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>
#define Nu 50
#define SUM_MAX 3000


long long int dp[Nu+1][Nu+1][SUM_MAX+1]={0};

int main(void)
{
	int i;
	int j;
	int k;
	int n;
	int a;
	int x[Nu+1];
	int k_max;
	long long int ans=0;
	scanf("%d %d",&n,&a);
	for(i=0;i<n;i++){
		scanf("%d",&x[i]);
	}
	for(i=0;i<n+1;i++){
		dp[i][0][0]=1;
	}
	for(i=0;i<n;i++){
		k_max=(i+1)*50;
		for(j=0;j<=i;j++){
			for(k=0;k<k_max+1;k++){
				if(k>=x[i]){
					dp[i+1][j+1][k]=dp[i][j][k-x[i]]+dp[i][j+1][k];
				}else{
					dp[i+1][j+1][k]=dp[i][j+1][k];
				}
			}
		}
	}
	for(i=0;i<n;i++){
		ans+=dp[n][i][i*a];
	}
	printf("%lld",ans);
}