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(){
  long N,A;cin>>N>>A;
  vector<long>X(N);for(long i=0;i<N;i++)cin>>X[i];
  vector<vector<vector<long>>>DP(N,vector<vector<long>>(N+1,vector<long>(A*N+1,0)));
  //i番目までj枚使って合計をkにするような個数
  DP[0][1][X[0]]=1;
  for(long i=0;i<N;i++)DP[i][0][0]=1;
  
  for(long i=1;i<N;i++)for(long j=1;j<=N;j++)for(long k=1;k<=A*N;k++){
    DP[i][j][k]=(k>=X[i] ? DP[i-1][j-1][k-X[i]]:0)
      +DP[i-1][j][k];
  }  
  long ans=0;
  for(long j=1;j<=N;j++){
    ans+=DP[N-1][j][A*j];
  }
  cout<<ans;
}