Design a meeting scheduler API

## Meeting Scheduler (OOD + data structures) Design and implement an in-memory **meeting scheduler** that stores existing bookings and can answer availability queries. You must support two operations: 1. **`addBooking(start, duration)`** - Adds a booking covering the time interval **[start, start + duration)**. - Assume `start` is an integer timestamp (e.g., minutes) and `duration > 0`. 2. **`earliestStart(requestStart, duration)`** - Given a desired start time and meeting duration, return the **earliest time `t >= requestStart`** such that the interval **[t, t + duration)** does **not overlap** any existing booking. ### Overlap definition Two bookings overlap if their half-open intervals intersect. For example, [10, 20) and [20, 30) do **not** overlap. ### Follow-ups - Can you make `earliestStart` run in **O(N)** time (where N is the number of bookings) by changing how you store data? - Can you support faster than O(N) (e.g., **O(log N)** insert/query) with a better data structure? - Make the scheduler **thread-safe**. Assume the workload is **write-heavy**. State any assumptions you need (e.g., whether `addBooking` is guaranteed not to conflict, or whether conflicts should be rejected/merged).