A. Card Exchange

You have a hand of 𝑛 cards, where each card has a number written on it, and a fixed integer 𝑘. You can perform the following operation any number of times:

• Choose any 𝑘 cards from your hand that all have the same number.
• Exchange these cards for 𝑘−1 cards, each of which can have any number you choose (including the number written on the cards you just exchanged).

Here is one possible sequence of operations for the first example case, which has 𝑘=3:

What is the minimum number of cards you can have in your hand at the end of this process?