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 9.2.1) (judge verdict: Wrong Answer)

#include <bits/stdc++.h>
using namespace std;

#define all(x) begin(x), end(x)
#define sz(x) (int)(x).size()
typedef long long ll;

int n, a;

ll ans;
map<ll, ll> m;

int main() {
	cin.sync_with_stdio(0); cin.tie(0);
	cin >> n >> a;
	ll zc = 0;
	for (int i = 0; i < n; ++i) {
		int x; cin >> x;
		x -= a;
		if (x == 0) ++zc;
		else if (x > 0) {
			// WHY DO YOU HAVE TO DO THAT FIRST ONE
			for (auto it = m.rbegin(); it != m.rend(); ++it) {
				m[x + it->first] += it->second;
				if (it == m.rbegin()) ++it;
			}
			++m[x];
		} else {
			for (auto it = m.begin(); it != m.end(); ++it) {
				m[it->first + x] += it->second;
			}
			++m[x];
		}
	}
	ans = m[0];
	ans *= powl(2, zc);
	ans += powl(2, zc) - 1ll;
	cout << ans;
}