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>

const int M = 50 * 50 + 1;

long long ways[M + M];

int main()
{
    int n, a;
    scanf("%d%d", &n, &a);
    ways[M] = 1;
    for (int i = 0, x; i < n; ++ i) {
        scanf("%d", &x);
        x -= a;
        if (x >= 0) {
            for (int j = M + M - 1; j >= x; -- j) {
                ways[j] += ways[j - x];
            }
        } else {
            for (int j = 0; j - x < M + M; ++ j) {
                ways[j] +=ways[j - x];
            }
        }
    }
    printf("%lld\n", ways[M] - 1);
}
