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G. Greedy Subsequences
time limit per test
2 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output

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.

Input

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 $$$a$$$.

Output

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.

Examples
Input
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 
Note

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 $$$2, 3, 5$$$ ($$$[c_2, c_3, c_5] = [2, 5, 6]$$$).