CF1773L Lisa's Sequences

Lisa loves playing with the sequences of integers. When she gets a new integer sequence $ a_i $ of length $ n $ , she starts looking for all monotone subsequences. A monotone subsequence $ [l, r] $ is defined by two indices $ l $ and $ r $ ( $ 1 \le l < r \le n $ ) such that $ \forall i = l, l+1, \ldots, r-1: a_i \le a_{i+1} $ or $ \forall i = l, l+1, \ldots, r-1: a_i \ge a_{i+1} $ . Lisa considers a sequence $ a_i $ to be boring if there is a monotone subsequence $ [l, r] $ that is as long as her boredom threshold $ k $ , that is when $ r - l + 1 = k $ . Lucas has a sequence $ b_i $ that he wants to present to Lisa, but the sequence might be boring for Lisa. So, he wants to change some elements of his sequence $ b_i $ , so that Lisa does not get bored playing with it. However, Lucas is lazy and wants to change as few elements of the sequence $ b_i $ as possible. Your task is to help Lucas find the required changes.

The first line of the input contains two integers $ n $ and $ k $ ( $ 3 \le k \le n \le 10^6 $ ) — the length of the sequence and Lisa's boredom threshold. The second line contains $ n $ integers $ b_i $ ( $ 1 \le b_i \le 99\,999 $ ) — the original sequence that Lucas has.

On the first line output an integer $ m $ — the minimal number of elements in $ b_i $ that needs to be changed to make the sequence not boring for Lisa. On the second line output $ n $ integers $ a_i $ ( $ 0 \le a_i \le 100\,000 $ ), so that the sequence of integers $ a_i $ is not boring for Lisa and is different from the original sequence $ b_i $ in exactly $ m $ positions.