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)

#define _CRT_SECURE_NO_WARNINGS
#include "bits/stdc++.h"
using namespace std;

#define int long long

#define CHOOSE(a) CHOOSE2 a
#define CHOOSE2(a0,a1,a2,a3,x,...) x
#define REP1(i, s, cond, cal) for (signed i = signed(s); i cond; i cal)
#define REP2(i, s, n) REP1(i, s, < signed(n), ++)
#define REP3(i, n) REP2(i, 0, n)
#define rep(...) CHOOSE((__VA_ARGS__,REP1,REP2,REP3))(__VA_ARGS__)
#define rrep(i, s) rep(i, s, >= 0, --)

#define all(c) begin(c), end(c)

template<typename T, typename U>bool maxup(T& a, U&& b) { if (a < b) { a = b; return true; }; }
template<typename T, typename U>bool minup(T& a, U&& b) { if (a > b) { a = b; return true; }; }

#define X first
#define Y second

using VV = vector<vector<int>>;
using V = vector<int>;
using P = pair<int, int>;
using IP = pair<int, P>;

template<typename T>
inline void input(vector<T>& v) { for (auto& x : v) cin >> x; }

int dp[51][2501];

signed main() {
	int n, a; cin >> n >> a;
	V xs(n); input(xs);
	dp[0][0] = 1;
	rep(i, n) for (int k = n; k >= 0; k--) rep(j, 2501) {
		dp[k][j] += dp[k - 1][j - xs[i]];
	}
	int ans = 0;
	rep(i, 1, n + 1) rep(j, 2501) if(dp[i][j]) ans += ((j % i == 0) && (j / i == a) ? dp[i][j] : 0);
	cout << ans << endl;
	system("pause");
}