Crazy-Primey Sticks

There are $N$ sticks of integer lengths placed on ground one after the other, the length of each of these sticks is given in an array $L$.Now you have to play a game in which you are asked $Q$ questions, in each of these questions you are given $l$ and $r$ you need to find the stick of maximum length $S$ such that $l \leq |S| \leq r$ and $|S|$ is a prime number. If you could find such stick $S$ pr