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;

int n,a;
long long x[55];
long long sol[55][2505];

int main()
{
    long long rez=0;
    int i,j,k,l;
    cin>>n>>a;
    for(i=1;i<=n;i++)
        cin>>x[i];

    int tot=n*a;
    for(i=1;i<=n;i++)
    {
        for(l=i;l>=1;l--)
            for(j=x[i];j<=tot;j++)
                sol[l][j]+=sol[l-1][j-x[i]];
        sol[1][x[i]]++;
    }

    for(i=1;i<=n;i++)
        rez+=sol[i][i*a];
    cout<<rez;
    return 0;
}
