Design a Delivery Driver Salary System

You are designing an in-memory payroll service that calculates and pays delivery drivers based on their worked time. The system must provide accurate cost accruals, support partial payments up to a boundary time, and avoid double-paying overlapping work intervals.

Assumptions (make minimal changes if needed):

• Time values are Unix timestamps in seconds; intervals use half-open semantics [start_time, end_time).
• Each driver has a constant USD hourly rate after Add_driver (rate changes are out of scope but can be added as an extension).
• Record_delivery only records completed deliveries (end_time > start_time). Deliveries can be inserted out of chronological order.
• For a given driver, overlapping or adjacent delivery intervals should be merged so the driver is not double-paid for the same minute twice.
• Monetary values are tracked in integer cents to avoid floating-point error.

APIs to support:

1. Add_driver(driver_id, usd_hourly_rate)
2. Record_delivery(driver_id, start_time, end_time)
3. Get_Total_Cost()
4. Pay_Up_To(pay_time)
5. Total_Cost_Unpaid()

Explain:

• Data structures to store drivers, delivery intervals, rates, and payments.
• State-mutation logic for each API, including handling overlaps and partial payments.
• Object-oriented design that enables accurate and efficient payroll computation, plus complexity trade-offs.