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: Accepted)

import java.util.ArrayList;
import java.util.HashMap;
import java.util.List;
import java.util.Map.Entry;
import java.util.Scanner;

class Main {

	@SuppressWarnings("resource")
	public static void main(final String args[]) {
		
		Scanner scanner = new Scanner(System.in);
		int n = scanner.nextInt();
		int a = scanner.nextInt();
		List<Integer> x = new ArrayList<>();

		for (int i = 0; i < n; i++) {
			int tmp = scanner.nextInt();
			x.add(tmp - a);
		}
		
		HashMap<Integer,Long> mapa=new HashMap<Integer,Long>();
		HashMap<Integer,Long> mapb=new HashMap<Integer,Long>();
		
		mapa.put(0,1L);
		mapb.put(0, 1L);

		
		for (Integer num : x) {
			for (Entry<Integer, Long> entry : mapb.entrySet()) {
				int sum = entry.getKey() + num;
				long way = entry.getValue();
				if(mapa.containsKey(sum)){
					mapa.put(sum, mapa.get(sum) + way);
				}else{
					mapa.put(sum, way);
				}
			}
			mapb.clear();
			mapb.putAll(mapa);
		}
		System.out.println(mapb.get(0)-1);
	}
}