Given an integer array nums of unique positive integers, find the largest subset such that every pair of elements (a, b) in this subset satisfies either a % b == 0 or b % a == 0.

If multiple valid subsets have the maximum size, return any one of them.

Note: The elements in the subset may be returned in any order.

Constraints:

• $1 \leq$ nums.length $\leq 1000$

• $1 \leq$ nums[i] $\leq 2 imes 10^9$

• All integers in nums are unique.

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.