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.Threading.Tasks;

namespace C
{
    class Program
    {
        static long Solve2(int N, int A, int[] x)
        {
            var X = Math.Max(x.Max(), A);
            var dp = new long[N + 1, N + 1, N*X + 1];

            for (int j = 0; j < N+1; j++)
            {
                for (int k = 0; k < N+1; k++)
                {
                    for (int s = 0; s < N*X+1; s++)
                    {
                        if (j == 0 && k == 0 && s == 0)
                        {
                            dp[j, k, s] = 1;
                        }else if (j >= 1 && s < x[j])
                        {
                            dp[j, k, s] = dp[j - 1, k, s];
                        }else if (j >= 1 && k >= 1 && s >= x[j])
                        {
                            dp[j, k, s] = dp[j - 1, k, s] + dp[j - 1, k - 1, s - x[j]];
                        }
                        else
                        {
                            dp[j, k, s] = 0;
                        }
                    }
                }
            }
            var sum = 0L;
            var k2 = 1;
            while (k2 <= N && k2*A <= N*X)
            {
                sum += dp[N,k2,k2*A];
                k2++;
            }

            return sum;
        }

        static long Solve(int N, int A, int[] x)
        {
            var X = Math.Max(x.Max(), A);
            var dp = new long[N + 1, 2 * N * X + 1];
            var y = new int[x.Length];
            for (int i = 0; i < x.Length; i++)
            {
                y[i] = A - x[i];
            }

            for (int j = 0; j < N + 1; j++)
            {
                for (int t = 0; t < 2*N*X + 1; t++)
                    if (j == 0 && t == N*X)
                    {
                        dp[j, t] = 1;
                    }
                    else if (j >= 1 && (t - y[j - 1] < 0 || t - y[j - 1] > 2*N*X))
                    {
                        dp[j, t] = dp[j - 1, t];
                    }
                    else if (j >= 1 && 0 <= t - y[j - 1] && t - y[j - 1] <= 2*N*X)
                    {
                        dp[j, t] = dp[j - 1, t] + dp[j - 1, t - y[j - 1]];
                    }
                    else
                    {
                        dp[j, t] = 0;
                    }
            }
            return dp[N, N * X] - 1;


        }

        static void Main(string[] args)
        {
            var buff = Console.ReadLine().Split(' ').Select(int.Parse).ToArray();
            var N = buff[0];
            var A = buff[1];
            var x = Console.ReadLine().Split(' ').Select(int.Parse).ToArray();
            var ans = Solve(N, A, x);
            Console.WriteLine(ans);

        }
    }
}