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::stdin;

fn read_line() -> Vec<String> {
    let mut line = String::new();
    stdin().read_line(&mut line).expect("Failed to read line");
    return line.trim().split_whitespace().map(|s| s.to_string()).collect();
}

struct Reader {
    v: Vec<String>,
    n: usize,
}

impl Reader {
    fn new() -> Reader {
        let v = read_line();
        return Reader { v: v, n: 0 };
    }
    fn next<T>(&mut self) -> T where T: std::str::FromStr, T::Err: std::fmt::Debug {
        if self.n == self.v.len() {
            self.v = read_line();
            self.n = 0;
        }
        let x = self.v[self.n].parse().unwrap();
        self.n += 1;
        return x;
    }
    fn nexts<T>(&mut self, n: usize) -> Vec<T>
    where T: std::str::FromStr, T::Err: std::fmt::Debug {
        let mut v = Vec::with_capacity(n);
        for _ in 0..n {
            v.push(self.next());
        }
        return v;
    }
}

fn main() {
    let mut r = Reader::new();
    let n: usize = r.next();
    let k: usize = r.next();
    let q: usize = r.next();
    let a: Vec<i64> = r.nexts(n);

    let mut ai: Vec<(&i64, usize)> = a.iter().enumerate()
        .map(|(i, x)| (x, i)).collect();
    ai.sort();

    let mut ok: Vec<bool> = vec![true; n];
    let mut ans = 1e15_f64 as i64;
    for i in 0..n {
        let mut mins: Vec<i64> = Vec::new();
        let mut ms: Vec<i64> = Vec::new();
        for j in 0..n {
            if !ok[j] {
                if ms.len() >= k {
                    ms.sort();
                    mins.extend_from_slice(&ms[0..ms.len()-k+1]);
                }
                ms.clear();
            } else {
                ms.push(a[j]);
            }
        }
        if ms.len() >= k {
            ms.sort();
            mins.extend_from_slice(&ms[0..ms.len()-k+1]);
        }
        if mins.len() < q {
            break;
        }
        mins.sort();
        ans = std::cmp::min(ans, mins[q-1]-mins[0]);
        ok[ai[i].1] = false;
        //println!("{} {:?} {}", i, mins, ans);
    }

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