Školjka

%V0 Let $p$ be a prime number and let $A$ be a set of positive integers that satisfies the following conditions: (1) the set of prime divisors of the elements in $A$ consists of $p-1$ elements; (2) for any nonempty subset of $A$, the product of its elements is not a perfect $p$-th power. What is the largest possible number of elements in $A$ ?