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<vector>
#include<cstdio>
#include<string>
#include<algorithm>

#define ll long long

using namespace std;

int main(){
    long long n,a;
    cin>>n>>a;
    vector<vector<ll> > dp(n+1, vector<ll>(50*50+1,0));
    vector<int> x(n);
    for(int i=0; i<n; i++){
	cin>>x[i]; 
	for(int k=i; k>=1; k--){
	for(int j=0; j<=50*50; j++){
		if(dp[k][j]){
		    dp[k+1][j+x[i]] += dp[k][j];
		}
	    }
	}
	dp[1][x[i]]++;
    }
    ll res=dp[1][a];
    for(int i=2; i<=n; i++){
	res+=dp[i][a*i];
    }
    cout<<res;

}