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)

def main(nums, k, q)
  numslist = [nums.dup]

  ans = 10**9
  # puts "ans:      #{ans}"
  # puts
  nums.sort.each do |x|
    numscand = numslist.flat_map do |ns|
      next [] if ns.size < k
      ns.sort[0..(ns.size - k)]
    end
    numscand = numscand.sort.take(q)
    break if numscand.size < q
    ans = [ans, numscand.sort.take(q).max - x].min
    # puts "numslist: #{numslist}"
    # puts "numscand: #{numscand}"
    # puts "x:        #{x}"
    # puts "ans:      #{ans}"
    # puts

    idx = nil
    ns_idx = numslist.find_index { |l| idx = l.index x }
    ns = numslist[ns_idx]
    if idx == ns.size - 1
      numslist[ns_idx] = ns[0..(idx - 1)]
    elsif idx == 0
      numslist[ns_idx] = ns[1..-1]
    else
      numslist << ns[(idx + 1)..-1]
      numslist[ns_idx] = ns[0..(idx - 1)]
    end
  end
  ans
end

_, k, q = gets.chomp.split(' ').map(&:to_i)
nums = gets.chomp.split(' ').map(&:to_i)
puts main(nums, k, q)