OMCPLP 2012 Problem 5

5)Players $A$ and $B$ play the following game: a player writes, in a board, a positive integer $n$ , after this they delete a number in the board and write a new number where can be: i)The last number $p$ , where the new number will be $p - 2^k$ where $k$ is greatest number such that $p\ge 2^k$ ii) The last number $p$ , where the new number will be $\frac{p}{2}$ if $p$ is even. The players play alternately, a player win(s) if the new number is equal to $0$ and player $A$ starts.

a)Which player has the winning strategy with $n = 40$ ?? b)Which player has the winning strategy with $n = 2012$ ??