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: Runtime Error)

#include<stdio.h>

int main(){
    int n, a;
    scanf("%d%d", &n, &a);
    int t[n+1][n+1][251];
    int x[n+1];
    for(int i=1; i<=n; i++){
        for(int j=1; j<=n; j++){
            for(int k=1; k<=250; k++){
                t[i][j][k] = 0;
            }
        }
        scanf("%d", &x[i]);
    }
    t[1][1][x[1]]++;
    for(int i=2; i<=n; i++){
        t[i][1][x[i]]++;
        for(int j=1; j<i; j++){
            for(int k=1; k<=50*j; k++){
                if(t[i-1][j][k] > 0){
                    t[i][j][k] += t[i-1][j][k];
                    t[i][j+1][k+x[i]] += t[i-1][j][k];
                }
            }
        }
    }
    /*for(int i=250; i>=0; i--){
        for(int j=n; j>=1; j--){
            printf("%d ", t[j][2][i]);
        }
        printf("\n");
    }*/
    unsigned long int ans = 0;
    for(int i=1; i<=n; i++){
        ans += t[n][i][a*i];
    }
    printf("%lu", ans);

    return 0;
}