Implement an in-memory key-field-value DB with TTL

## In-Memory DB with TTL + Scan + Backup/Restore Implement an in-memory database storing records by `(key, field) -> value` with optional TTL. ### Data model / rules - `key` and `field` are strings. - `value` is a string (or integer; choose one and be consistent). - Each stored `(key, field)` has an expiration time `expire_at`. - If a value is set without TTL, `expire_at = +∞`. - A value is **visible** at query time `t` iff `t < expire_at`. ### API 1. `set(key, field, value, timestamp) -> void` - Store `(value, +∞)`. 2. `set_with_ttl(key, field, value, timestamp, ttl) -> void` - Store `(value, timestamp + ttl)`. 3. `get(key, field, timestamp) -> value | null` - Return `null` if missing or expired at `timestamp`. 4. `delete(key, field, timestamp) -> bool` - Delete the field (regardless of TTL). - Return `false` if `(key, field)` does not exist; otherwise `true`. 5. `scan(key, timestamp) -> list<(field, value)>` - Return all non-expired fields for `key` at `timestamp`. - Sort results by `field` ascending. 6. `scan_with_prefix(key, prefix, timestamp) -> list<(field, value)>` - Like `scan`, but only include `field`s that start with `prefix`. 7. `backup(timestamp) -> void` - Persist a full snapshot of the DB state at `timestamp`. 8. `restore(timestamp, restore_to_time) -> void` - Restore DB state from the **most recent** backup with `backup_time <= restore_to_time`. - If no such backup exists, restore to an empty DB. ### Notes - Assume timestamps are integers. - Assume up to ~1e5 operations; aim for efficient scans and correct TTL handling.