200912: [AtCoder]ARC091 E - LISDL

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