The unbalance of an array ~B~ is the maximum value of the array minus the minimum. Given an array ~A~ of length ~N~, can you find the unbalance of every subarray of length ~K~?

A subarray of an array ~A~ is defined as a set of consecutive elements in ~A~

Constraints

~1\le N\le 10^5~

~1\le K\le N~

~1\le A_i\le 10^6~

Input Specification

The first line contains two integers: ~N~ and ~K~.

The second line contains ~N~ integers, the elements of ~A~.

Output Specification

~N-K+1~ integers, the ~i~-th of which is the unbalance of the subarray from the ~i~-th index to the ~i+k-1~-th index.

Sample Input

5 3
2 6 4 4 1

Sample Output

4 2 3

Sample Explanation

The three subarrays of length ~3~ are: ~[2,6,4]~, ~[6,4,4]~, and ~[4,4,1]~.

The first one has a maximum of ~6~ and a minimum of ~2~, so its unbalance is ~6-2=4~ The second one has an unbalance of ~6-4=2~ And the third has an unbalance of ~4-1=3~