Sliding Cost

• Time limit: 1.00 s
• Memory limit: 512 MB

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.

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