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>
long long d[55][5005];
int main() {
	int i, j, n, a, x, z=0;
	scanf("%d%d", &n, &a);
	d[0][2500] = 1;
	for(i=1; i<=n; i++) {
		scanf("%d", &x);
		x -= a;
		for(j=0; j<=5000; j++) {
			d[i][j] += d[i-1][j];
			d[i][j+x] += d[i-1][j];
		}
	}
	printf("%lld", d[n][2500]-1);
}
