Service Desk Patience

Simulate a help desk in which customers wait in a single line, give up if they wait too long, and agents take regular breaks.

The desk has agents agents numbered 0 to agents - 1. customers[i] = [arrival, service, patience] arrives at time arrival, needs service ticks of an agent's time, and will wait at most patience ticks. Everyone who is waiting is in one first-in-first-out line. Time moves in whole ticks starting at 0, and at every tick t the following happens in this order:

1. Arrivals. Customers whose arrival is t join the back of the line, in input order if several arrive at the same tick.
2. Service. Go through the agents in increasing order of number. Each agent who is free at t takes the customer at the front of the line, if any, and starts serving them at t. (An agent is free at t if they are not serving anyone and not on a break, with the rule below.) The customer's start time is t.
3. Abandonment. Every customer still in the line whose arrival + patience equals t gives up and leaves the line. A customer with patience 0 therefore leaves at their arrival tick unless an agent could take them in step 2.

A customer served from t for service ticks leaves the agent at t + service (so that agent is free again at tick t + service). An agent also counts the customers they have served: when an agent starts serving their cycle-th customer since their last break (that is, cycle, 2 * cycle, ... customers in total), they go on a break as soon as they finish that customer. The break lasts rest ticks, so the agent is free again at t + service + rest. With rest = 0 there is no break. Customers who give up never count as served.

Input: agents, cycle and rest, integers, and customers, a list of [arrival, service, patience] triples.

Output: a list with one entry per customer, in input order: [agent, start] for a customer who was served, or [-1, -1] for one who gave up.