You are given a 0-indexed array `arr` consisting of `n` positive integers, and a positive integer `k`.

The array `arr` is called K-increasing if `arr[i-k] <= arr[i]` holds for every index `i`, where `k <= i <= n-1`.

- For example, `arr = [4, 1, 5, 2, 6, 2]` is K-increasing for `k = 2` because:
  - `arr[0] <= arr[2] (4 <= 5)`
  - `arr[1] <= arr[3] (1 <= 2)`
  - `arr[2] <= arr[4] (5 <= 6)`
  - `arr[3] <= arr[5] (2 <= 2)`
- However, the same `arr` is not K-increasing for `k = 1` (because `arr[0] > arr[1]`) or `k = 3` (because `arr[0] > arr[3]`).

In one operation, you can choose an index `i` and change `arr[i]` into any positive integer.

Return the minimum number of operations required to make the array K-increasing for the given `k`.

Example 1:

    Input: arr = [5,4,3,2,1], k = 1
    Output: 4
    Explanation:
    For k = 1, the resultant array has to be non-decreasing.
    Some of the K-increasing arrays that can be formed are [5,6,7,8,9], [1,1,1,1,1], [2,2,3,4,4]. All of them require 4 operations.
    It is suboptimal to change the array to, for example, [6,7,8,9,10] because it would take 5 operations.
    It can be shown that we cannot make the array K-increasing in less than 4 operations.

Example 2:

    Input: arr = [4,1,5,2,6,2], k = 2
    Output: 0
    Explanation:
    This is the same example as the one in the problem description.
    Here, for every index i where 2 <= i <= 5, arr[i-2] <= arr[i].
    Since the given array is already K-increasing, we do not need to perform any operations.

Example 3:

    Input: arr = [4,1,5,2,6,2], k = 3
    Output: 2
    Explanation:
    Indices 3 and 5 are the only ones not satisfying arr[i-3] <= arr[i] for 3 <= i <= 5.
    One of the ways we can make the array K-increasing is by changing arr[3] to 4 and arr[5] to 5.
    The array will now be [4,1,5,4,6,5].
    Note that there can be other ways to make the array K-increasing, but none of them require less than 2 operations.

Constraints:

- `1 <= arr.length <= 105`
- `1 <= arr[i], k <= arr.length`