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

typedef long long ll;

const int N=51;
ll dp[N][N][N*N];

int main(){
	int n,a;
	cin >> n >> a;

	vector<int> x(n);
	for(int i=0;i<n;i++)	cin >> x[i];

	dp[0][0][0]=1;

	for(int i=0;i<n;i++){
		for(int j=0;j<n+1;j++){
			for(int k=0;k<N*N;k++){
				dp[i+1][j][k]+=dp[i][j][k];

				if(j && k>=x[i])
					dp[i+1][j][k]+=dp[i][j-1][k-x[i]];
			}
		}
	}
	ll ans=0;

	for(int i=1;i<=n;i++)	ans+=dp[n][i][i*a];

	cout << ans << endl;

	return 0;
}