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>
#include<string>
using namespace std;
typedef long long ll;
ll dp[55][55][2505]={0};
int main(){
  ll n,a;
  cin>>n>>a;
  dp[0][0][0]=1;
  for(int i=0;i<n;i++){
    int x;
    cin>>x;
    for(int j=0;j<=i;j++){
      for(int k=0;k<2505;k++){
        dp[i+1][j][k]+=dp[i][j][k];
        if(k+x<2505) dp[i+1][j+1][k+x]+=dp[i][j][k];
      }
    }
  }
  ll ans=0;
  for(int i=1;i<=n;i++) ans+=dp[n][i][a*i];
  cout<<ans<<endl;
}
