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 Python (3.8.2) (judge verdict: Time Limit Exceeded)

import sys
input = sys.stdin.readline
def main():
  n, k = map(int, input().split())
  m = n**2
  mod = 10**9+7
  dp = [[[0]*(m+1) for j in range(i+1)] for i in range(n+1)]
  dp[0][0][0] = 1
  for i in range(n):
    for j in range(i+1):
      for l in range(m+1):
        if j and l+2*(j-1) <= m:
          dp[i+1][j-1][l+2*(j-1)] += dp[i][j][l]*j**2
        if l+2*j <= m:
          dp[i+1][j][l+2*j] += dp[i][j][l]*(2*j+1)
          if l+2*(j+1) <= m: 
            dp[i+1][j+1][l+2*(j+1)] += dp[i][j][l]
  ans = dp[n][0][k]%mod
  print(ans)
if __name__ == "__main__":
  main()