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Suppose an infinite number of balls are thrown into N bins (uniformly distributed)

What is the expectancy of the number of balls needed in order to fill all bins with at least K balls in each bin.

I found answers to this problem with K=1 and even a partial answer to K=2 but nothing for the generalized form.

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    Can you provide us with your solution for K = 1 and K = 2? – 2017-01-04

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I think I found the answer in the following paper:

https://faculty.wharton.upenn.edu/wp-content/uploads/2012/04/Double-dixie-cup-problem.pdf

the expectancy of collecting m balls each bins (having n bins) is:

n(log(n) + (m-1)loglogn + o(1) )

*** this analysis is done for m-fixed and n-large