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 Ruby (2.3.3) (judge verdict: Wrong Answer)

nkq = gets.chomp.split(" ").map(&:to_i)
a = gets.chomp.split(" ").map(&:to_i)
s = a.uniq
current_min = a.max - a.min
s.each do |i|
  candidates = []
  head_pointer = a.length
  a.each.with_index do |t, idx|
    if t >= i
      head_pointer = idx if head_pointer == a.length
    elsif head_pointer < idx
      candidates << a[head_pointer..idx-1]
      head_pointer = idx + 1
    end
  end
  candidates << a[head_pointer..-1]
  #p candidates
  new_candidates = []
  candidates.each do |s|
    if s.length > nkq[1]
      new_candidates << s.sort[0..(s.length - nkq[1] + 1)]
    end
  end
  #p new_candidates.flatten.sort
  if new_candidates.flatten.length > nkq[2]
    cd = new_candidates.flatten.sort[nkq[2]-1] - i
    current_min = cd if current_min > cd && cd  > 0
  end
end

puts current_min