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;

const int Max=51;
int n,m,now,num[Max];
long long ans;
long long f[3][Max][Max*Max];

int main()
{
	scanf("%d%d",&n,&m);
	for(int i=1;i<=n;i++) scanf("%d",&num[i]);
	f[1][0][0]=f[0][0][0]=1;
	for(int i=1;i<=n;i++)
	{
	  for(int j=1;j<=i;j++)
	    for(int k=0;k<=2500;k++)
	    {
	      f[now][j][k]=f[now^1][j][k];
	      if(k>=num[i]) f[now][j][k]+=f[now^1][j-1][k-num[i]];
	    }
	  now^=1;
	}
	for(int i=1;i<=n;i++) ans+=f[now^1][i][i*m];
	cout<<ans<<"\n";
	return 0;
}