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;

int main(){
   long n,a;

   cin >> n >> a;
  
  vector<long> x(n);
  long y=a;
  for(int i=0;i<n;i++) {
    cin >> x[i];
    y=max(y,x[i]);
    x[i]-=a;
  }
  
 long dp[n+1][2*n*y+1];
  
  for(int i=0;i<2*n*y+1;i++) dp[0][i]=0;
  dp[0][n*y]=1;
  
  for(int j=1;j<n+1;j++){
   for(int t=0;t<2*n*y+1;t++){
  if(0<=t-x[j-1]&&t-x[j-1]<=2*n*y) dp[j][t]=dp[j-1][t]+dp[j-1][t-x[j-1]];
  else  dp[j][t]=dp[j-1][t];
   }
  }
  
  cout << dp[n][n*y]-1 << endl;
  
}
    