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: Accepted)

#include <iostream>
#include <map>
#define int long long
using namespace std;

int a[55];
map<int, map<int, int> > f;

signed main() {
#ifdef _DEBUG
	freopen("_in" , "r", stdin );
	//freopen("_out", "w", stdout);
#endif
	ios::sync_with_stdio(0); cin.tie(0);
	int n, x; cin >> n >> x;
	for (int i = 1; i <= n; i++) {
		cin >> a[i];
		a[i] -= x;
	}
	f[0][0] = 1;
	for (int i = 1; i <= n; i++)
	for (int j = -250; j <= 250; j++) {
		f[i][j] += f[i - 1][j - a[i]] + f[i - 1][j];
	}
	cout << f[n][0] - 1 << '\n';
}