Problem:
Score : 300 points

Problem Statement

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.

Partial Score

200 points will be awarded for passing the test set satisfying 1 \leq N \leq 16.

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.

Sample Input 1

4 8
7 9 8 9

Sample Output 1

5

The following are the 5 ways to select cards such that the average is 8:

Select the 3-rd card.

Select the 1-st and 2-nd cards.

Select the 1-st and 4-th cards.

Select the 1-st, 2-nd and 3-rd cards.

Select the 1-st, 3-rd and 4-th cards.

Sample Input 2

3 8
6 6 9

Sample Output 2

0

Sample Input 3

8 5
3 6 2 8 7 6 5 9

Sample Output 3

19

Sample Input 4

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

Sample Output 4

8589934591

The answer may not fit into a 32-bit integer.

Solution in C++ (GCC 9.2.1) (judge verdict: Runtime Error)

#include <bits/stdc++.h>
using namespace std;

int main(){
  long long N,A;
  cin >> N >> A;
  vector<int> v(N);
  for(int i=0; i<N; i++){
    cin >> v[i];
  }
  long long cnt[51][3000][51]={};
  cnt[0][0][0]=1;
  for(int i=0; i<N; i++){
    for(int sum=0; sum<3000; sum++){
      for(int k=0; k<N; k++){
        cnt[i+1][sum+v[i]][k+1] += cnt[i][sum][k];
        cnt[i+1][sum][k] += cnt[i][sum][k];
      }
    }
  }
  
  long long ans=0;
  
  for(int sum=0; sum<3000; sum++){
     for(int k=0; k<51; k++){
       if(k==0) continue;
       if(A*k==sum){
         ans+=cnt[N][sum][k];
       }
     }
  }
  cout << ans << endl;
}