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.Linq;

namespace ABC044_C_TakAndCards
{
    /// <summary>
    /// 復習
    /// </summary>
    public static class ABC044_C_Review
    {
        static void Main(string[] args)
        {
            string[] split = Console.ReadLine().Split(' ');
            int N = int.Parse(split[0]);
            int A = int.Parse(split[1]);

            int[] X = Console.ReadLine().Split(' ').Select(s => int.Parse(s)).ToArray();

            // 場合の数[選んだ枚数, 合計]のDP表
            int S = X.Sum();
            ulong[,] dp = new ulong[N + 1, S + 1];
            dp[0, 0] = 1;

            foreach (int x in X)
            {
                for (int i = N; i >= 0; i--)
                {
                    for (int j = S; j >= 0; j--)
                    {
                        if (dp[i, j] == 0)
                        {
                            continue;
                        }

                        dp[i + 1, j + x] += dp[i, j];
                    }
                }
            }

            ulong answerCount = 0;
            for (int i = 1; i <= N; i++)
            {
                for (int j = 0; j <= S; j++)
                {
                    if (j == A * i)
                    {
                        answerCount += dp[i, j];
                    }
                }
            }

            Console.WriteLine(answerCount);
        }
    }
}