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: Time Limit Exceeded)

#include <cstdio>
#include <iostream>
#include <string>
#include <algorithm>
#include <list>
#include <map>
#include <queue>
#include <stack>
#include <set>
#include <vector>

#define REP(i,s,n) for(ll i=(ll)(s);i<(ll)(n);i++)

using namespace std;
typedef long long ll;

int main() {
  ll n, a;
  ll x[50];
  cin >> n >> a;
  REP(i,0,n) {
    cin >> x[i];
  }
  ll ans = 0LL;
  REP(i,0,1LL<<n) {
    ll s = 0;
    ll c = 0;
    REP(j,0,n) {
      if(i & (1LL << j)) {
        c++;
        s += x[j];
      }
    }
    if(c && s == a * c) {
      ans++;
    }
  }
  cout << ans << endl;
  return 0;
}