P7957 [COCI 2014/2015 #6] KRATKI

We are all very familiar with the “Longest Monotone Subsequence” problem: > Given a sequence of length $n$, you need to find the length of its LMS (i.e., the longest monotone subsequence). > **Note** that here “LMS” means **the longer one** between the increasing subsequence and the decreasing subsequence. > That is, you need to take the maximum of the lengths of LIS and LDS. Now you need to solve an inverse problem of LMS.

Given the length $n$ of a sequence. You need to construct a permutation of length $n$ such that its LMS length is $k$.

A single line with two integers $n, k$.

If there is no solution, output $\texttt{-1}$. Otherwise, output one line with $n$ integers, the sequence you constructed. **If there are multiple solutions, output any one.**

#### Explanation of Sample 1 The **LMS** of $\{1,4,2,3\}$ is $\{1,2,3\}$, with length $3$, which meets the requirement. #### Constraints **This problem uses Special Judge.** For $100\%$ of the testdata, $1 \le k \le n \le 10^6$. #### Notes According to the original settings, the full score is 120 points. Translated from **[COCI 2014-2015](https://hsin.hr/coci/archive/2014_2015/)** [Contest #6](https://hsin.hr/coci/archive/2014_2015/contest6_tasks.pdf) Task D _**KRATKI**_. Since the original testdata lacked some special cases, testdata #11 has been added to this problem. If you do not pass it, you will get 120 Unaccept. Translated by ChatGPT 5