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;

const int N=50;
long long A[N],dp[N+1][N*N+1]; 
int main() {
  int n,x;
  cin >> n >> x;
  for ( int i=0; i<n; i++ ) cin >> A[i];
  dp[0][0]=1;
  int sum=0;
  for ( int i=0; i<n; i++ ) {
    for ( int j=i; ~j; j-- ) {
      for ( int k=sum; ~k; k-- ) {
        if  ( k+A[i]<=N*N ) dp[j+1][k+A[i]]+=dp[j][k];
      }
    }
    sum+=A[i];
  }
  long long ans=0;
  for ( int i=1; i<=n; i++ ) {
    ans+=dp[i][x*i];
  }
  cout << ans << '\n';
  return 0;
}
