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>

#define NREP() for(ll i = 0; i < n; i++)
#define MREP() for(ll j = 0; j < m; j++)
#define REP(i, x, y) for(ll i = x; i < y; i++)
#define ALL(x) (x).begin(), (x).end()
#define MSG(x) cout << x << endl;
#define MSGF(x, n) MSG(fixed << setprecision(n) << x)
#define END(x) cout << x << endl; exit(0);
#define IPT(v, n) REP(i, 0, n){ cin >> v[i]; }
#define YN(x) x ? cout << "YES" << endl : cout << "NO" << endl;
#define Yn(x) x ? cout << "Yes" << endl : cout << "No" << endl;
#define yn(x) x ? cout << "yes" << endl : cout << "no" << endl;

using namespace std;
typedef long long ll;
typedef vector<ll> vl;
typedef vector<vector<ll>> vvl;
typedef vector<string> vs;
typedef vector<vector<string>> vvs;

const static ll MOD = 1e9 + 7;
const static ll INF = 1 << 30;

ll a, b, c, d, k, l, m, n, h, w, q, x, y;
string s, t;

ll ans = 0;
ll sum = 0;
ll cnt = 0;
ll tmp = 0;
ll mini = INF;
ll maxi = 0;

double ave = 0.0;

int main() {
    cin >> n >> a;
    vl x(n);
    NREP() {
        cin >> x[i];
    }

    for (ll bit = 0; bit < (1 << n); ++bit) {
        vector<int> s;
        for (int i = 0; i < n; ++i) {
            if (bit & (1 << i)) {
                s.push_back(i);
            }
        }

        sum = 0;
        cnt = 0;
        for (auto &&i : s) {
            sum += x[i];
            cnt++;
        }
        if (((double) sum / cnt) == a) ans++;
    }

    MSG(ans)
}