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 5.4.1) (judge verdict: Wrong Answer)

#include <stdio.h>
#include <math.h>
int main()
{
    int s;
    int i,k;
    scanf("%d",&s);
    int q;
    int su=0;
    scanf("%d",&q);
    int arr[s];
    int cnt=0;
    int p=0;
    for(i=0;i<s;i++)
    {
        scanf("%d",&arr[i]);
    }
    int size=pow(2,s);
    for(k=0;k<size;k++)
    {
        //printf("chall");
        for(i=0;i<s;i++)
        {
            //printf("chal na bhai");
            if(k &(1<<i))
            {
                p++;
               // printf("%d",arr[i]);
                su+=arr[i];

            }
        }
if(p!=0){
        if((su%p)==0 && (su/p)==q  )
        {
             //printf("\nthis\n");
            cnt++;
        }
}
        
        su=0;
        p=0;
    }
    printf("%d",cnt);
}