Choose a subset $S$ from $(a_i,b_i)_{i=1}^n$ to maximize
$$
\frac{\sum_{i\in S} a_i}{\Pi_{i\in S} b_i}.
$$
Hot to efficiently solve it? Is it NP-hard? Here, each $a_i$ and $b_i$ are given, strictly positive. We want to find the best $S$. Thanks a lot.