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