Recently I've come up with this problem:

You are given an array $$$a_1, a_2, \dots, a_n$$$ of positive integers.

You need to find $$$l$$$, $$$r$$$ such that $$$\frac{\prod_{i=l}^{r} a_i}{r-l+1}$$$ is maximum over all possible $$$l,r$$$ $$$(l \leq r)$$$.

Is it possible to solve this faster than $$$O(n^2)$$$? This problem looks like something well-known, but I am not sure.