def f(m, n)
  cc = []
  count_permutations = ->s, w {
    if s < 1 || w < 1
      0
    elsif s <= 5 && w == 1
      1
    elsif cc[s] && cc[s][w]
      cc[s][w]
    else
      (cc[s] ||= [])[w] = (1..5).inject(0) {|c, d|
        c + count_permutations.(s - d, w - 1)
      }
    end
  }
  aux = ->acc, b, s, w {
    return acc if s < 1 || w < 1
    return acc << s if w == 1
    (1..5).inject(b) {|b, d|
      c = count_permutations.(s - d, w - 1)
      return aux.(acc << d, b, s - d, w - 1) if n <= b + c
      b + c
    } && nil
  }
  (1..m).inject(0) {|b, w|
    c = count_permutations.(m, w)
    return aux.([], b, m, w).join.to_i if n <= b + c
    b + c
  } && 0
end
g = ->m, n {puts "(#{m},#{n}) → #{f(m, n)}"}
g.(2,1)
g.(2,2)
g.(2,3)
g.(20,1)
g.(20,2)
g.(20,3)
g.(20,400096)
g.(20,400097)
g.(32,1)
g.(32,2)
g.(32,3)
g.(32,1000)
g.(32,1000000)
g.(32,1000000000)
g.(32,1333610936)
g.(32,1333610937)
 

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