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.

Note

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.