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++14 (GCC 5.4.1) (judge verdict: Wrong Answer)

#include<iostream>
#include<cstdio>
#include<cstdlib>
#include<cstring>
#include<algorithm>
using namespace std;
int a[2020];
int t[2020],tt[2020],nt;
int aa[2020],an;
bool ch[2020],in[2020];
bool cmp(int x,int y)
{
	return a[x]<a[y];
}
void insertv(int num)
{
	if(in[num])
		return ;
	in[num]=true;
	int x=a[num],now;
	an++;
	now=an-1;
	while(now>=1&&aa[now]>x)
	{
		aa[now+1]=aa[now];
		now--;
	}
	aa[now+1]=x;
}
int main()
{
	int n,k,q;
	int ans=2147483647;
	scanf("%d%d%d",&n,&k,&q);
	for(int i=1;i<=n;i++)
		scanf("%d",&a[i]);
	memset(ch,0,sizeof(ch));
	memset(in,0,sizeof(in));
	for(int i=1;i<=n;i++)
		t[i]=i;
	sort(t+1,t+1+n,cmp);
	an=0;
	ch[0]=ch[n+1]=false;
	for(int i=n;i>=1;i--)
	{
		ch[t[i]]=true;
		nt=0;
		for(int j=1;j<=n+1;j++)
		{
			if(ch[j])
				tt[++nt]=j;
			else
			{
				sort(tt+1,tt+1+nt,cmp);
				for(int kk=1;kk<=nt-k+1;kk++)
					insertv(tt[kk]);
				nt=0;
			}
		}
		if(an>=q)
			ans=min(ans,aa[q]-aa[1]);
	}
	printf("%d",ans);
	return 0;
}