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;

class Program
{
    static string InputPattern = "InputX";

    static List<string> GetInputList()
    {
        var WillReturn = new List<string>();

        if (InputPattern == "Input1") {
            WillReturn.Add("4 8");
            WillReturn.Add("7 9 8 9");
            //5
        }
        else if (InputPattern == "Input2") {
            WillReturn.Add("3 8");
            WillReturn.Add("6 6 9");
            //0
        }
        else if (InputPattern == "Input3") {
            WillReturn.Add("8 5");
            WillReturn.Add("3 6 2 8 7 6 5 9");
            //19
        }
        else if (InputPattern == "Input4") {
            WillReturn.Add("33 3");
            WillReturn.Add("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");
            //8589934591
        }
        else {
            string wkStr;
            while ((wkStr = Console.ReadLine()) != null) WillReturn.Add(wkStr);
        }
        return WillReturn;
    }

    static void Main()
    {
        List<string> InputList = GetInputList();
        int[] wkArr = InputList[0].Split(' ').Select(X => int.Parse(X)).ToArray();
        int A = wkArr[1];
        int[] XArr = InputList[1].Split(' ').Select(X => int.Parse(X)).ToArray();

        //場合の数[枚数,合計]なDP表
        int UB_I = wkArr[0];
        int UB_J = XArr.Sum();
        int[,] DPArr = new int[UB_I + 1, UB_J + 1];
        DPArr[0, 0] = 1;

        foreach (int EachX in XArr) {
            for (int I = UB_I; 0 <= I; I--) {
                for (int J = UB_J; J >= 0; J--) {
                    if (DPArr[I, J] == 0) continue;
                    int NewI = I + 1;
                    int NewJ = J + EachX;
                    DPArr[NewI, NewJ] += DPArr[I, J];
                }
            }

            //Console.WriteLine("DPの結果");
            //for (int I = 0; I <= UB_I; I++) {
            //    for (int J = 0; J <= UB_J; J++) {
            //        Console.WriteLine("DPArr[{0},{1}]={2}", I, J, DPArr[I, J]);
            //    }
            //}
        }

        long AnswerCnt = 0;
        for (int I = 1; I <= UB_I; I++) {
            for (int J = 0; J <= UB_J; J++) {
                if (J == A * I)
                    AnswerCnt += DPArr[I, J];
            }
        }
        Console.WriteLine(AnswerCnt);
    }
}