#ARC091C. [ARC091E] LISDL

[ARC091E] LISDL

Score : 700700 points

Problem Statement

Determine if there exists a sequence obtained by permuting 1,2,...,N1,2,...,N that satisfies the following conditions:

  • The length of its longest increasing subsequence is AA.
  • The length of its longest decreasing subsequence is BB.

If it exists, construct one such sequence.

Notes

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

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

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

Constraints

  • 1N,A,B3×1051 \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:

NN AA BB

Output

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

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

5 3 2
2 4 1 5 3

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

7 7 1
1 2 3 4 5 6 7
300000 300000 300000
-1