408305: GYM103091 E Longest Sequences

The Stanford Axe Committee, which is in charge of guarding the Stanford Axe, is holding tryouts for new members in preparation for the annual faceoff against Cal. Applicants are numbered 1 through $$$N$$$ and come to try out. As the committee lines everyone up to call them in for an interview, the Stanford tree waltzes by and issues the first challenge:

Rearrange yourselves such that the longest increasing subsequence is of length $$$X$$$ and the longest decreasing subsequence must be of length $$$Y$$$, or say it's impossible.

Can you help the applicants pass their first test?

Definition: A subsequence of an array is defined as any array that can be reachable by deleting some number of elements. For example, if we have array [4, 2, 7, 5, 1], valid subsequences include [4, 7, 1] and [2, 7], but not [2, 4] or [3, 7, 5].

The input consists of $$$3$$$ space separated integers, $$$N$$$, $$$X$$$, and $$$Y$$$ ($$$1 \leq X, Y \leq N \leq 10^3$$$).

Output one line containing your permutation of the integers $$$1$$$ to $$$N$$$. If there is no such permutation, output $$$-1$$$.

10 4 5

7 6 3 2 5 9 10 4 1 8

5 1 1

-1

Given a sequence of elements, a subsequence is a subset of these elements in the same order. An increasing subsequence means every element is greater than the element before it. For example, the largest increasing subsequence of $$$1, 2, 5, 4, 3, 6, 9, 7, 8$$$ is of length 6, such as $$$1, 2, 3, 6, 7, 8$$$.