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;
using System.Collections.Generic;
class Program {
  static void Main(string[] args) {
    int[] input = Console.ReadLine().Split(' ').Select(int.Parse).ToArray();
    int N = input[0];
    int A = input[1];

    int[] x = new int[N + 1];
    input = Console.ReadLine().Split(' ').Select(int.Parse).ToArray();
    for (int i = 0; i < N; ++i) {
      x[i + 1] = input[i];
    }

    long[,,] dp = new long[N + 1, N + 1, N * A + 1];

    for (int i = 0; i < N; ++i) dp[i, 0, 0] = 1;

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

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

    Console.WriteLine(ans);
  }
}