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: Accepted)

use std::io::*;
use std::cmp;

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

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

fn read_vec_char() -> Vec<char> {
    read::<String>().chars().collect()
}

fn read_mat<T: std::str::FromStr>(n: usize) -> Vec<Vec<T>> {
    (0..n).map(|_| read_vec()).collect()
}

fn read_mat_char(n: usize) -> Vec<Vec<char>> {
    (0..n).map(|_| read_vec_char()).collect()
}

fn main() {
    let v = read_vec::<usize>();
    let (n,k,q) = (v[0],v[1],v[2]);
    let a = read_vec::<usize>();
    let mut xs: Vec<usize> = Vec::new();
    for i in 0..n-k+1 {
        let mut m = a[i];
        for j in i+1..i+k {
            m = cmp::min(m,a[j]);
        }
        if !xs.contains(&m) {
            xs.push(m);
        }
    }
    let mut ans = usize::max_value();
    for x in xs {
        let mut ups: Vec<usize> = Vec::new();
        for sub in a.split(|&y| y < x) {
            let l = sub.len();
            if l < k {
                continue;
            }
            let mut ssub = sub.to_vec();
            ssub.sort();
            let mut ssub2 = ssub[0..l-k+1].to_vec();
            ups.append(&mut ssub2);
        }
        if ups.len() >= q {
            ups.sort();
            ans = cmp::min(ans,ups[q-1]-x);
        }
    }
    println!("{}",ans);
}