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(){
  int n,a;
  cin>>n>>a;
  vector<int> x(n);
  for(int i=0;i<n;i++)
    cin>>x.at(i);
  vector<vector<vector<int64_t>>> c(n+1,vector<vector<int64_t>>(n+1,vector<int64_t>(n*a+1,0)));
  for(int i=0;i<n;i++)
    c[i][0][0]=1;
  for(int i=1;i<=n;i++)
    for(int j=1;j<=n;j++)
      for(int k=0;k<=a*n;k++)
        c[i][j][k]=c[i-1][j][k]+(k>=x.at(i-1)?c[i-1][j-1][k-x.at(i-1)]:0);
  int64_t s=0;
  for(int i=1;i<=n;i++)
    s+=c[n][i][a*i];
  cout<<s<<endl;
}