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>
#include<cmath>
#include<algorithm>
#include<vector>
#define SF scanf
#define PF printf
#define MAXN 3010
using namespace std;
int n,v,x;
typedef long long ll;
ll dp[MAXN][MAXN];
int main(){
	SF("%d%d",&n,&x);
	dp[0][0]=1;
	for(int i=1;i<=n;i++){
		SF("%d",&v);	
		for(int j=i;j>=1;j--)
			for(int k=3000;k>=v;k--){
				dp[j][k]+=dp[j-1][k-v];
			}
	}
	ll ans=0;
	for(int i=1;i<=n;i++)
		ans+=dp[i][x*i];
	PF("%lld",ans);
}