You are given two integer arrays arr and brr of equal length, and an integer k.

You can perform the following operations on arr:

• Split arr into contiguous subarrays and rearrange them in any order. This operation costs k in total and can be performed at most once.

• Increment or decrement any element of arr by $1$. The cost of each such modification is $1$.

Return the minimum total cost required to make arr equal to brr.

Constraints:

• $1 \leq$ arr.length $=$ brr.length $\leq 10^5$

• $0 \leq$ k $\leq 2 imes 10^{10}$

• $-10^5 \leq$ arr[i] $\leq 10^5$

• $-10^5 \leq$ brr[i] $\leq 10^5$

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.