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>

const int N = 51;
const int M = 2501;

typedef long long LL;

LL dp[N][M];
int n, m, x, sum, a[N];

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