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>
#define N 55
#define ll long long
using namespace std;
ll f[N][N*N],ans=0;
int x,a,n;
int main(){
	f[0][0]=1,scanf("%d%d",&n,&a);
	for(int i=1;i<=n;++i){
		scanf("%d",&x);
		for(int j=i;j;--j)for(int k=2500;k>=x;--k)f[j][k]+=f[j-1][k-x];
	}
	for(int i=1;i<=n;++i)ans+=f[i][i*a];
	cout<<ans;
	return 0;
}
