In a school there are $2021$ doors with the numbers $1,2,\dots,2021$. In a day $2021$ students play the following game: Initially all the doors are closed, and each student receive a card to define the order, there are exactly $2021$ cards. The numbers in the cards are $1,2,\dots,2020,2021$. The order will be student $1$ first, student $2$ will be the second, and going on. The student $k$ will change the state of the doors $k,2k,4k,8k,\dots,2^pk$ with $2^pk\leq 2021\leq 2^{p+1}k$. Change the state is if the door was close, it will be open and vice versa. a) After the round of the student $16$, determine the configuration of the doors $1,2,\dots,16$ b) After the round of the student $2021$, determine how many doors are closed.