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 5.4.1) (judge verdict: Accepted)

#include<stdio.h>
#include<stdlib.h>
#include<math.h>

typedef long long int int64;

#define MAX(a,b) ((a)>(b)?(a):(b))
#define MIN(a,b) ((a)<(b)?(a):(b))
#define ABS(a) ((a)>(0)?(a):-(a))

int cmp(const void *a,const void *b){
  return *(int *)a-*(int *)b;
}

void run(void){
  int n,k,q;
  scanf("%d%d%d",&n,&k,&q);
  int *a=(int *)malloc(sizeof(int)*n);
  int i;
  for(i=0;i<n;i++) scanf("%d",a+i);
  int min=1000000000;
  for(i=0;i<n;i++){
    int local=a[i];
    int b[2000];
    int c[2000];
    int clen=0;
    int j;
    for(j=0;j<n;j++){
      if(a[j]<local) continue;
      int blen=0;
      while(j+blen<n && a[j+blen]>=local){
	b[blen]=a[j+blen];
	blen++;
      }
      if(blen>=k){
	qsort(b,blen,sizeof(int),cmp);
	int l;
	for(l=0;l<blen-k+1;l++) c[clen++]=b[l];
      }
      j+=blen;
    }
    if(clen>=q){
      qsort(c,clen,sizeof(int),cmp);
      min=MIN(min,c[q-1]-local);
    }
  }
  printf("%d\n",min);
}

int main(void){
  run();
  return 0;
}