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

In one operation, you can choose an integer $x$ such that $-k \leq x \leq k$ for each index i and update nums[i] to nums[i] + x. You can apply this operation at most once for each element.

The score of the array nums is defined as the difference between the maximum element and the minimum element in nums.

Return the minimum possible score of nums after modifying each element.

Constraints:

• $1 \leq$ nums.length $\leq 10^4$

• $0 \leq$ nums[i] $\leq 10^4$

• $0 \leq$ k $\leq 10^4$

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.