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<algorithm>
using namespace std;
const int MAXN = 50;
int x[MAXN + 5];
long long dp[MAXN + 5][MAXN + 5][MAXN*MAXN + 5];
int main() {
	int N, A;
	scanf("%d%d", &N, &A);
	for(int i=1;i<=N;i++)
		scanf("%d", &x[i]);
	long long ans = 0;
	for(int i=1;i<=N+1;i++)
		dp[i][0][0] = 1;
	for(int i=1;i<=N;i++) {
		for(int j=0;j<=N*A;j++) {
			for(int k=N-i+1;k>=1;k--) {
				dp[k][i][j] = dp[k+1][i][j];
				if( j >= x[k] )
					dp[k][i][j] += dp[k+1][i-1][j-x[k]];
			}
		}
		ans += dp[1][i][i*A];
	}
	printf("%lld\n", ans);
}