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.

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.

Constraints

• $1 \leq N,A,B \leq 3\times 10^5$
• All input values are integers.

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

见题面 Input 部分

见题面 Output 部分