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


class Program
{
    public void Proc()
    {
        Reader.IsDebug = false;
        int[] inpt = Reader.ReadLine().Split(' ').Select(a => int.Parse(a)).ToArray();
        this.CardCount = inpt[0];
        this.Heikin = inpt[1];
        this.Cards = Reader.ReadLine().Split(' ').Select(a => int.Parse(a)).ToArray();

        long ans = this.GetAns(0, 0, 0);
        Console.WriteLine(ans);
    }


    Dictionary<int, Dictionary<int, Dictionary<int, long>>> dic = new Dictionary<int, Dictionary<int, Dictionary<int, long>>>();
    private long GetAns(int idx, int maisu, int total)
    {
        if (!dic.ContainsKey(idx))
        {
            dic.Add(idx, new Dictionary<int,Dictionary<int,long>>());
        }
        if (!dic[idx].ContainsKey(maisu))
        {
            dic[idx].Add(maisu, new Dictionary<int, long>());
        }
        if (dic[idx][maisu].ContainsKey(total))
        {
            return dic[idx][maisu][total];
        }

        if (idx >= this.CardCount)
        {
            if (maisu == 0)
            {
                return 0;
            }
            if (total % maisu == 0 && total / maisu == Heikin)
            {
                return 1;
            }
            else
            {
                return 0;
            }
        }

        long ans = this.GetAns(idx + 1, maisu, total);
        ans += this.GetAns(idx + 1, maisu + 1, total + this.Cards[idx]);
        dic[idx][maisu].Add(total, ans);
        return ans;
        
    } 


    private int CardCount = 0;
    private int Heikin = 0;
    private int[] Cards;





    public class Reader
    {
        public static bool IsDebug = true;
        private static String PlainInput = @"


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



";
        private static System.IO.StringReader Sr = null;
        public static string ReadLine()
        {
            if (IsDebug)
            {
                if (Sr == null)
                {
                    Sr = new System.IO.StringReader(PlainInput.Trim());
                }
                return Sr.ReadLine();
            }
            else
            {
                return Console.ReadLine();
            }
        }
    }
    static void Main()
    {
        Program prg = new Program();
        prg.Proc();
    }
}