Problem:
Score : 600 points

Problem Statement

Let us define the oddness of a permutation p = {p_1,\ p_2,\ ...,\ p_n} of {1,\ 2,\ ...,\ n} as \sum_{i = 1}^n |i - p_i|.

Find the number of permutations of {1,\ 2,\ ...,\ n} of oddness k, modulo 10^9+7.

Constraints

All values in input are integers.

1 \leq n \leq 50

0 \leq k \leq n^2

Input

Input is given from Standard Input in the following format:

n k

Output

Print the number of permutations of {1,\ 2,\ ...,\ n} of oddness k, modulo 10^9+7.

Sample Input 1

3 2

Sample Output 1

2

There are six permutations of {1,\ 2,\ 3}. Among them, two have oddness of 2: {2,\ 1,\ 3} and {1,\ 3,\ 2}.

Sample Input 2

39 14

Sample Output 2

74764168

Solution in Ruby (2.3.3) (judge verdict: Accepted)

N, K = gets.split.map(&:to_i)
MOD = 10**9 + 7

dp = Array.new(N + 1){Array.new(N + 1){Array.new(K + 2*N + 1, 0)}}
dp[0][0][0] = 1
(0 ... N).each do |i|
  (0 .. N).each do |j|
    (0 .. K).each do |k|
      next if (d = dp[i][j][k]) == 0
      l = k + 2*j
      dp[i + 1][j][l] = (dp[i + 1][j][l] + (2*j + 1)*d) % MOD
      dp[i + 1][j - 1][l] = (dp[i + 1][j - 1][l] + j*j*d) % MOD if j > 0
      dp[i + 1][j + 1][l] = (dp[i + 1][j + 1][l] + d) % MOD
    end
  end
end
puts  dp[N][0][K]