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++ (GCC 9.2.1) (judge verdict: Accepted)

#include <iostream>
#include <cstdio>
#include <cstring>
#include <cassert>
#include <algorithm>
typedef long long lint;
const int N=2005;
int n,m,q,val[N],dv[N],dcnt,dlim;

namespace utils{
#define eprintf(...) fprintf(stderr,__VA_ARGS__)
	template <class T> inline void apn(T &x,const T y){x=x<y?x:y;}
	template <class T> inline void apx(T &x,const T y){x=x>y?x:y;}
	inline int nxi(){
		int x=0;
		char c;
		while(((c=getchar())>'9'||c<'0')&&c!='-');
		const bool f=(c=='-')&&(c=getchar());
		while(x=x*10-48+c,(c=getchar())>='0'&&c<='9');
		return f?-x:x;
	}
}
using namespace utils;

int getans(){
	static int buk[N];
	int cnt=0;
	for(int j,i=1; i<=n; i=j+1){
		for(j=i; val[j]>=dlim; ++j);
		if(j-i<m) continue;
		std::nth_element(val+i,val+j-m,val+j);
		for(int k=i; k+m<=j; ++k){
			buk[++cnt]=val[k];
		}
	}
	std::sort(buk+1,buk+cnt+1);
	return cnt<q?1e9:buk[q]-buk[1];
}

int main(){
	n=nxi(),m=nxi(),q=nxi();
	for(int i=1; i<=n; ++i){
		dv[i]=val[i]=nxi();
	}
	std::sort(dv+1,dv+n+1);
	dcnt=std::unique(dv+1,dv+n+1)-dv-1;
	int ans=1e9;
	for(int i=dcnt; i>=1; --i){
		dlim=dv[i];
		apn(ans,getans());
	}
	printf("%d\n",ans);
	return 0;
}