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++14 (GCC 5.4.1) (judge verdict: Wrong Answer)

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

int n, a, x[50];
long long dp[51][2501] = {};
int main(void)
{
  cin >> n >> a;
  for(int i = 0; i != n; i++){
    cin >> x[i];
    x[i] -= a;
  }
  for(int i = 0; i <= n; i++){
    for(int j = 0; j <= 2500; j++){
      if(i == 0 && j == 0){
        dp[i][j] = 1;
      }else if(i == 0){
        dp[i][j] = 0;
      }else if(j - a < 0 && j - x[i - 1] - a < 0){
        dp[i][j] = 0;
      }else if(x[i - 1] < 0 && j - a < 0){
        dp[i][j] = dp[i - 1][j - a];
      }else if(x[i - 1] > 0 && j - x[i - 1] - a < 0){
        dp[i][j] = dp[i - 1][j - a];
      }else{
        dp[i][j] = dp[i - 1][j - a] + dp[i - 1][j - x[i - 1] - a];
      }
    }
  }
  cout << dp[n][n * a] - 1 << endl;
  return 0;
}