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 <algorithm>
#include <vector>
using namespace std;
typedef long long int ll;

ll dp[51][51][2501];
//何番目まで見たか、何個選んだか、合計

int main(){
	int n,a; cin >> n >> a;
	vector<int> x(n);
	dp[0][0][0]=1;
	for(int i=0;i<n;i++){
		cin >> x[i];
		for(int j=0;j<50;j++){
			for(int k=0;k<2501;k++){
				if(dp[i][j][k]){
					dp[i+1][j][k]+=dp[i][j][k];
					dp[i+1][j+1][k+x[i]]+=dp[i][j][k];
				}
			}
		}
	}
	ll ans=0;
	for(int i=1;i<=n;i++){
		ans+=dp[n][i][i*a];
	}
	cout << ans << endl;
}