Find earliest common meeting slot

Given K participants' calendars, each a list of busy intervals [start, end) within a working window [workStart, workEnd], and a meeting duration d minutes, return the earliest interval [t, t + d) that is within every participant's working window and does not overlap any busy interval. Times are integers in minutes from 00:00. Busy intervals are non-overlapping and sorted within each calendar. If no slot exists, return an empty list. Design an algorithm, state its time and space complexity, and describe how you would handle unsorted or overlapping inputs and large K efficiently.