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"

int main(){
    int n,a,c1=0;
     long int ans=0;
    scanf("%d %d",&n,&a);
    int x[n];
    for(int i=0;i<n;i++)
        scanf("%d",&x[i]);

    for(long int bit=0;bit < (1<<n);bit++){
        int sum=0;
        for(int i=0;i<n;i++){
            if (bit & (1 << i)){
               sum+=x[i];
               c1++;
            }
        }
        if(sum==0||c1==0)    continue;
       if(sum/c1==a&&sum%c1==0) ans++;
       //printf("%d %d %ld\n",sum,c1,bit );
        c1=0;
        sum=0;
    }

    printf("%ld\n",ans );

}