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 n,a,i,j,flag;
int x[200];
double ave;

int main (){

    scanf("%d %d",&n,&a);

    for (i=0;i<n;i++){
        
        scanf("%d", &x[i]);
        printf("%d\n", x[i]);
        
        

    }

    for (i=0;i<n;i++){
        
        //printf("%d\n", x[i]);
        
    }

   
    
        for (i=0;i<n;i++) {
            
            
            for (j=i+1;j<n;++j){

                ave = (x[i] + x[j]) / 2;

                printf("%f\n",ave);

                if (ave == a){
                    flag++;
                }
                
                if (ave == a){
                    flag++;
                }
                
            }
     
    
        }

    
    printf("%d\n",flag);
    
    return 0;


}