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;
const int N = 55;
int n, A;
long long F[N*N][N] = {0};

int main() {
    cin >> n >> A;
    F[0][0] = 1;
    for (int i = 1; i <= n; i++) {
        int x; cin >> x;
        for (int j = 2500; j >= x; j--) {
            for (int k = n; k >= 1; k--)
            if (F[j-x][k-1]) F[j][k] += F[j-x][k-1];
        }
    }
    long long res = 0;
    for (int i = 1; i <= n; i++) {
        int j = i*A;
        res += F[j][i];
    }
    cout << res << endl;
}
