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: Time Limit Exceeded)

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using System.Threading.Tasks;

namespace C
{
    class Program
    {
        static long SubSolve(int N, int M, int MA, int[] x, int start)
        {
            if (M == 0 && MA == 0) { return 1; }
            else if (M == 0 || MA == 0 || start >= N) { return 0; }

            var ret = 0L;
            if (x[start] <= MA)
            {
                ret += SubSolve(N, M - 1, MA - x[start], x, start + 1);
            }
            ret += SubSolve(N, M, MA, x, start + 1);

            return ret;
        }
        static long Solve(int N, int A, int[] x)
        {
            var ans = 0L;
            for (var m = 1; m <= N; m++)
            {
                ans += SubSolve(N, m, m * A, x, 0);
            }
            return ans;
        }
        static void Main(string[] args)
        {
            var buff = Console.ReadLine().Split(' ').Select(int.Parse).ToArray();
            var N = buff[0];
            var A = buff[1];
            var x = Console.ReadLine().Split(' ').Select(int.Parse).ToArray();
            var ans = Solve(N, A, x);
            Console.WriteLine(ans);

        }
    }
}