Volunteer availability

Find the times of the week when enough volunteers are available to run the community pantry.

Each element of availability describes one volunteer: day sections separated by ;, each "<Day> <range>,<range>,..." where <Day> is Mon, Tue, Wed, Thu, Fri, Sat or Sun and a range is "HH:MM-HH:MM" (24-hour; 24:00 is allowed as an end). A day may appear in several sections, and the ranges of one volunteer may overlap or touch each other. An empty string means a volunteer with no availability.

A range covers the minutes from its start up to, but not including, its end. A volunteer counts once in any minute they are covered, however many of their ranges include it.

Report the blocks of time in which at least k different volunteers are available. A block is maximal: it stretches over every consecutive minute of the same day that has at least k volunteers, even if the volunteers change along the way. Blocks never continue across midnight, so one ending at 24:00 and one starting at 00:00 the next day are separate. Drop blocks shorter than min_minutes minutes (a block of exactly min_minutes is kept).

Input: availability, a list of strings; k and min_minutes, integers.

Output: a list of strings "<Day> HH:MM-HH:MM", one per block, ordered by day of the week (Mon first) and then by start time. If there are no blocks, return [].