You are given an array of unique positive integers nums and a positive integer k.

A subset of nums is called $k$ free if it does not contain any pair of elements with an absolute difference equal to k.

Return the total number of $k$ free subsets of nums.

Note: The empty set is considered a valid subset.

Constraints:

• $1 \leq$ nums.length $\leq 50$

• $1 \leq$ nums[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.