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;

const int nax = 55;

int main()
{
	using ll = long long;
	int n, a;
	cin >> n >> a;
	vector<int> x(n);
	for(int& i: x) cin >> i;
		
	vector<vector<ll>> dp(nax, vector<ll>(nax*nax));
	dp[0][0] = 1;
	for(int i = 1; i <= n; i++) {
		for(int j = i; j >= 0; j--) {
			for(int k = 0; k < nax*nax; k++) {
				if(k + x[i] < nax*nax) {
					dp[j+1][k+x[i]] += dp[j][k];
				}
			}
		}
	}
	
	ll ans = 0;
	for (int i = 1; i <= n; i++) {
		ans += dp[i][i * a];
	}
	cout << ans << endl;
}