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;
long long int knapsack[51][3000]={};
long long int ans=0;
int main(){
	int n,a,t;
	knapsack[0][0]=1;
	scanf("%d %d",&n,&a);
	for(int i=1;i<=n;i++){
		scanf("%d",&t);
		for(int k=i-1;k>=0;k--){
			for(int j=2500;j>=t;j--){
				knapsack[k+1][j]+=knapsack[k][j-t];
			}
		}
	}
	for(int i=1;i<=n;i++)
		ans+=knapsack[i][a*i];
	printf("%lld",ans);
}