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: Wrong Answer)

#define _CRT_SECURE_NO_WARNINGS
#include <iostream>
#include <fstream>
#include <string>
#include <algorithm>
#include <cstdlib>
#include <vector>
#include <stack>
#include <queue>
#include <complex>
#include <set>
#include <list>
#include <iomanip>
#include <map>
#include <memory.h>



using namespace std;
static const double EPS = 1e-9;
typedef long long ll;
typedef unsigned long long ull;
#define FOR(i,n) for(int i=0;i<(int)n;++i)
#define FORNUM(p, x) for (int num = p; num < (int)(x); ++num)
#define FORI(p, x) for (int i = p; i < (int)(x); ++i)
#define FORJ(p, x) for (int j = p; j < (int)(x); ++j)
#define FORK(p, x) for (int k = p; k < (int)(x); ++k)
#define FORL(p, x) for (int l = p; l < (int)(x); ++l)

typedef pair<int,int>P;
#define INF 1000000000
 
struct edge { 
	int from, to; 
	edge (int from, int to){
		this->from=from; this->to=to;
	}
};
 
int V,E;
typedef vector<edge> edges;
vector<edges> G;

int x[55];
int dp[55][55][2555];

int main(){
	int n, a;
	cin >> n >> a;
	int sum = 0;
	FORI(0, n) {
		cin >> x[i];
		sum += x[i];
	}
	dp[0][0][0] = 1;

	for (int i = 0; i < n; i++)
	{
		for (int j = 0; j < n; j++) {
			for (int k = 0; k < 2555; k++) {
				dp[i+1][j][k] += dp[i][j][k];
				dp[i+1][j+1][k+x[i]] += dp[i][j][k];
			}
		}

	}
	ll ans = 0;
	for(int i=1;i<=n;i++){
		ans += dp[n][i][i*a];
	}
	cout << ans << endl;
	return 0;
}