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;
typedef long long int ll;
const int INF = 1<<30;
int main(){
  ll n, a;cin>>n>>a;
  vector<int> x(n);
  for(int i=0;i<n;i++){
    ll s;cin>>s;x[i]=s-a;
  }
  vector<vector<ll>> dp(n+1, vector<ll>(2*n*50+1, 0));
  dp[0][n*50]=1;
  for(int i=1;i<=n;i++){
    for(int j=0;j<=2*n*50;j++){
      if(0<=j-x[i-1] && j-x[i]<=2*n*50){
      	dp[i][j]=dp[i-1][j-x[i-1]]+dp[i-1][j];
      }else{
	    dp[i][j]=dp[i-1][j];
      }
    }
  }
  cout<<dp[n][n*50]-(ll)1<<endl;
}