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

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`