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;
using System.Threading.Tasks;

namespace _0910 {
    class Program {
        static void Main(string[] args) {
            string[] str = Console.ReadLine().Split(' ');
            int N = int.Parse(str[0]);
            int A = int.Parse(str[1]);
            string[] str1 = Console.ReadLine().Split(' ');
            int[] xi = new int[N];
            for(int i = 0; i < N; i++) {
                xi[i] = int.Parse(str1[i]);
            }
            uint[,,] dp = new uint[50+1,50+1,5000];
            uint ans = 0;
            dp[0, 0, 0] = 1;
            for(int i = 0; i < N; i++) {
                for(int j = 0; j < N; j++) {
                    for(int k = 0; k < 2500; k++) {
                        if (dp[i,j,k]==0) {
                            continue;
                        }else {
                            dp[i + 1, j + 1, k + xi[i]] += dp[i, j, k];
                            dp[i + 1, j, k] += dp[i, j, k];
                        }
                    }
                }

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