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>

using namespace std;

int64_t d[55][2510] = {1};

int main()
{
    int n, a;
    cin >> n >> a;

    for (int x, i = 1; i <= n; ++i) {
        cin >> x;
        for (int j = i; j; --j)
            for (int k = 0; k <= (j - 1) * 50; ++k)
                d[j][k+x] += d[j-1][k];
    }

    int64_t res = 0;

    for (int i = 1; i <= n; ++i)
        res += d[i][a * i];

    cout << res;
    return 0;
}
