2 players A and B play a game. At the start of the game, $n$ positive integers (not necessarily distinct) are written on a notebook. First, player A chooses a number from the notebook and declares it the "current number". After that, they play alternately starting with B. At each turn, they do the following: if the current number is $x$, then the player erases $x$ from the notebook (if multiplicity > 1, leaves the rest unerased), chooses some other number $y$ from the notebook, and declares it the "current number". $y$ can be chosen provided either
1) $x|y$ and $y/x$ is prime, or 2) $y|x$ and $x/y$ is prime.
The first player who is unable to make a move loses. When does A have a winning strategy?