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# (Mono 4.6.2.0) (judge verdict: Wrong Answer)

using System;
using System.Linq;

public class Program
{
	public static void Main()
	{
		int[] NA = Console.ReadLine().Split().Select(i => int.Parse(i))
			.ToArray();
		int N = NA[0], A = NA[1];
		int[] x = Console.ReadLine().Split().Select(i => int.Parse(i))
			.ToArray();
		long ans = 0;
		for (long i = 1; i < (1 << N); i++)
		{
			int counter = 0;
			int sum = 0;
			for (int j = 0; j < N; j++)
			{
				if (((i >> j) % 2) == 1)
				{
					counter++;
					sum += x[j];
				}
			}
			if (sum == counter * A) {
				ans++;
			}
		}
		Console.WriteLine(ans);
	}
}