Problem:
Score : 600 points

Problem Statement

You are given an integer sequence A of length N and an integer K.
You will perform the following operation on this sequence Q times:

Choose a contiguous subsequence of length K, then remove the smallest element among the K elements contained in the chosen subsequence (if there are multiple such elements, choose one of them as you like).

Let X and Y be the values of the largest and smallest element removed in the Q operations. You would like X-Y to be as small as possible.
Find the smallest possible value of X-Y when the Q operations are performed optimally.

Constraints

1 \leq N \leq 2000

1 \leq K \leq N

1 \leq Q \leq N-K+1

1 \leq A_i \leq 10^9

All values in input are integers.

Input

Input is given from Standard Input in the following format:

N K Q
A_1 A_2 ... A_N

Output

Print the smallest possible value of X-Y.

Sample Input 1

5 3 2
4 3 1 5 2

Sample Output 1

1

In the first operation, whichever contiguous subsequence of length 3 we choose, the minimum element in it is 1.
Thus, the first operation removes A_3=1 and now we have A=(4,3,5,2).
In the second operation, it is optimal to choose (A_2,A_3,A_4)=(3,5,2) as the contiguous subsequence of length 3 and remove A_4=2.
In this case, the largest element removed is 2, and the smallest is 1, so their difference is 2-1=1.

Sample Input 2

10 1 6
1 1 2 3 5 8 13 21 34 55

Sample Output 2

7

Sample Input 3

11 7 5
24979445 861648772 623690081 433933447 476190629 262703497 211047202 971407775 628894325 731963982 822804784

Sample Output 3

451211184

Solution in C# (Mono 4.6.2.0) (judge verdict: Wrong Answer)

using System;
using System.Collections.Generic;
class Program
{
	static void Main(string[] args)
	{
		string[] str = Console.ReadLine().Split();
		long N = long.Parse(str[0]);
		long K = long.Parse(str[1]);
		long Q = long.Parse(str[2]);
		long[] A = new long[N];
		string[] str2 = Console.ReadLine().Split();
		for(var i=0;i<N;i++){
			A[i] = long.Parse(str2[i]);
		}
		long mmin = 9999999999;
		long imin = Math.Max(N-(K+Q-1),0);
		long imax = Math.Min(K+Q-1,N);
		for(var i=imin+1;i<imax-1;i++){
			mmin = Math.Min(A[i],mmin);
		}
		Array.Sort(A);
		long min = 9999999999;
		for(var i=0;i<N-Q+1;i++){
			long sum = A[i+Q-1] - A[i];
			min = Math.Min(min, sum);
			if(A[i] >= mmin){
				break;
			}
		}
		Console.WriteLine(min);
	}
}