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 Rust (1.15.1) (judge verdict: Wrong Answer)

#[allow(unused_imports)]
use std::cmp::*;
#[allow(unused_imports)]
use std::collections::*;

fn read<T: std::str::FromStr>() -> T {
    let mut s = String::new();
    std::io::stdin().read_line(&mut s).ok();
    s.trim().parse().ok().unwrap()
}

fn read_vec<T: std::str::FromStr>() -> Vec<T> {
    read::<String>()
        .split_whitespace()
        .map(|e| e.parse().ok().unwrap())
        .collect()
}

fn argsort<T: std::cmp::Ord + std::marker::Copy>(v: &Vec<T>) -> Vec<usize> {
    let mut sort_v = Vec::new();
    for i in 0..v.len() {
        sort_v.push((v[i], i));
    }
    sort_v.sort();
    sort_v.iter().map(|x| x.1).collect::<Vec<usize>>()
}

#[derive(Debug)]
struct Pocket {
    width: usize,
    used_count: usize,
}

fn construct_pockets(min_candidate_a: u64, a: &Vec<u64>) -> (Vec<Pocket>, HashMap<usize, usize>) {
    let mut array_idx_to_pocket_idx = HashMap::<usize, usize>::new();
    let mut pockets = Vec::new();

    // make pocket
    let mut is_seeking = false;
    let mut start_seeking_index = 0usize;

    for j in 0..a.len() {
        if a[j] >= min_candidate_a {
            if !is_seeking {
                is_seeking = true;
                start_seeking_index = j;
            }
        }
        if is_seeking && (a[j] < min_candidate_a || j == a.len() - 1) {
            let mut end_idx = j;
            if j == a.len() - 1 {
                end_idx += 1;
            }
            is_seeking = false;
            let new_pocket = Pocket {
                width: end_idx - start_seeking_index,
                used_count: 0,
            };
            pockets.push(new_pocket);
            for k in start_seeking_index..end_idx {
                array_idx_to_pocket_idx.insert(k, pockets.len() - 1);
            }
        }
    }

    (pockets, array_idx_to_pocket_idx)
}

fn main() {
    let v = read_vec::<usize>();
    let (n, k, q) = (v[0], v[1], v[2]);
    let a = read_vec::<u64>();
    let sorted_indexes = argsort(&a);
    let mut sorted_indexes_dict = vec![0; n];

    for i in 0..n {
        sorted_indexes_dict[sorted_indexes[i]] = i;
    }

    let mut ans = std::u64::MAX;
    for i in 0..n - q + 1 {
        let min_candidate_a = a[i];
        let (pockets, array_idx_to_pocket_idx) = construct_pockets(min_candidate_a, &a);
        let mut pockets = pockets;
        // println!("pocket {:?}", (min_candidate_a, &pockets));
        // println!("{:?}", array_idx_to_pocket_idx);

        let mut total_used_count = 0;
        let mut next_a_index = i;
        loop {
            let mut next_pocket = &mut pockets[array_idx_to_pocket_idx[&next_a_index]];
            if next_pocket.width - next_pocket.used_count >= k {
                next_pocket.used_count += 1;
                total_used_count += 1;
            }
            if sorted_indexes_dict[next_a_index] == n - 1 {
                break;
            }
            if total_used_count == q {
                break;
            }
            next_a_index = sorted_indexes[(sorted_indexes_dict[next_a_index] + 1)];
        }
        if total_used_count == q {
            // println!("{0} {1}", a[next_a_index], min_candidate_a);
            ans = min(ans, a[next_a_index] - min_candidate_a);
        }
    }
    println!("{}", ans);
}