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 <cstdio>
#include <algorithm>
#include <iostream>
#include <vector>
#include <cmath>
#include <string>
#define pb push_back
#define mod 1000000007
using namespace std;
typedef long long int ll;

ll dp[55][55][555];
int main(void){
  ll n,a,t;
  cin>>n>>a;
  vector<int> x;
  x.pb(-1);
  for(int i=0;i<n;i++){
    cin>>t;
    x.pb(t);
  }

  for(int j=0;j<=n;j++){
    for(int k=0;k<=n;k++){
      for(int s=0;s<=n*50;s++){
        if(j==0&&k==0&&s==0) dp[j][k][s]=1;
        else if(j>=1&&k>=1&&s>=x[j]) dp[j][k][s]=dp[j-1][k][s]+dp[j-1][k-1][s-x[j]];
        else if(j>=1&&s<x[j]) dp[j][k][s]=dp[j-1][k][s];
        else dp[j][k][s]=0;
      }
    }
  }
  ll ans=0;
  for(int i=1;i<=n;i++){
    ans+=dp[n][i][i*a];
  }
  cout<<ans<<endl;
  return 0;
}