Problem:
Score : 300 points

Problem Statement

Takahashi made N problems for competitive programming.
The problems are numbered 1 to N, and the difficulty of Problem i is represented as an integer d_i (the higher, the harder).

He is dividing the problems into two categories by choosing an integer K, as follows:

A problem with difficulty K or higher will be for ARCs.

A problem with difficulty lower than K will be for ABCs.

How many choices of the integer K make the number of problems for ARCs and the number of problems for ABCs the same?

Problem Statement

2 \leq N \leq 10^5

N is an even number.

1 \leq d_i \leq 10^5

All values in input are integers.

Input

Input is given from Standard Input in the following format:

N
d_1 d_2 ... d_N

Output

Print the number of choices of the integer K that make the number of problems for ARCs and the number of problems for ABCs the same.

Sample Input 1

6
9 1 4 4 6 7

Sample Output 1

2

If we choose K=5 or 6, Problem 1, 5, and 6 will be for ARCs, Problem 2, 3, and 4 will be for ABCs, and the objective is achieved.
Thus, the answer is 2.

Sample Input 2

8
9 1 14 5 5 4 4 14

Sample Output 2

0

There may be no choice of the integer K that make the number of problems for ARCs and the number of problems for ABCs the same.

Sample Input 3

14
99592 10342 29105 78532 83018 11639 92015 77204 30914 21912 34519 80835 100000 1

Sample Output 3

42685

Solution in C# (Mono 4.6.2.0) (judge verdict: Runtime Error)

using System;
using System.Linq;
 
namespace ABC132
{
    class D
    {
        static void Main(string[] args)
        {
            long[] input = Console.ReadLine().Split().Select(long.Parse).ToArray();
            long N = input[0];
            long K = input[1];
 
            init(4005);
 
            long red = 0;
            long blue = 0;
            for (long i = 1; i <= K; i++)
            {
                if (N - K + 1 < i) red = 0;
                else red = CalcCombination(N - K + 1, i);
 
                blue = CalcCombination(K - 1, i - 1);
 
                Console.WriteLine((blue * red) % 1000000007);
 
            }
 
        }
 
        // Combination
        static long[,] c;
        public static long[,] init(long x)
        {
            c = new long[x + 5, x + 5];
            c[0, 0] = 1;
            for (long i = 1; i <= x; i++)
            {
                for (long j = 0; j <= i; j++)
                {
                    if (j == 0) c[i, j] = c[i - 1, j];
                    else c[i, j] = (c[i - 1, j] + c[i - 1, j - 1]) % 1000000007;
                }
            }
            return c;
        }
 
        public static long CalcCombination(long n, long k)
        {
            return c[n, k];
        }
 
    }
 
 
 
}