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: Time Limit Exceeded)

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using System.Threading.Tasks;

namespace AtCoder
{
	class Program
	{
		static void Main(string[] args)
		{
			var firstLine = Console.ReadLine().Split(' ').Select(value => int.Parse(value)).ToList();
			var n = firstLine[0];
			var a = firstLine[1];

			var input = Console.ReadLine().Split(' ').Select(value => int.Parse(value)).ToList();

			long count = 0;

			var pow = Math.Pow(2, n);

			for (long b = 1; b < pow; b++)
			{
				long sum = 0;
				var byteString = Convert.ToString(b, 2);
				var byteStringLength = byteString.Length;

				for (int j = 0; j < byteStringLength; j++)
				{
					if (byteString[byteStringLength - j - 1] == '1')
					{
						sum += input[j];
					}
				}

				if (sum == a * byteString.Count(value => value == '1'))
				{
					count++;
				}
			}

			Console.WriteLine(count);
		}
	}
}