A12390. Greedy Subsequences

For some array $c$ , let's denote a greedy subsequence as a sequence of indices $p_1$ , $p_2$ , ..., $p_l$ such that $1 \le p_1 < p_2 < \dots < p_l \le |c|$ , and for each $i \in [1, l - 1]$ , $p_{i + 1}$ is the minimum number such that $p_{i + 1} > p_i$ and $c[p_{i + 1}] > c[p_i]$ .

You are given an array $a_1, a_2, \dots, a_n$ . For each its subsegment of length $k$ , calculate the length of its longest greedy subsequence.

The first line contains two integers $n$ and $k$ ( $1 \le k \le n \le 10^6$ ) — the length of array $a$ and the length of subsegments.

The second line contains $n$ integers $a_1, a_2, \dots, a_n$ ( $1 \le a_i \le n$ ) — array $a$ .

Print $n - k + 1$ integers — the maximum lengths of greedy subsequences of each subsegment having length $k$ . The first number should correspond to subsegment $a[1..k]$ , the second — to subsegment $a[2..k + 1]$ , and so on.

In the first example:

- $[1, 5, 2, 5]$ — the longest greedy subsequences are $1, 2$ ( $[c_1, c_2] = [1, 5]$ ) or $3, 4$ ( $[c_3, c_4] = [2, 5]$ ).
- $[5, 2, 5, 3]$ — the sequence is $2, 3$ ( $[c_2, c_3] = [2, 5]$ ).
- $[2, 5, 3, 6]$ — the sequence is $1, 2, 4$ ( $[c_1, c_2, c_4] = [2, 5, 6]$ ).

In the second example:

- $[4, 5, 2, 5, 3, 6]$ — the longest greedy subsequences are $1, 2, 6$ ( $[c_1, c_2, c_6] = [4, 5, 6]$ ) or $3, 4, 6$ ( $[c_3, c_4, c_6] = [2, 5, 6]$ ).
- $[5, 2, 5, 3, 6, 6]$ — the subsequence is $2, 3, 5$ ( $[c_2, c_3, c_5] = [2, 5, 6]$ ).