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 FOR(i,a,b) for (int i = (a); i < (b); ++i)
#define RFOR(i,a,b) for (int i = (b)-1; i >= (a); --i)
#define rep(i,n) FOR(i,0,(n))
#define REPS(i,n) FOR(i,1,(n)+1)
#define RREP(i,n) RFOR(i,0,(n))
#define ALL(x) (x).begin(),(x).end()
#define RALL(x) (x).rbegin(),(x).rend()
#define debug(x) cout << #x << " = " << (x) << endl;
#define SORT(x) sort(ALL(x));
#define RSORT(x) sort(RALL(x));
#define SUM(x) accumulate(ALL(x),0)
#define fi first
#define se second
#define pb push_back
#define eb emplace_back
#define sz(x) (int)(x).size()
#define bn(x) ((1<<x)-1)
#define dup(x,y) (((x)+(y)-1)/(y))
using namespace std;
using ll = long long;
using vi = vector<int>;
using vvi = vector<vi>;
using vll = vector<ll>;
using pii = pair<int, int>;
using tiii = tuple<int, int, int>;
const ll mod = 1e9+7;
const int INF = (1<<30)-1;
const ll INFLL = (1LL<<62)-1;
const int dx[4] = {1,0,-1,0};
const int dy[4] = {0,1,0,-1};
//cout << fixed << setprecision(10);

template<class T> inline bool chmax(T& a, T b) { if (a < b) { a = b; return true; } return false; }
template<class T> inline bool chmin(T& a, T b) { if (a > b) { a = b; return true; } return false; }

ll gcd(ll a, ll b) { return b ? gcd(b,a%b) : a;}
ll lcm(ll a, ll b) { return a/gcd(a,b)*b;}

int main () {
  ll n, a; cin >> n >> a;
  vector<ll> x(n); rep(i,n) cin >> x[i];

  ll ans = 0;
  FOR(b,1,1<<n) {
    vector<ll> getx;
    rep(i,n) {
      if (b&(1<<i)) {
        getx.pb(x[i]);
      }
    }
    if (SUM(getx) == a*sz(getx)) ans++;
  }

  cout << ans << endl;
}