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 <iostream> 
#include <math.h> 
using namespace std; 

typedef long long ll;  

ll SumSubsets(int * set, int n, int k) 
{ 
    unsigned int pow_set_size = pow(2, n); 
    int counter, j; 

    ll result = 0;

    for(counter = 0; counter < pow_set_size; counter++) 
    { 
        ll temp_result = 0, temp_cnt = 0;

        for(j = 0; j < n; j++) 
        { 
            if(counter & (1 << j)) {
                temp_cnt++;
                temp_result += set[j];

                cout << "in here .." << endl;
                
            }
        } 

        if  (temp_cnt > 0 && temp_result > 0 && ((float)temp_result / (float)temp_cnt) == (float)k ){

            cout << temp_result << " " << temp_cnt << endl;

            result++;
        }
        cout << endl; cout << endl;
    } 

    return result;
} 

int main() 
{  
    int n, k;
    cin >> n >> k;

    int set[n]; 
    for (int i = 0; i < n; i++) cin >> set[i];

    ll result = SumSubsets(set, n, k); 
    cout << result << endl;

    return 0; 
}