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: Accepted)

#include<iostream>
#include<array>
#include<vector>
#include <algorithm>
#include <stdio.h>
#include <string>
#include <utility>
#include <set>
#include <map>
#include <tuple>
#include<cmath>

using llint = long long int;
using namespace std;

namespace CsF {
#define MIN_INT -2147483648
#define MAX_INT 2147483647
#define FOR(I,J,K) for(int I = J;I < K;I++)
#define WriteLine(n) cout << n << "\n"; 

	string ConvertBit(int N, int e) {
		string s = "";
		int r = 0;
		while (N != 0) {
			r = N % e;
			s = to_string(r) + s;
			N -= r;
			N /= e;
		}
		return s;
	}

	int GCD(int a, int b) {
		if (a < b)swap(a, b);
		int r = a % b;
		while (r != 0) {
			a = b;
			b = r;
			r = a % b;
		}
		return b;
	}

	int LCM(int a, int b) {
		int n = a * b;
		return (n / GCD(a, b));
	}

	int Count(string s, char c) {
		int cou = 0;
		FOR(i, s.length(), 1) {
			if (s[i] == c)cou++;
		}
		return cou;
	}

	vector<int> SieveOfEratosthenes(int N) {
		vector<bool> memo(N + 1);
		vector<int> ret;
		memo[0] = true;
		memo[1] = true;
		for (int i = 2; i < N; i++) {
			if (memo[i])continue;
			ret.push_back(i);
			for (int b = 2; true; b++) {
				if (i*b <= N) {
					memo[i*b] = true;
				}
				else break;
			}
		}
		return ret;
	}

	vector<int> SpInput(int N) {
		vector<int> ret(N);
		FOR(i, N, 1) { cin >> ret[i]; }
		return ret;
	}
}

using namespace CsF;

int N, A;
llint dp[55][55][2600];
int x[55];

int main() {
	cin >> N >> A;
	for (int i = 0; i < N; i++) {
		cin >> x[i];
	}
	dp[0][0][0] = 1;
	for (int i = 0; i < N; i++) {
		//総枚数 : i
		for (int j = 0; j < N; j++) {
			//見てる場所 : j
			for (int k = 0; k <= 2500; k++) {
				//とる
				dp[i + 1][j + 1][k + x[i]] += dp[i][j][k];
				//とらない
				dp[i + 1][j][k] += dp[i][j][k];
			}
		}
	}
	llint ans = 0;
	for (int j = 1; j <= N; j++) {
		for (int k = 0; k <= A * N; k++) {
			if (A * j == k) ans += dp[N][j][k];
		}
	}
	cout << ans << endl;

	return 0;
}