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 <bits/stdc++.h>
using namespace std;
#define int long long

const int maxV=51;
int dp[maxV][maxV][maxV*maxV];

signed main(){
	int n,a;cin>>n>>a;
	vector<int> x(n);
	for(auto&& w:x)cin>>w;

	fill(dp[0][0],dp[maxV][0],0);
	dp[0][0][0]=1;

	for(int i=0;i<n;i++){
		for(int j=0;j<=i;j++){
			for(int s=0;s<maxV*maxV;s++){
   //           if(dp[i][j][s]==0)continue;
				dp[i+1][j][s]+=dp[i][j][s];
				dp[i+1][j+1][s+x[i]]+=dp[i][j][s];
			}
		}
	}
	int ans=0;
	for(int i=1;i<=n;i++)ans+=dp[n][i][i*a];
	cout<<ans<<endl;

}