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CSES Problem Set

Sliding Cost


Task | Statistics


CSES - 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 each element the same.

You can increase or decrease each element, and the cost is $x$ where $x$ is the difference between the new and 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
Example

Input:
8 3
2 4 3 5 8 1 2 1


Output:
2 2 5 7 7 1