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 MAXN = 51;
const int ZERO = 2550;
const int MAXM = ZERO * 2;
typedef long long LL;
LL F[2][MAXM];
int main() {
	int n, a, i, j, x;
	scanf ( "%d%d", &n, &a );
	F[0][ZERO] = 1;
	for ( i = 1; i <= n; ++i ) {
		scanf ( "%d", &x );
		x -= a;
		for ( j = MAXN; j + MAXN < MAXM; ++j )
			F[i & 1][j] = F[ ( i - 1 ) & 1][j] + F[ ( i - 1 ) & 1][j - x];
	}
	printf ( "%lld\n", F[n & 1][ZERO] - 1 );
}
