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: Time Limit Exceeded)

#N, K, Q = 2000, 1000, 1000
#as = (0...N).to_a.shuffle
N, K, Q = gets.split.map(&:to_i)
as = gets.split.map(&:to_i)

ia = N.times.map{|i|[i, as[i]]}.sort_by{|arr|arr[1]}
comp = []
N.times do |i|
    comp[ia[i][0]] = i
end
comp += [-1]

ans = Float::INFINITY
used = Array.new(N) + [true]
(N-Q+1).times do |i|
    if ia[i+Q-1][1] - ia[i][1] >= ans
        used[ia[i][0]] = true
        next
    end
    max_i = ((i+Q-1)...N).bsearch do |j|
        tmp = 0
        d = 0
        sum = 0
        (N+1).times do |k|
            if used[k]
                if d >= K
                    sum += tmp < d-K+1 ? tmp : d-K+1
                end
                tmp = 0
                d = 0
            else
                d += 1
                tmp += 1 if comp[k] <= j
            end
        end
        sum >= Q
    end
    if max_i
        cand = ia[max_i][1] - ia[i][1]
        ans = cand if ans > cand
    end
    used[ia[i][0]] = true
end

puts ans