GOOGLE interview question

You are given a list of intervals, each with a start and end time, and they don't overlap. You also have a new interval to add. Insert the new interval into the list in the correct order, and if it overlaps with any intervals, merge them together. Return the updated list of intervals.

[leetcode](https://leetcode.com/problems/insert-interval/description/)

Start by reviewing the repository's existing Java interview-question entries and the linked LeetCode statement. Confirm whether this issue expects a question entry or an implementation; done should follow the repository's established format and represent the stated interval insertion and merging behavior.

Written by the indexing model from the issue text.