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 C++14 (GCC 5.4.1) (judge verdict: Accepted)

#include<iostream>
using namespace std;
long mod=1e9+7,dp[51][51][2505];
int N,K;
main()
{
	cin>>N>>K;
	dp[0][0][0]=1;
	for(int i=0;i<N;i++)for(int j=0;j<=i;j++)
	{
		for(int k=0;k<=K-2*j+2;k++)
		{
			if(dp[i][j][k]==0)continue;
			(dp[i+1][j][k+2*j]+=dp[i][j][k]*(2*j+1)%mod)%=mod;
			if(j>0)(dp[i+1][j-1][k+2*j-2]+=dp[i][j][k]*j*j%mod)%=mod;
			(dp[i+1][j+1][k+2*j+2]+=dp[i][j][k])%=mod;
		}
	}
	cout<<dp[N][0][K]<<endl;
}