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>
const int N=25005;
using namespace std;
typedef long long ll;
ll c[100][N],ar[N],n,a;
int main()
{
    cin>>n>>a;
    c[0][0]=1;
    ll ans=0;
    for(int i=1;i<=n;i++){
        cin>>ar[i];
        for(int j=N-ar[i];j>=0;j--){
            for(int cn=0;cn<=i;cn++){
                if(j+ar[i]>=N)continue;
                 c[cn+1][j+ar[i]]+=c[cn][j];
            }

        }
    }
    for(int i=1;i<=n;i++){
        ans+=c[i][i*a];
    }
    cout<<ans<<'\n';
    return 0;
}
