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>
using namespace std;
long dp[55][55][55*50];
int main(){
  long n,v;
  cin>>n>>v;
  long x[n];
  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<55*50;++k){
        dp[i+1][j][k]+=dp[i][j][k];
        dp[i+1][j+1][k+x[i]]+=dp[i][j][k];
      }
    }
  }
  
  long ans=0;
  for(int i=1;i<=n;++i)
    ans+=dp[n][i][i*v];
  cout<<ans<<endl;
}
