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



Sample input:
3 2


Sample output:
2

Submission status: Runtime Error

Solution code:
N, K = map(int, input().split())
dp = [[[0]*N**2*2 for a in range(N+1)] for b in range(N+1)]

dp[0][0][0] = 1
for i in range(N):
    for j in range(N):
        for k in range(N**2):
            dp[i+1][j+1][k+2*j+2] += dp[i][j][k]
            dp[i+1][j][k+2*j] += dp[i][j][k] * (2*j+1)
            if j: dp[i+1][j-1][k+2*j-2] += dp[i][j][k] * j**2

print(dp[N][0][K] % (10**9+7))

Submission status: Runtime Error

Solution code:
mod = 10**9+7
N,K = map(int,input().split())
dp = [[[0]*(K+1) for i in range(N+1)] for j in range(N+1)]
dp[0][0][0] = 1

for i in range(1,N+1):
    for j in range(N+1):
        for k in range(K+1):
            if k-2*j >= 0:
                dp[i][j][k] = (2*j+1)*dp[i-1][j][k-2*j]+(j+1)**2*dp[i-1][j+1][k-2*j]
                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])