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>
#define int long long
#define N 51
using namespace std;

int n, a, x[N], dp[N][N][N*N];

signed main(){
  
  cin>>n>>a;
  
  for(int i=0;i<n;i++) cin>>x[i];
  
  dp[0][0][0]=1;
  
  for(int i=0;i<n;i++){
    for(int j=0;j<n;j++){
      for(int k=0;k<N*N;k++){
	dp[i+1][j][k]+=dp[i][j][k];
	dp[i+1][j+1][k+x[i]]+=dp[i][j][k];
      }
    }
  }
  
  int ans=0;
  
  for(int i=1;i<=n;i++)
    for(int j=0;j<N*N;j++)
      if(j%i==0&&j/i==a) ans+=dp[n][i][j];

  cout<<ans<<endl;
  
  return 0;
}
