Rate-Limited Message Sender

A system sends messages at a rate of at most one message every C seconds. When a message arrives at time T, it is placed in a queue. If the sender is busy, the message waits. The sender processes the next message in the queue as soon as C seconds have passed since the START of the previous message's transmission (or immediately if the sender is idle). Given C and a sequence of (Name, ArrivalTime), output the time each message starts being sent. Example: Input: 5 MsgA 0 MsgB 1 MsgC 2 Output: MsgA:0 MsgB:5 MsgC:10