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;

public class GFG
{
    static public void Main()
    {
        try
        {
            // var n = Console.ReadLine();
            var input1 = Console.ReadLine().Split(' ');
            var n = int.Parse(input1[0]);
            var b = int.Parse(input1[1]);

            var aar = Console.ReadLine().Split(' ').Select(x => Int32.Parse(x)).ToArray();

            CardTask(n, b, aar);
        }
        catch (Exception ex)
        {
            Console.Write(ex);
        }
    }

    static void CardTask(int n, int b, int[] arr)
    {

        int[,] dp = new int[n, n];
        long count = 0;
        for (int i = 0; i < n; i++)
        {
            dp[i, i] = arr[i];
            if (arr[i] == b)
                count++;
        }
        for (int l = 2; l < n; l++)
        {
            for (int j = 0; j < n - l + 1; j++)
            {

                int k = j + l-1;

                dp[j, k] = dp[j, k - 1] + arr[k];

                if (dp[j, k] / l == b)
                    count++;
            }
        }
        Console.Write(count);

    }


}