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: Runtime Error)

#include<bits/stdc++.h>
using namespace std;
int64_t n, s, b = 1e11 + 1;
int64_t calc(int64_t b, int64_t n)
{
    if(n < b) return n;
    return calc(b, n/b) + (n % b);
}
signed main()
{
    ios::sync_with_stdio(false);
    cin.tie(0);
    cin>>n>>s;
    if(n == s)
    {
        cout<<n + 1<<endl;
        return 0;
    }
    if(s == 1)
    {
        if(n == 1) cout<<2<<endl;
        else
        cout<<n<<endl;
        return 0;
    }
    for(int i = 2; i <= sqrt(n); ++i)
    {
        if(s == calc(i,n))
        {
            cout<<i<<endl;
            return 0;
        }
    }

    for(int i = sqrt(n); i >= 1; i--)
    {
        if( (n - s) % i == 0){
            int64_t t = ((n - s)/i + 1);
            if(s == calc(t,n)){
                b = min(b,t);
            }
        }
    }
        if(b  < 1e11 + 1)
            cout<<b<<endl;
        else cout<<-1<<endl;
    return 0;
}