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)

// code test
using System;
using System.Linq;
using System.Collections.Generic;
using System.Text;
using static System.Console;
using static System.Math;

class Program
{
    static void Main(string[] args)
    {
        int[] NA = ReadLineParseIntArray();
        long N = NA[0];
        long A = NA[1];
        long[] X = ReadLine().Split(' ').Select(x => int.Parse(x) - A).ToArray();
        long max = X.Max();
        if (max < 0) {
            WriteLine(0);
            return;
        }

        long[] dp = new long[2 * max * N + 1];
        dp[N * max] = 1;
        for(int i = 0; i < N; i++)
        {
            long first = Max(0, X[i]);
            long last = Min(dp.Length, dp.Length + X[i]);
            if (X[i] <= 0)
                for (long t = first; t < last; t++)
                    dp[t] += dp[t - X[i]];
            else
                for (long t = last - 1; t >= first; t--)
                    dp[t] += dp[t - X[i]];
        }
        WriteLine(dp[N * max] - 1);
    }

    static int ReadLineParseInt() => int.Parse(ReadLine());
    static int[] ReadLineParseIntArray() => ReadLine().Split(' ').Select(int.Parse).ToArray();
}