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<math.h>
#include<algorithm>
typedef long long int ll;
using namespace std;
ll f(ll n,ll b){
    ll a=0;
    while(n>0){
        a+=n%b;
        n=n/b;
    }

    return a;
}
int main(){
    ll b,n,s,ans=-1;
    cin>>n>>s;
       if(s<=(n+1)/2){
        ll k=1;
        bool flag=true;
        do{
          if(k*k>n-s||k==s)flag=false;
            if((n-s)%k==0){
            b=(n-s)/k+1;
            if(b<=s-k)flag=false;
            else ans=b;
            }
            k++;
        }while(flag);
    }
    b=2;
        while(b*b<n){
            if(f(n,b)==s){
                ans=b;
                goto end;
            }
          b++;
        }
    end:
    cout<<ans<<endl;
}