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 <bits/stdc++.h>
typedef long long ll;
const int INF = 1e9;
const int MOD = 1e9+7;
const ll LINF = 1e18;

using namespace std;

#define rep(i, a, b) for (int i = a; i < b; i++)
#define rrep(i, a, b) for (int i = a; i <= b; i++)
#define all(a)  begin((a)),end((a))
#define uniq(c) (c).erase(unique(all((c))), end((c)))

void print_idx(vector<long long> arr) {
    cout << "idx: ";
    for (auto a : arr) {
        cout << a;
    }
    cout << endl;
}

int main()
{
    int N; double A; cin >> N >> A;
    vector<long long> x(N);
    rep (i, 0, N) cin >> x[i];

    long long cnt = 0;
    for (long long bit = 0; bit < (1<<N); ++bit) {
        vector<long long> idx;
        for (long long i = 0; i < N; ++i) {
            if (bit & (1 << i)) {
                idx.push_back(i);
            }
        }

        double sum = 0;
        for (auto id : idx)
            sum += x[id];

        if (idx.size() != 0)
            sum /= idx.size();

        if (A == sum) {
            ++cnt;
        }
    }
    cout << cnt << endl;
}