Implement a search procedure in terms of a set test procedure
Hint: Suppose you asked your oracle whether there is a subset of $\{x_2,\ldots,x_n\}$ whose product is $t$. What can you deduce if the answer is YES? What can you deduce if the answer is NO?

Here is the full solution:


   If the oracle answers YES, we deduce that we can remove $x_1$ from $S$. If the oracle answers NO, we deduce that every solution must contain $x_1$. We therefore remove $x_1$ from $S$ and update our target product to $t/x_1$. Continuing in this vein for $n-1$ more iterations, we find a solution. This requires at most $n$ calls to $\mathsf{Prod}$ in total.