Design a time-versioned key-value store and find common free time

You are given two coding tasks. ## Task 1: Time-versioned key-value store Design an in-memory data structure that supports: - `set(key, value, timestamp)`: store the string `value` for string `key` at integer `timestamp`. - `get(key, timestamp) -> value`: return the value associated with `key` at the largest stored timestamp `t` such that `t <= timestamp`. If there is no such timestamp (or `key` was never set), return an empty string. **Notes / assumptions** - Multiple `set` operations may occur for the same `key` at different timestamps. - Timestamps are integers; you may assume `set` calls for a given key arrive in non-decreasing timestamp order unless stated otherwise. ## Task 2: Find time slots when everyone is available You are given schedules for `N` people. Each person’s schedule is a list of **busy** time intervals during the day. - Each busy interval is `[start, end)` with `start < end`. - For each person, their busy intervals are non-overlapping and sorted by start time. Return all time intervals (also as `[start, end)`) when **everyone is available** (i.e., when no one is busy). Only include intervals with positive length. **Clarify in your solution** - What overall day bounds apply (e.g., `[0, 24*60)` minutes) and how to handle availability outside provided busy intervals. ### Input / Output format (for Task 2) - **Input:** `schedules: List[List[Interval]]`, where `schedules[i]` is person `i`’s busy intervals. - **Output:** `List[Interval]` representing common free time intervals.