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 "iostream"
# include "cstdio"

using namespace std;

const int maxm=50+10;

int N,A;
int X[maxm];
long long DP[maxm][maxm*maxm];

int main(){
	register int i,j,k;
	register long long Ans=0;
	scanf("%d%d",&N,&A);
	DP[0][0]=1;
	for(i=1;i<=N;i++) scanf("%d",X+i);
	for(i=1;i<=N;i++){
		for(j=i;j;j--){
			for(k=X[i];k<=2500;k++){
				DP[j][k]+=DP[j-1][k-X[i]];
			}
		}
	}
	for(i=1;i<=N;i++){
		Ans+=DP[i][i*A];
	}
	printf("%lld",Ans);
	return 0;
}