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;
  long long A;
  cin >> n >> A;
  long long x[n];
  for(auto& y:x){
    cin >> y;
    y-=A;
  }
  vector<map<long long,long long>> dp(n+1);
  dp[0][0] = 1;
  for(int i=0;i<n;i++){
    for(const auto& y:dp[i]){
      dp[i+1][y.first]+=y.second;
      dp[i+1][y.first+x[i]] += y.second;
    }
  }
  long long ret = 0;
  cout << dp[n][0]-1 << endl;
  return 0;
}
