Problem:
Score : 700 points

Problem Statement

Determine if there exists a sequence obtained by permuting 1,2,...,N that satisfies the following conditions:

The length of its longest increasing subsequence is A.

The length of its longest decreasing subsequence is B.

If it exists, construct one such sequence.

Notes

A subsequence of a sequence P is a sequence that can be obtained by extracting some of the elements in P without changing the order.

A longest increasing subsequence of a sequence P is a sequence with the maximum length among the subsequences of P that are monotonically increasing.

Similarly, a longest decreasing subsequence of a sequence P is a sequence with the maximum length among the subsequences of P that are monotonically decreasing.

Constraints

1 \leq N,A,B \leq 3\times 10^5

All input values are integers.

Input

Input is given from Standard Input in the following format:

N A B

Output

If there are no sequences that satisfy the conditions, print -1.

Otherwise, print N integers. The i-th integer should be the i-th element of the sequence that you constructed.

Sample Input 1

5 3 2

Sample Output 1

2 4 1 5 3

One longest increasing subsequence of this sequence is {2,4,5}, and one longest decreasing subsequence of it is {4,3}.

Sample Input 2

7 7 1

Sample Output 2

1 2 3 4 5 6 7

Sample Input 3

300000 300000 300000

Sample Output 3

-1

Solution in Rust (1.15.1) (judge verdict: Accepted)

use std::cmp::{max, min};

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

fn reads<T>() -> Vec<T>
where
    T: std::str::FromStr,
    <T as std::str::FromStr>::Err: std::fmt::Debug,
{
    read_line()
        .split_whitespace()
        .map(|w| w.parse().unwrap())
        .collect()
}

fn main() {
    let (n, a, b): (i64, i64, i64) = {
        let t = reads();
        (t[0], t[1], t[2])
    };

    let rep = (n + a - 1) / a;

    if rep > b || a + b - 1 > n {
        println!("-1");
        return;
    }

    let mut ans: Vec<i64> = vec![];

    for i in 0..a {
        ans.push(i);
    }

    let mut base = -1;
    let mut rest = n - a;
    let mut rest_b = b - 1;
    while (rest + a - 1) / a < rest_b {
        rest -= 1;
        rest_b -= 1;
        ans.push(base);
        base -= 1;
    }

    while rest > 0 {
        let c = min(a, rest);
        for i in 0..c {
            ans.push(base - c + 1 + i);
        }
        base -= c;
        rest -= c;
    }

    assert_eq!(n as usize, ans.len());

    for i in 0..n {
        if i > 0 {
            print!(" ");
        }
        print!("{}", ans[i as usize] - base);
    }
    println!();
}