Sliding Window Inversions

You are given an array of n integers. Your task is to calculate the number of inversions in each window of k elements, from left to right. An inversion is a pair of elements where the left element is larger than the right element.

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

Print n-k+1 values: the numbers of inversions.

Constraints

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

$1 \le x_i \le 10^9$

Example

Input

8 3
1 2 3 2 5 2 4 4

Output

0 1 1 1 2 0