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;
typedef long long ll; 
int a[55];
int sum[55];
ll dp[55][2550];
int main()
{
	int n,m;
	scanf("%d%d",&n,&m);
	for(int i=1;i<=n;i++)
	{
		scanf("%d",&a[i]);
		sum[i]=a[i]+sum[i-1];
//		printf("%d\n",sum[i]);
	}
	dp[0][0]=1;
	for(int i=1;i<=n;i++)
	{
		for(int j=i;j>=1;j--)
		{
			for(int k=sum[i];k>=a[i];k--)
			{
				dp[j][k]+=dp[j-1][k-a[i]];
			}
		}
	}
	ll res=0;
	for(int i=1;i<=n;i++)
	{
		res+=dp[i][i*m];
	}
	printf("%lld\n",res);
	return 0;
}