**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