You are given a $0$ indexed integer array arr and an integer k. The array is circular, which means the element immediately following the last element is arr[0], and the element immediately preceding arr[0] is the last element.

In a single operation, you can select any index i and increment or decrement arr[i] by $1$.

Return the minimum number of operations required to make the sum of every contiguous subarray of length k equal.

Note: A subarray of length k starting at index i consists of the elements from arr[i] up to arr[(i + k - 1) % arr.length].

Constraints:

• $1 \leq$ k $\leq$ arr.length $\leq 10^5$

• $1 \leq$ arr[i] $\leq 10^9$

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.