Pondo Minimum

Problem Statement

Pondo has an array of integers $a$ of length $n$ as well as an integer $k$ . He wishes to form the array $b$ of length $n - k + 1$ by taking taking all the subarrays of length $k$ and taking their minimums, i.e. $b_i = \min_{0\leq j \leq k-1}(a_{i+j})$ .

Input Format

Your first line will contain two space-separated integers $n$ and $k$ . Your next line will contain $n$ integers representing $a$ .

Output Format

You should output $n - k + 1$ integers representing $b$ .

Constraints

$1 \leq n \leq 10^5$
$1 \leq a_i \leq 10^9$

Sample Cases

Input 1

10 5
10 9 8 7 6 5 4 3 2 1

Output 1

6 5 4 3 2 1

Input 2

10 4
684839257 302743967 551107459 232951579 483565957 241081121 553311714 547334166 25972405 997164454

Output 2

232951579 232951579 232951579 232951579 241081121 25972405 25972405