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 Perl (v5.18.2) (judge verdict: Time Limit Exceeded)

$line = <STDIN>;
chomp $line;
($N,$K,$Q) = split(/ /, $line);
$line = <STDIN>;
chomp $line;
@A = split(/ /, $line);

$minXmY=-1;

@A0 = sort {$a <=> $b} @A;

for($i=0;$i<=$N-$Q;$i++){
	$Y=$A0[$i];
	
	@A3=();
	@A2=();
	for($j=0;$j<$N;$j++){
		if($A[$j]>=$Y) {
			#push @A2, $A[$j];
			for($k=0; $k<=$Q+$K-1 && $k<=$#A2 && $A[$j]>$A2[$k];$k++){}
			splice @A2, $k, 0, $A[$j] if ($k<=$Q+$K-1);
		} else {
			$c=($#A2+1)-$K+1;
			if($c>0) {
				#@A2 = sort {$a <=> $b} @A2;
				#push @A3,@A2[0..$c-1];
				$l=0;
				for($k=0; $k<$c;$k++){
					for(; $l<=$Q && $l<=$#A3 && $A2[$k]>$A3[$l];$l++){}
					splice @A3, $l, 0, $A2[$k] if ($l<=$Q);
				}
			}
			@A2=();
		}
	}
	$c=($#A2+1)-$K+1;
	if($c>0) {
		#@A2 = sort {$a <=> $b} @A2;
		#push @A3,@A2[0..$c-1];
		$l=0;
		for($k=0; $k<$c;$k++){
			for(; $l<=$Q && $l<=$#A3 && $A2[$k]>$A3[$l];$l++){}
			splice @A3, $l, 0, $A2[$k] if ($l<=$Q);
		}
	}
	#@A3 = sort {$a <=> $b} @A3;
	
	if($#A3+1>=$Q) {
		$XmY=$A3[$Q-1]-$Y;
		$minXmY = $XmY if($minXmY > $XmY || $minXmY<0);
	}
}

print "$minXmY\n";