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<cstdio>
#include<algorithm>
#define MAXN 56
using namespace std;
long long d[MAXN][MAXN][MAXN*MAXN],ans;
int n,A,a[MAXN],sum[MAXN];
int main()
{
	scanf("%d%d",&n,&A);
	for(int i=1;i<=n;i++)
	{
		scanf("%d",&a[i]);
		sum[i]=sum[i-1]+a[i];
	}
	for(int i=0;i<=n;i++)
		d[i][0][0]=1;
	for(int i=1;i<=n;i++)
		for(int j=1;j<=i;j++)
			for(int k=1;k<=sum[i];k++)
			{
				d[i][j][k]=d[i-1][j][k];
				if(k>=a[i]) d[i][j][k]=d[i][j][k]+d[i-1][j-1][k-a[i]];
			}
	for(int i=1;i<=n;i++)
		ans+=d[n][i][A*i];
	printf("%lld",ans);
}