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: Runtime Error)

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

 class Program
    {
        static void Main(string[] args)
        {
            // get a inputs
            var hotelcount = int.Parse(Console.ReadLine());
            var hotels = Console.ReadLine().Split(' ').Select(int.Parse).ToArray();
            var lethargyLimit = int.Parse(Console.ReadLine());
            var queriescount = int.Parse(Console.ReadLine());
            var queries = new List<int[]>();
            while(queriescount > 0)
            {
                queriescount--;
                queries.Add(Console.ReadLine().Split(' ').Select(int.Parse).ToArray());
            }

            foreach(var query in queries)
                Console.WriteLine(FindDays(query[0] - 1, query[1] - 1, hotels, lethargyLimit));
        }

        public static int FindDays(int start, int end, int[] arr, int limit)
        {
            var dir = start < end ? 1 : -1;
            var days = 1;
            var walked = 0;
            while(start != end)
            {
                var next = start + dir;
                var dis = Math.Abs(arr[start] - arr[next]);
                if (dis + walked > limit)
                {
                    walked = dis;
                    days++;
                }
                else
                {
                    walked += dis;
                }
start = next;
            }
            return days;
        }
    }