Given an array of positive integers nums, determine if it is possible to choose a subset of nums, multiply each selected integer by an integer, and sum the results to obtain $1$.

Return true if such a selection exists, or false otherwise.

Constraints:

• $1 \le$ nums.length $\le 10^5$

• $1 \le$ nums[i] $\le 10^9$

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.