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

namespace ARC060_C2
{
    class Program
    {
        static void Main(string[] args)
        {
            long ans = 0;
            var t = scan;
            int n = t[0];
            int a = t[1];
            var x = scan;
            int S = 1 << n;
            if (n > 16) goto end;
            for (int i = 1; i < S; i++)
            {
                int k = i;
                var P = new HashSet<int>();
                int count = 0;
                while (k>0)
                {
                    if ((k & 1) == 1) P.Add(x[count]);
                    k = k >> 1;
                    count++;
                }
                if (P.Sum() % P.Count == 0 && P.Sum() / P.Count == a)
                {
                    ans++;
                    //Console.WriteLine(i);
                }
            }
            end:;
            Console.WriteLine(ans);        
        }

        static int[] scan
        {
            get { return Console.ReadLine().Split().Select(int.Parse).ToArray(); }
        }
    }
}