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;
typedef long long ll;

int main(){
  int N,A;
  int x[50];
  cin>>N>>A;
  for(int i=0;i<N;i++){
    cin>>x[i];
    x[i]-=A;
  }
  map<int,ll> dp[51];
  dp[0][0]=1;
  for(int i=0;i<N;i++){
    for(auto p:dp[i]){
      int j=p.first;
      ll c=p.second;
      dp[i+1][j]+=c;
      dp[i+1][j+x[i]]+=c;
    }
  }
  cout<<dp[N][0]-1<<endl;
  return 0;
}
