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>
#define fi first
#define se second
#define ll long long
using namespace std;

int n,a,x[55];
ll dp[55][55][2555];

int main() {
	#ifdef kvutxdy
	freopen("C:/Users/khanh/OneDrive/RoadtoPurple/Code/Codeforces/input.in", "r", stdin);
	#endif
	ios_base::sync_with_stdio(false);
	cin.tie(nullptr);
	cout.tie(nullptr);
	cin>>n>>a;
	for(int i=1;i<=n;++i) cin>>x[i];
	dp[0][0][0]=1LL;
	for(int i=1;i<=n;++i){
		for(int j=0;j<=i;++j){
			for(int k=0;k<=2500;++k){
				dp[i][j][k]=dp[i-1][j][k];
				if(j>0&&k-x[i]>=0) dp[i][j][k]+=dp[i-1][j-1][k-x[i]];
			}
		}
	}
	ll res=0LL;
	for(int i=1;i<=n;++i) res+=dp[n][i][a*i];
	cout<<res; 
}