[Combinatorics] Suppose a door is locked (with a single lock), and next to the door there is a large box with many keys. Each key in the box is one of k = N types and only a single type can open the door. We assume that the keys are visually identical and all key types are presented in the box in equal proportions. What is the minimum number of keys one should randomly pick from the box in order to have at least a 99% chance to open the door with one of selected keys? Express the result as a function of k. [Hint: here we can assume that the key box is huge and drawing some finite number of keys from the box has a negligible effect on the proportion of remaining keys in there]