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 Julia (0.5.0) (judge verdict: Runtime Error)

#include <bits/stdc++.h>
using namespace std;

constexpr int64_t mod = 1'000'000'007;

int main(){    
    int n, k;
    cin >> n >> k;
    static int64_t dp[50+1][50+1][50*50+1];
    dp[1][0][0] = 1;
    dp[1][1][2] = 1;
    for(int i=2;i<=n;i++){
        for(int j=0;j<=i;j++){
            for(int c=0;c<=k;c++){
                dp[i][j][c] = 0;
                if(c-2*j >= 0)
                    dp[i][j][c] = (dp[i][j][c] + (2*j+1)*dp[i-1][j][c-2*j]) % mod;
                if(j+1 <= 50 && c-2*j >= 0)
                    dp[i][j][c] = (dp[i][j][c] + (j+1)*(j+1)*dp[i-1][j+1][c-2*j]) % mod;
                if(j-1 >= 0 && c-2*j >= 0)
                    dp[i][j][c] = (dp[i][j][c] + dp[i-1][j-1][c-2*j]) % mod;
            }
        }
    }

    cout << dp[n][0][k] << endl;
    
    return 0;
}