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: Accepted)

#include <stdio.h>

int N, A;
int x[55];

typedef long long ll;

ll dp[55][2510];

int main() {

	int i, j, k;

	scanf("%d %d",&N,&A);

	int ma = 0;

	for (i = 1; i <= N; i++) {
		scanf(" %d",&x[i]);
		ma += x[i];
	}

	dp[0][0] = 1ll;

	for (k = 1; k <= N; k++) {
		for (i = k - 1; i >= 0; i--) {
			for (j = 0; j <= ma; j++) {
				dp[i + 1][j + x[k]] += dp[i][j];
			}
		}
	}

	ll ans = 0;
	for (i = 1; i <= N; i++) {
		ans += dp[i][A*i];
	}
	printf("%lld\n",ans);
	return 0;
}