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++14 (GCC 5.4.1) (judge verdict: Wrong Answer)

#include<iostream>

using namespace std;

int N, A;
int k, s;
int X[55];
int dp[55][55][2505];  //dp[x_i][k][sum]

int main(){
	cin >> N >> A;
	int maxnx = 0;
	for(int i = 1; i <= N; i++){
		cin >> X[i];
		if(X[i] * N > maxnx) maxnx = X[i] * N;
	}

	for(s = 0; s <= maxnx; s++){
		for(k = 0; k <= N; k++){
			for(int i = 0; i <= N; i++){
				dp[i][k][s] = 0;
			}
		}
	}

	dp[0][0][0] = 1;
	for(s = 0; s <= maxnx; s++){
		for(k = 0; k <= N; k++){
			for(int i = 1; i <= N; i++){
				if(s < X[i]){
					dp[i][k][s] = dp[i - 1][k][s];
				}else if(k >= 1 && s >= X[i]){
					dp[i][k][s] = dp[i - 1][k][s] + dp[i - 1][k - 1][s - X[i]];
				}
			}
		}
	}
	long long ans = 0;
	for(int k = 1; k <= N; k++){
		ans += dp[N][k][k * A];
	}
	cout << ans << endl;

	return 0;

}