Design a delivery cost system

Design an object-oriented Delivery Cost System. Each driver registers with an hourly rate. The system must support: RegisterDriver(driverId, hourlyRate) to add/update a driver; RecordDelivery(driverId, startTime, endTime) to record a delivery; getTotalCost() to return the total cost across all recorded deliveries, computed as the sum over deliveries of hourlyRate(driverId) × duration. Define whether times are inclusive/exclusive and how to handle partial hours and rounding. Implement payUpTo(timestamp) to mark all accrued costs up to the given timestamp as paid, splitting overlapping deliveries so only the portion up to timestamp is paid; and getTotalUnpaid() to return the remaining unpaid amount. Provide class design, core data structures, method signatures, and discuss idempotency, time zones, numeric precision, and time/space complexity.