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>
#define BASE 3000
#define RANGE 2500

using namespace std;
typedef long long ll;

int main() {
    int n, a, x;
    ll f[BASE*2+1], tmp[BASE*2+1];
    cin >> n >> a;
    f[BASE] = 1;
    for(int i=0; i<n; i++) {
        cin >> x;
        x -= a;
        fill(tmp, tmp+(BASE*2+1), 0);
        for(int t=BASE-RANGE; t<=BASE+RANGE; t++) {
            tmp[t+x] = f[t];
        }
        for(int t=0; t<=BASE*2; t++) {
            f[t] += tmp[t];
        }
    }
    cout << f[BASE]-1 << endl;
    
}