You are given an integer array nums and an integer k.

You are allowed to perform the following operation on each index at most once: replace nums[i] with any integer in the range $[$nums[i] $- k,$ nums[i] $+ k]$.

Return the maximum possible number of distinct elements in nums after applying these operations.

Constraints:

• $1 \leq$ nums.length $\leq 10^5$

• $1 \leq$ nums[i] $\leq 10^9$

• $0 \leq$ k $\leq 10^9$

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.