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>
#include<cstring>

int n, A;
int x[55];
long long f[55][3333];
long long ans;

int main() {
	scanf("%d%d", &n, &A);
	for(int i=1;i<=n;i++) scanf("%d", &x[i]);
	
	memset(f, 0, sizeof f);
	f[0][0] = 1;
	for(int i=1;i<=n;i++) {
		for(int cnt = i-1;cnt>=0;cnt--)
			for(int j=0;j<=n*A;j++)
				f[cnt+1][j+x[i]] += f[cnt][j];
	}
	ans=0LL;
	for(int i=1;i<=n;i++)
		ans+=f[i][i*A];
	printf("%lld\n", ans);
	
	return 0;
}