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)

macro_rules ! input { ( source = $ s : expr , $ ( $ r : tt ) * ) => { let mut iter = $ s . split_whitespace ( ) ; input_inner ! { iter , $ ( $ r ) * } } ; ( iter = $ iter : ident , $ ( $ r : tt ) * ) => { let s = { use std :: io :: Read ; let mut s = String :: new ( ) ; std :: io :: stdin ( ) . read_to_string ( & mut s ) . unwrap ( ) ; s } ; let mut $ iter = s . split_whitespace ( ) ; input_inner ! { $ iter , $ ( $ r ) * } } ; ( $ ( $ r : tt ) * ) => { let s = { use std :: io :: Read ; let mut s = String :: new ( ) ; std :: io :: stdin ( ) . read_to_string ( & mut s ) . unwrap ( ) ; s } ; let mut iter = s . split_whitespace ( ) ; input_inner ! { iter , $ ( $ r ) * } } ; }
macro_rules ! input_inner { ( $ iter : expr ) => { } ; ( $ iter : expr , ) => { } ; ( $ iter : expr , mut $ var : ident : $ t : tt $ ( $ r : tt ) * ) => { let mut $ var = read_value ! ( $ iter , $ t ) ; input_inner ! { $ iter $ ( $ r ) * } } ; ( $ iter : expr , mut $ var : ident $ ( $ r : tt ) * ) => { input_inner ! { $ iter , mut $ var : usize $ ( $ r ) * } } ; ( $ iter : expr , $ var : ident : $ t : tt $ ( $ r : tt ) * ) => { let $ var = read_value ! ( $ iter , $ t ) ; input_inner ! { $ iter $ ( $ r ) * } } ; ( $ iter : expr , $ var : ident $ ( $ r : tt ) * ) => { input_inner ! { $ iter , $ var : usize $ ( $ r ) * } } ; }
macro_rules ! read_value { ( $ iter : expr , ( $ ( $ t : tt ) ,* ) ) => { ( $ ( read_value ! ( $ iter , $ t ) ) ,* ) } ; ( $ iter : expr , [ $ t : tt ; $ len : expr ] ) => { ( 0 ..$ len ) . map ( | _ | read_value ! ( $ iter , $ t ) ) . collect ::< Vec < _ >> ( ) } ; ( $ iter : expr , { chars : $ base : expr } ) => { read_value ! ( $ iter , String ) . chars ( ) . map ( | c | ( c as u8 - $ base as u8 ) as usize ) . collect ::< Vec < usize >> ( ) } ; ( $ iter : expr , { char : $ base : expr } ) => { read_value ! ( $ iter , { chars : $ base } ) [ 0 ] } ; ( $ iter : expr , chars ) => { read_value ! ( $ iter , String ) . chars ( ) . collect ::< Vec < char >> ( ) } ; ( $ iter : expr , char ) => { read_value ! ( $ iter , chars ) [ 0 ] } ; ( $ iter : expr , usize1 ) => { read_value ! ( $ iter , usize ) - 1 } ; ( $ iter : expr , $ t : ty ) => { $ iter . next ( ) . unwrap ( ) . parse ::<$ t > ( ) . unwrap ( ) } ; }
// pub mod at {
//     use std;
// }
// use at::*;
fn main() {
    input! { n, k, q, a: [usize; n] };
    let mut b = a
        .iter()
        .enumerate()
        .map(|(i, &x)| (x, i))
        .collect::<Vec<_>>();
    b.sort();
    let mut ans = 1_001_001_001;
    'outer: for i in 0..n - q + 1 {
        let l = b[i].0;
        let r = b[i + q - 1].0;
        let mut rem = 0;
        for j in i..i + q {
            if b[j].0 == r {
                rem += 1;
            }
        }
        let mut c1 = 0isize;
        let mut c2 = 0isize;
        let mut c3 = 0isize;
        for j in 0..n {
            if l <= a[j] {
                c1 += 1;
                if a[j] < r {
                    c2 += 1;
                }
                if a[j] == r {
                    c3 += 1;
                }
            } else {
                if c2 > 0 && c1 - c2 + 1 < k as isize {
                    continue 'outer;
                }
                if c1 - c2 + 1 - k as isize > 0 {
                    if c3 > 0 {
                        rem -= std::cmp::min(c3, c1 - c2 + 1 - k as isize);
                    }
                }
                c1 = 0;
                c2 = 0;
                c3 = 0;
            }
        }
        if c2 > 0 && c1 - c2 + 1 < k as isize {
            continue 'outer;
        }
        if c1 - c2 + 1 - k as isize > 0 {
            if c3 > 0 {
                rem -= std::cmp::min(c3, c1 - c2 + 1 - k as isize);
            }
        }
        if rem > 0 {
            continue 'outer;
        }
        ans = std::cmp::min(ans, b[i + q - 1].0 - b[i].0);
    }
    println!("{}", ans);
}