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 ll long long 
#define ld long double
#define X first
#define Y second
#define pb push_back
#define max_el(x) max_element(x.begin(),x.end())-x.begin()
#define min_el(x) min_element(x.begin(),x.end())-x.begin()
#define mp make_pair
#define endl '\n'
#define fastread ios_base::sync_with_stdio(false);cin.tie(NULL);cout.tie(NULL);
using namespace std;
// DONT USE MEMSET, USE VECTORS

ll n,av;
vector<ll> a;
ll dp[60][3000][60];

ll f(int i, int su, int cnt){
	if(i== n){
		return(su == cnt*av);
	}
	if(dp[i][su][cnt] != -1){
		return dp[i][su][cnt];
	}

	ll ans = 0;
	ans += f(i+1,su,cnt);
	ans += f(i+1,su+a[i],cnt+1);
	dp[i][su][cnt] = ans;
	return ans;
}


int main(){
	fastread;
	cin>>n>>av;
	a.resize(n);
	memset(dp,-1,sizeof(dp));
	for(int i=0;i<n;i++){
		cin>>a[i];
	}
	cout<<f(0,0,0)-1<<endl;

	return 0;
}