Number of expected turns to get k distinct numbers

We have a random number generator, which generates random numbers from 1 to N. Each number has an equal probability of occurring (equiprobable). Find the expected number of turns to get 'k' distinct numbers from the random number generator.

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PS: This question came in the placement test of some company, and I was unable to solve it. Moreover, I couldn't find any good theorem or resource on the internet for this. Any help will be appreciated.

Thank you