This problem is a Mooshak version of a CSES problem with relaxed time limit (3s) so that Java solutions with the desired complexity can pass.


[PC005] Sliding Window Cost

You are given an array of \(n\) integers. Your task is to calculate for each window of \(k\) elements, from left to right, the minimum total cost of making all elements equal.

You can increase or decrease each element with cost \(x\) where \(x\) is the difference between the new and the original value. The total cost is the sum of such costs.

Input

The first input line contains two integers \(n\) and \(k\): the number of elements and the size of the window.

Then there are \(n\) integers \(x_1,x_2\ldots,x_n\)​: the contents of the array.

Output

Output \(n−k+1\) values: the costs.

Don't forget to print a new line in the end and in this problem all printed integers should have a space after it, including the last number in the output.

Constraints

Example Input Example Output
8 3
2 4 3 5 8 1 2 1
2 2 5 7 7 1

Competitive Programming (CC3032) 2024/2025
DCC/FCUP - University of Porto