Lisa's Sequences

5000ms

1048576K

Description:

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.

Input:

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.

Output:

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.

Sample Input:

5 3
1 2 3 4 5

Sample Output:

2
1 0 3 0 5

Sample Input:

6 3
1 1 1 1 1 1

Sample Output:

3
1 100000 0 1 0 1

Sample Input:

6 4
1 1 4 4 1 1

Sample Output:

1
1 1 4 0 1 1

Sample Input:

6 4
4 4 4 2 2 2

Sample Output:

2
4 4 0 2 0 2

Sample Input:

6 4
4 4 4 3 4 4

Sample Output:

1
4 4 100000 3 4 4

Sample Input:

8 4
2 1 1 3 3 1 1 2

Sample Output:

2
2 1 1 3 0 1 0 2

Sample Input:

10 4
1 1 1 2 2 1 1 2 2 1

Sample Output:

2
1 1 100000 2 2 100000 1 2 2 1

Sample Input:

7 5
5 4 4 3 4 4 4

Sample Output:

0
5 4 4 3 4 4 4

Sample Input:

10 10
1 1 1 1 1 1 1 1 1 1

Sample Output:

1
1 1 1 1 1 1 1 1 0 1

Informação

Provedor Codeforces

Código CF1773L