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)

#include <iostream>
#include <array>
#include <vector>
#include <iomanip>
#include <string>
#include <cmath>
#include <algorithm>
#include <queue>
#include <map>
#include <set>
using namespace std;

typedef  pair<int,int> P;
typedef long long LL;

const LL  INF=1<<31;



int main(){
     int n,a,x[50];
     cin>>n>>a;
     for(int i=0;i<n;++i){
          cin>>x[i];
     }
     int dp[55][55][5505]={0};
     dp[0][0][0]=1;
     for(int i=0;i<=n;++i){
          for(int j=0;j<=n;++j){
               for(int k=0;k<=n*a;++k){
                    dp[i+1][j][k]+=dp[i][j][k];
                    if(k>=x[i])dp[i+1][j+1][k]+=dp[i][j][k-x[i]];
               }
          }
     }

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