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;

class Program
{
    static int n;
    static int a;
    static int[] x;

    static void Main(string[] args)
    {
        var na = Console.ReadLine().Split();
        n = int.Parse(na[0]);
        a = int.Parse(na[1]);
        x = new int[n];

        var s = Console.ReadLine().Split();
        for (int i = 0; i < n; i++)
        {
            x[i] = int.Parse(s[i]);
        }

        var ans = dfs(0, 0, 0);
        Console.WriteLine(ans);
    }

    static Dictionary<int, long> memo = new Dictionary<int, long>();
    static long dfs(int i, int count, int sum)
    {
        var hash = i * 10000 + count * 100 + sum;
        if (memo.ContainsKey(hash)) return memo[hash];

        if (n <= i)
        {
            if (0 < count &&
                sum % count == 0 &&
                sum / count == a)
            {
                return memo[hash] = 1;
            }
            else
            {
                return memo[hash] = 0;
            }
        }

        return memo[hash] =
            dfs(i + 1, count, sum) +
            dfs(i + 1, count + 1, sum + x[i]);
    }
}