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 (1.42.0) (judge verdict: Accepted)

use proconio::{
   fastout, input,
   marker::{Bytes, Chars, Isize1, Usize1},
};

#[fastout]
fn main() {
   input! {
      n:usize,a:usize,b:usize
   }
   if a + b > n + 1 || a * b < n {
      println!("-1");
      return;
   }
   let mut remove = a * b - n;
   for i in (1..=b).rev() {
      print!("{} ", i);
   }
   let mut start = b;
   let mut prev = b;
   let mut count = b;
   while count < n {
      start = if start + b <= start + remove {
         start + 1
      } else {
         start + b - remove
      };
      remove -= b + prev - start;
      for i in (prev + 1..=start).rev() {
         print!("{} ", i);
         count += 1;
      }
      prev = start;
   }
   println!("");
}