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 Java8 (OpenJDK 1.8.0) (judge verdict: Time Limit Exceeded)

import java.math.BigInteger;
import java.util.ArrayList;
import java.util.Collections;
import java.util.List;
import java.util.Scanner;
import java.util.Stack;

public class Main {
	public static int i = 0;
	public static int result = 0;
	public static BigInteger count = new BigInteger("0");
	
	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		String[] n_a = sc.nextLine().split(" ");
		int n = Integer.parseInt(n_a[0]);
		int a = Integer.parseInt(n_a[1]);
		String[] xs = sc.nextLine().split(" ");
		List<Integer> xsInts = new ArrayList<Integer>();

		for (int i = 0; i < xs.length; i++) {
			xsInts.add(new Integer(xs[i]));
		}
		Collections.sort(xsInts);
		Integer[] xsIntsA = xsInts.toArray(new Integer[n]);

		for(int i = 0; i < xsIntsA.length; i++){
			int[] cache = new int[i+1];
			int ceng = -1;
			int cengQuit = i;
			int startPoint = 0;
			result(ceng, cengQuit, startPoint, xsIntsA, cache, a);
		}
		System.out.println(count.toString());
	}

	private static void result(int level, int levelQuit, int startPoint, Integer[] xsIntsA, int[] cache,
			int a) {
		level++;
		for(int i = startPoint; i < xsIntsA.length; i++){
			// for every search level, make the value of such level every possible number in array
			cache[level] = xsIntsA[i];
			if(level == levelQuit){
				if(getSum(cache) >= a && getSum(cache) == a * (levelQuit + 1)){
					count = count.add(BigInteger.ONE);
				}
			}
			
			if(level < levelQuit){
				startPoint = i + 1;
				result(level, levelQuit, startPoint, xsIntsA, cache, a);
			}
		}
	}

	private static int getSum(int[] cache) {
		int sum = 0;
		for(int i = 0; i < cache.length; i++){
			sum += cache[i];
		}
		return sum;
	}
}