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: Time Limit Exceeded)

use io::*;
use std::cmp::{max, min};
use std::collections::{BTreeMap, BTreeSet};

fn main() {
    let con = read_string();
    let mut sc = Scanner::new(&con);

    let n: usize = sc.next();
    let k: usize = sc.next();
    let q: usize = sc.next();

    let a: Vec<u32> = sc.next_vec(n);

    let mut mm: BTreeMap<u32, i32> = BTreeMap::new();
    for i in 0..k {
        *mm.entry(a[i]).or_insert(0) += 1;
    }

    // let mut ok = 0, ng = u32::max_value();

    // while (ok-ng).abs() > 1 {

    // }

    let mut cands = BTreeSet::new();
    cands.insert(*mm.iter().next().unwrap().0);

    for i in 0..n - k {
        *mm.entry(a[i + k]).or_insert(0) += 1;
        *mm.entry(a[i]).or_insert(0) -= 1;
        if mm[&a[i]] == 0 {
            mm.remove(&a[i]);
        }
        cands.insert(*mm.iter().next().unwrap().0);
    }

    let cands: Vec<u32> = cands.iter().cloned().collect();

    let mut ans = u32::max_value();

    for cand in cands {
        let mut a2 = a.clone();
        let ix = a2.iter().position(|&e| e == cand).unwrap();
        a2.remove(ix);

        let cur = solve(a2, cand, k, q);
        if cur == u32::max_value() {
            break;
        }

        ans = min(ans, cur);
    }

    println!("{}", ans);
}

fn solve(mut v: Vec<u32>, th: u32, k: usize, q: usize) -> u32 {
    let mut ma = th;

    for _ in 0..q - 1 {
        let n = v.len();

        let mut mm: BTreeMap<u32, i32> = BTreeMap::new();
        for i in 0..k {
            *mm.entry(v[i]).or_insert(0) += 1;
        }

        let mut cand = u32::max_value();
        let t = *mm.iter().next().unwrap().0;
        if t >= th {
            cand = min(cand, t);
        }

        for i in 0..n - k {
            *mm.entry(v[i + k]).or_insert(0) += 1;
            *mm.entry(v[i]).or_insert(0) -= 1;
            if mm[&v[i]] == 0 {
                mm.remove(&v[i]);
            }
            let t = *mm.iter().next().unwrap().0;
            if t >= th {
                cand = min(cand, t);
            }
        }

        if cand == u32::max_value() {
            return u32::max_value();
        }

        ma = max(ma, cand);

        let ix = v.iter().position(|&e| e == cand).unwrap();
        v.remove(ix);
    }

    ma - th
}

//-----

pub mod io {
    use std;
    use std::str::FromStr;

    pub struct Scanner<'a> {
        iter: std::str::SplitWhitespace<'a>,
    }

    impl<'a> Scanner<'a> {
        pub fn new(s: &'a str) -> Scanner<'a> {
            Scanner {
                iter: s.split_whitespace(),
            }
        }

        pub fn next<T: FromStr>(&mut self) -> T {
            let s = self.iter.next().unwrap();
            if let Ok(v) = s.parse::<T>() {
                v
            } else {
                panic!("Parse error")
            }
        }

        pub fn next_vec_len<T: FromStr>(&mut self) -> Vec<T> {
            let n: usize = self.next();
            self.next_vec(n)
        }

        pub fn next_vec<T: FromStr>(&mut self, n: usize) -> Vec<T> {
            (0..n).map(|_| self.next()).collect()
        }
    }

    pub fn read_string() -> String {
        use std::io::Read;

        let mut s = String::new();
        std::io::stdin().read_to_string(&mut s).unwrap();
        s
    }

    pub fn read_line() -> String {
        let mut s = String::new();
        std::io::stdin().read_line(&mut s).unwrap();
        s.trim_right().to_owned()
    }
}