, 1, 1, 1, 2, 5, 11, 23], [1, 1, 1, 1, 1, 1, 1, 3, 7, 15, 31], [1, 1, 1, 1, 1, 1, 1, 2, 5, 11, 23, 47], [1, 1, 1, 1, 1, 1, 1, 1, 3, 7, 15, 31, 63], [1, 1, 1, 1, 1, 1, 1, 1, 2, 5, 11, 23, 47, 95], [1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 7, 15, 31, 63, 127]]
[[], [1], [1, 1], [1, 1, 1], [1, 1, 1, 2], [1, 1, 1, 1, 3], [1, 1, 1, 1, 2, 5], [1, 1, 1, 1, 1, 3, 7], [1, 1, 1, 1, 1, 2, 5, 11], [1, 1, 1, 1, 1, 1, 3, 7, 15], [1, 1, 1, 1, 1, 1, 2, 5, 11, 23], [1, 1, 1, 1, 1, 1, 1, 3, 7, 15, 31], [1, 1, 1, 1, 1, 1, 1, 2, 5, 11, 23, 47], [1, 1, 1, 1, 1, 1, 1, 1, 3, 7, 15, 31, 63], [1, 1, 1, 1, 1, 1, 1, 1, 2, 5, 11, 23, 47, 95], [1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 7, 15, 31, 63, 127]]
[13, 14, true]