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 <vector>

using namespace std;

int main()
{
    int N, A;
    cin>>N>>A;

    vector<vector<long long>> T(N+1, vector<long long>(50*N+1));
    T[0][0] = 1LL;

    for (int i=0; i<N; i++)
    {
        int x;
        cin>>x;

        vector<vector<long long>> P = T;

        for (int j=0; j<=i; j++)
        for (int k=0; k<=50*i; k++)
            T[j+1][k+x] += P[j][k];
    }
    long long ans = 0;
    for (int i=1; i<=N; i++)
        ans += T[i][i*A];
    cout<<ans<<endl;
}
