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 PyPy3 (7.3.0) (judge verdict: Runtime Error)

import numpy as np

N, K = map(int,input().split())
MOD = 10**9+7

# dp[i][j][k]:
# ウサギ1~i, カメ1~i (うちj個は相手が未定)まで見ていて，
# 確定している奇妙さがkであるような場合の数
dp = np.zeros((55,55,55*55), dtype='int64')
dp[0][0][0] = 1

for i in range(N+1):
    for j in range(N+1):
        for k in range(N*N+1):
            if k-2*j < 0 or i-1 < 0: continue

            dp[i][j][k] += (2*j+1) * dp[i-1][j][k-2*j] % MOD
            dp[i][j][k] %= MOD

            dp[i][j][k] += (j+1)*(j+1) * dp[i-1][j+1][k-2*j] % MOD
            dp[i][j][k] %= MOD

            if j > 0:
                dp[i][j][k] += dp[i-1][j-1][k-2*j]
                dp[i][j][k] %= MOD
            
print(dp[N][0][K])