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 ll = long long;
using namespace std;
ll mod=1e9+7;

int main(){
  int N,A,x[50];
  cin>>N>>A;
  for (int i(0);i<N;i++) cin>>x[i];
  for (int i(0);i<N;i++) x[i]-=A;
  ll dp[50][5001]={0};
  dp[0][2499]=1;
  dp[0][x[0]+2499]+=1;
  for (int i(0);i<N-1;i++){
    for (int j(0);j<=5000;j++){
      if (dp[i][j]!=0){
        dp[i+1][j] += dp[i][j];
        dp[i+1][j+x[i+1]] += dp[i][j];
      }
    }
  }
  cout << dp[N-1][2499] -1  << endl;
  return 0;
}

