Recurring appointment scheduling with different intervals

I am trying to set up an appointment booking system. They will be recurring at different intervals. I would like only the time/dates available to show so that it cannot be double booked.

Time slots: 500, 510, 520

Start dates: 3/21, 4/4, 4/18, 5/2

Occurrence: daily, M-F

Session durations in weeks: 2, 4, 6

For example, if someone books 5:00 on 3/21 for 6 weeks the next available spot for 5:00 is 5/2. If 5:10 is booked on 3/21 for 4 weeks the next spot for 5:10 is 4/18.

If possible I would like to not have any gaps in there as well but am more concerned with the availability and having them show up as recurring events in a calendar.

Any help is greatly appreciated!!!

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