G. Greedy Subsequencestime limit per test2 secondsmemory limit per test256 megabytesinputstandard inputoutputstandard outputFor 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.InputThe 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.OutputPrint 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.ExamplesInput
6 4
1 5 2 5 3 6
Output
2 2 3 
Input
7 6
4 5 2 5 3 6 6
Output
3 3 
NoteIn 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]). 
6 4
1 5 2 5 3 6

2 2 3  
['data structures', 'dp', 'trees', '*2400']