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 <cstdio>
typedef long long int64;
static const int MAXN = 52;
static const int MAXA = 50 * 52;

int n, a, x_i;
int64 ways[MAXN][MAXA] = {{ 1, 0 }};

int main()
{
    scanf("%d%d", &n, &a);
    for (int i = 0; i < n; ++i) {
        scanf("%d", &x_i);
        for (int j = i; j >= 0; --j)
            for (int k = MAXA - x_i; k >= 0; --k)
                ways[j + 1][k + x_i] += ways[j][k];
    }

    int64 ans = 0;
    for (int i = 1; i <= n; ++i) ans += ways[i][i * a];
    printf("%lld\n", ans);

    return 0;
}
