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# (.NET Core 3.1.201) (judge verdict: Accepted)

using System;
using System.Text;
using System.Collections.Generic;
using System.Collections;
using static System.Math;
using System.Linq;
using static System.Array;

namespace ConsoleApp2
{
    class Program
    {

        static void Main(string[] args)
        {
            //var N = long.Parse(Console.ReadLine());
            var NA = Console.ReadLine().Split(' ').Select(x => long.Parse(x)).ToArray();
            var N = NA[0];
            var A = NA[1];

            var X = Console.ReadLine().Split(' ').Select(x => long.Parse(x)).ToArray();
            var dp = new long[N+1,N+1, (N * A)+1];

            for (int j = 0; j <= N; j++)
            {
                dp[0, j, 0] = 1;
            }

            for (int i = 1; i <= N; i++)
            {
                for (int j = 1; j <= N; j++)
                {
                    for (int k = 0; k <= N*A; k++)
                    {
                        if(k - X[j - 1] >= 0)
                        {
                            dp[i,j,k] = dp[i, j - 1, k] + dp[i - 1,j - 1,k - X[j - 1]];
                        }
                        else
                        {
                            dp[i, j, k] = dp[i, j-1, k];
                        }
                        
                    }
                }
            }

            long ans = 0;
            for (int i = 1; i <= N; i++)
            {
                ans += dp[i, N, A * i];
            }


            Console.WriteLine(ans);
            

            
            
        }


    }


}