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 <iostream>
#include <cstdio>
#include <algorithm>
#include <cstring>
#include <cmath>
using namespace std;
typedef long long ll;
const int N=55;
ll f[N][N][N*N];
int main() {
    int n,A;
    ll ans=0;
    cin>>n>>A;
    f[0][0][0]=1;
    for(int i=0,x;i<n;i++) {
	cin>>x;
	for(int j=0;j<=i;j++)
	    for(int k=0;k<2500;k++)
		if(f[i][j][k]) {
		    f[i+1][j][k]+=f[i][j][k];
		    f[i+1][j+1][k+x]+=f[i][j][k];
		}
    }
    for(int i=1;i<=n;i++) ans+=f[n][i][i*A];
    cout<<ans;
    return 0;
}