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

The array arr is defined as $k$ increasing if arr[i - k] $\leq$ arr[i] holds for all indices i such that $k \leq$ i $<$ arr.length.

In a single operation, you can choose any index i and replace arr[i] with any positive integer.

Return the minimum number of operations required to make arr $k$ increasing.

Constraints:

• $1 \leq$ arr.length $\leq 10^5$

• $1 \leq$ arr[i], k $\leq$ arr.length

Now, let’s take a moment to make sure you’ve correctly understood the problem. The quiz below helps you check if you’re solving the correct problem:

We have a game for you to play. Rearrange the logical building blocks to develop a clearer understanding of how to solve this problem.

Implement your solution in the following coding playground.