OBM 2013 Problem 2

Arnaldo and Bernaldo play the following game: given a fixed finite set of positive integers $A$ known by both players, Arnaldo picks a number $a \in A$ but doesn't tell it to anyone. Bernaldo thens pick an arbitrary positive integer $b$ (not necessarily in $A$ ). Then Arnaldo tells the number of divisors of $ab$ . Show that Bernaldo can choose $b$ in a way that he can find out the number $a$ chosen by Arnaldo.