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 main()
{
    ios_base::sync_with_stdio(false);
    int mas , N  , A, x[56] , i , j , sum = 0;
    cin >> N >> A;
    for(i=0;i<N;i++)
        {
            cin >> x[i];
            sum = sum + x[i];
        }
    long long int ans = 0;
    for(mas = 1 ; mas < (1 << (N)) ; mas++)
    {
        int sumr = 0 , suml ,r=0 , l=0;
        for(j=0;j<N;j++)
        {
            if((1 << j)&mas)
            {
                sumr = sumr + x[j];
                r++;
            }
        }
        suml = sum - sumr;
        l = N - r;
        /*if(suml == l*A)
        {
            ans++;
        }*/
        if(sumr == r*A){
            ans++;
        }
    }
    cout << ans << endl;
    return 0;
}