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 <bits/stdc++.h>
#define int long long
#define rep(i, n) for(int i = 0; i < (int)(n); i++)
#define all(x) (x).begin(),(x).end()
#define pb push_back
#define F first
#define S second

using namespace std;
typedef pair<int,int> P;

const int MOD=1000000007;
int INF=100100100100100;
int a[2010];
signed main(){
  int n,k,q;cin>>n>>k>>q;
  int ans=INF;
  rep(i,n)cin>>a[i];
  rep(ima,n){
    vector<int> res;
    vector<int> v;
    rep(i,n){
      if(a[i]>=a[ima])v.pb(a[i]);
      if(a[i]<a[ima] || i==n-1){
        if(v.size()>=k){
          int m=v.size();
          sort(all(v));
          rep(po,m-k+1){
            res.pb(v[po]);
          }
        }
        v.clear();
      }
    }
    
    if(res.size()>=q){
      sort(all(res));
      ans=min(ans,res[q-1]-res[0]);
    }
  }
        
  cout<<ans<<endl;        
  return 0;
}