Needed subset draws to get all elements with a given probability

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I have a set of N elements. I draw (without replacement) a subset of M elements, then replace it.

What value M do I need, to have a probability greater than p to draw all N elements within X subset draws?

I found the answer when M is 1, but I am not sure how to adapt that in a general case.

Thin coupon problem is different from Coupon Collector Problem with packs since we do not have duplicates when we draw a subset.