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: Accepted)

#include <algorithm>
#include <array>
#include <cassert>
#include <cmath>
#include <cstdio>
#include <cstring>
#include <iomanip>
#include <iostream>
#include <iterator>
#include <map>
#include <memory>
#include <numeric>
#include <queue>
#include <set>
#include <stack>
#include <string>
#include <sstream>
#include <unordered_map>
#include <vector>


#define INF 1000000000
#define MOD 1000000007
#define ALL(x) std::begin(x), std::end(x)


int main(int argc, char** argv)
{
  std::cin.tie(0);
  std::ios_base::sync_with_stdio(0);

  std::cout << std::fixed << std::setprecision(6);
  std::cerr << std::fixed << std::setprecision(6);

  int N, K, Q, A[2222], dm = INF;
  
  std::cin >> N >> K >> Q;

  std::map<int, std::vector<int>> map;

  for (int i = 0; i < N; i ++) {
    std::cin >> A[i];

    map[A[i]].push_back(i);
  }

  for (const auto& kv : map) {
    int m = kv.first;

    std::vector<int> a, b;

    for (int i = 0, j = 0; i < N; )
      if (A[i] < m) {
        std::sort(ALL(b));

        for (int k = 0; k < static_cast<int>(b.size()) - K + 1; k ++)
          a.push_back(b[k]);

        b.clear();
        
        i = j = i + 1;
      }
      else {
        b.push_back(A[i]);

        i ++;
      }

    if (! b.empty()) {
      std::sort(ALL(b));

      for (int k = 0; k < static_cast<int>(b.size()) - K + 1; k ++)
        a.push_back(b[k]);
    }

    std::sort(ALL(a));
      
    if (a.size() >= Q) {
      int d = a[Q - 1] - a[0];

      dm = std::min(d, dm);
    }
  }

  std::cout << dm << std::endl;
  
  return 0;
}