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: Accepted)

using System;
using System.Collections.Generic;
using System.Linq;
using static System.Math;

class Program
{
    static int n, k, q;
    static int[] a;
    static void Main()
    {
        /* 入力の受け取り */
        string[] input = Console.ReadLine().Split();
        n = int.Parse(input[0]);
        k = int.Parse(input[1]);
        q = int.Parse(input[2]);
        a = Console.ReadLine().Split().Select(int.Parse).ToArray();
        /* Y=aiと固定して最小値を求めていく */
        int ans = int.MaxValue;
        for (int i = 0;i < n; i++) // Y=aiと固定
        {
            int Y = a[i];
            List<List<int>> sec = new List<List<int>>();
                                     // Y未満で分割した区間を管理
            sec.Add(new List<int>());
            for (int j = 0;j < n; j++)
            {
                if (a[j] < Y) // Y未満の処理
                {
                    sec.Add(new List<int>()); 
                    continue;
                }
                sec[sec.Count - 1].Add(a[j]);
            }
            List<int> removes = new List<int>(); // 取り除く候補を管理
            foreach (var b in sec) // 分割した各区間について
            {
                b.Sort();
                int m = Max(0,Min(q,b.Count - k + 1));
                for (int j = 0;j < m; j++)
                    removes.Add(b[j]);
            }
            removes.Sort();
            if (removes.Count < q) // q個も取り除けなかった場合
                continue;
            if (removes[0] != Y) // aiが取り除けなかった場合
                continue;
            ans = Min(ans,removes[q - 1] - Y); // 解の検討
        }
        Console.WriteLine(ans);
    }
}