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 ConsoleApp111 {
    class Program {
        static int N;
        static int[] x;
        static long[,,] dp;

        static void Main(string[] args) {
            var st = Console.ReadLine().Split().Select(int.Parse).ToArray();
            N = st[0];
            int A = st[1];

            var p = Console.ReadLine().Split().Select(int.Parse).ToArray();
            Array.Sort(p);

            x = new int[N];

            for (int i = 0; i < N; i++) {
                x[i] = p[i];
            }

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

            //全ての値を-1で初期化
            for (int i = 0; i <= N; i++) {
                for (int j = 0; j <= N; j++) {
                    for (int k = 0; k <= A * N; k++) {
                        dp[i, j, k] = -1;
                    }
                }
            }

            CalculateDP(N, N, A * N);

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

            Console.WriteLine(ans - 1);
        }

        static long CalculateDP(int a, int b, int c) {
            //すでにテーブルが埋まっていれば、値を返す
            if (dp[a, b, c] != -1) {
                return dp[a, b, c];
            }

            if (a == 0 && b == 0 && c == 0) {
                dp[a, b, c] = 1;
                return 1;
            }

            if (a >= 1 && b == 0 && c == 0) {
                dp[a, b, c] = 1;
                return 1;
            }

            if (a >= 1 && c < x[a - 1]) {
                dp[a, b, c] = dp[a - 1, b, c];
                return CalculateDP(a - 1, b, c);
            }

            if (a >= 1 && b >= 1 && x[a - 1] <= c) {
                dp[a, b, c] = dp[a - 1, b, c] + dp[a - 1, b - 1, c - x[a - 1]];
                return CalculateDP(a - 1, b, c) + CalculateDP(a - 1, b - 1, c - x[a - 1]);
            }

            dp[a, b, c] = 0;
            return 0;
        }
    }
}