Tak has N cards. On the i-th (1 \leq i \leq N) card is written an integer x_i. He is selecting one or more cards from these N cards, so that the average of the integers written on the selected cards is exactly A. In how many ways can he make his selection?

Constraints

* 1 \leq N \leq 50
* 1 \leq A \leq 50
* 1 \leq x_i \leq 50
* N,\,A,\,x_i are integers.

Input

The input is given from Standard Input in the following format:


N A
x_1 x_2 ... x_N


Output

Print the number of ways to select cards such that the average of the written integers is exactly A.

Examples

Input

4 8
7 9 8 9


Output

5


Input

3 8
6 6 9


Output

0


Input

8 5
3 6 2 8 7 6 5 9


Output

19


Input

33 3
3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3


Output

8589934591
#include <bits/stdc++.h>
using namespace std;

long long F[60][2601],n,K,a[210];
long long ans,tmp[60][2601];
int main()
{
	scanf("%lld%lld",&n,&K);
	for(int i=1;i<=n;i++) scanf("%lld",&a[i]); F[0][0]=1;
	for(int i=1;i<=n;i++)
	{
		memset(tmp,0,sizeof tmp);
		for(int j=0;j<i;j++)
			for(int k=0;k<=2501;k++)
			{		
				tmp[j+1][k+a[i]]+=F[j][k];
				tmp[j][k]+=F[j][k];
			}
		for(int j=0;j<=i;j++)
			for(int k=0;k<=2501;k++) 
				F[j][k]=tmp[j][k];
	}
	for(int i=1;i<=n;i++) if(i*K<=2500) ans+=F[i][i*K];
	cout << ans << endl; return 0;
}