You are given two integer arrays nums and cost of equal length, and an integer k.

You need to partition the array nums into one or more non-empty contiguous subarrays.

Suppose the array is divided into $m$ subarrays. For the $j^{ ext{th}}$ subarray (where $1 \leq j \leq m$) ending at index $i_j$ and starting after the end of the previous subarray:
The cost of this $j^{ ext{th}}$ subarray is calculated as:
$(\sum_{t=0}^{i_j} ext{`nums`}[t] + ext{`k`} imes j) imes ( ext{sum of `cost` in the } j^{ ext{th}} ext{ subarray})$

Return the minimum total cost to divide the array into subarrays.

Constraints:

• $1 \leq$ nums.length $\leq 1000$

• cost.length $==$ nums.length

• $1 \leq$ nums[i], cost[i] $\leq 1000$

• $1 \leq$ k $\leq 1000$

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.