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: Accepted)

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using System.Diagnostics;

class Program
{
    static int[] x;
    static long?[,,] memo;
    static long Solve(int i, int n, int sum)
    {
        if (sum == 0) { return (n == 0) ? 1 : 0; }
        if (i >= x.Length || n == 0) { return 0; }
        if (!memo[i, n, sum].HasValue)
        {
            long count = 0;
            if (sum >= x[i])
            {
                count += Solve(i + 1, n - 1, sum - x[i]);
            }
            count += Solve(i + 1, n, sum);
            memo[i, n, sum] = count;
        }
        return memo[i, n, sum].Value;
    }
    static void Main(string[] args)
    {
        var values = Array.ConvertAll(Console.ReadLine().Split(), int.Parse);
        int N = values[0];
        int A = values[1];
        x = Array.ConvertAll(Console.ReadLine().Split(), int.Parse);
        memo = new long?[N, N + 1, A * N + 1];
        long count = 0;
        for (int i = 1; i <= N; ++i)
        {
            count += Solve(0, i, A * i);
        }
        Console.WriteLine(count);
    }
}