Flora has many candies, which attract Preston. Flora told Preston "Let's play a game, after the game maybe you can get some candies."
Before the game starts, there is a piece of candy on the table.
Flora prepared a bag, there is $p$ balls in the bag, $q$ balls of them are sky-blue $(q < p)$, and the others are white.
The game will have $n$ rounds. The rule of each round is as follows:
Preston take out a ball from the bag, and write down its color, **then put it back into the bag.**
We assume that **the possibility of taking out every ball is equal.**
If the ball is blue, Flora will add a piece of candy on the table.
Otherwise, Flora will put all candies on the table into **a new box**, then put a new piece of candy on the table.
After n rounds, Flora put all candies on the table into **a new box**.
Flora told Preston , "you can choose a box,and eat all candies in it".
Of course, Preston will choose the box which has the most candies in it.
Now Preston wants to know the expectation of the number of candies he could eat.