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<cstring>
#include<algorithm>
#define MAXN 50
using namespace std;
typedef long long LL;
int a[MAXN+5];
LL dp[MAXN+5][MAXN*MAXN+5];
int main()
{
	int n,A;
	scanf("%d %d",&n,&A);
	for(int i=1;i<=n;i++)
		scanf("%d",&a[i]);
	dp[0][0]=1LL;
	for(int i=1;i<=n;i++)
		for(int j=A*n;j>=a[i];j--)
			for(int tot=n;tot>=1;tot--)
				dp[tot][j]+=dp[tot-1][j-a[i]];
	LL ans=0;
	for(int tot=1;tot<=n;tot++)
		ans+=dp[tot][A*tot];
	printf("%lld\n",ans);
	return 0;
}