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 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

Constraints

$1 \le k \le n \le 2 \cdot 10^5$

$1 \le x_i \le 10^9$

Example

Input

8 3
2 4 3 5 8 1 2 1

Output

2 2 5 7 7 1