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<vector<long>> dp(N + 1, vector<long> (2501));
  dp.at(0).at(0) = 1;
  long a;
  for(int i = 0; i < N; i++){
    cin >> a;
    for(int j = N - 1; j >= 0; j--){
      for(int k = 0; k < 2451; k++){
        if(dp.at(j).at(k) != 0)dp.at(j + 1).at(k + a) += dp.at(j).at(k);
      }
    }
  }
  long ans = 0;
  for(int i = 1; i <= N; i++){
    if(i * A >= 2501)break;
    else ans += dp.at(i).at(i * A);
  }
  cout << ans << endl;
  return 0;
}