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>
#define int long long
int v[50*101][51];
using namespace std;

signed main(){
  int N,A;
  cin>>N>>A;
  int x;
  std::vector<int> y(N);
  for(int i=0;i<N;i++){
    cin>>x;
    y[i]=x-A;
  }
  for(int i=0;i<N*101;i++)for(int j=0;j<N;j++)v[i][j]=0;
  v[N*50][0]=1;
  for(int j=1;j<N+1;j++){
    for(int i=50;i<N*101-50;i++){
      v[i][j]=v[i][j-1]+v[i-y[j-1]][j-1];
    }
  }
  cout<<v[N*50][N]-1<<endl;
}
