Product Mex Queries

You are given an array $a$ of length $N$ and $Q$ queries. Each query is described by a pair of integers, $l$ and $r$. Answer each query with the following: if we take every subsequence of the elements with indices between $l$ and $r$ (inclusive) and write down their products, what will be the smallest missing positive integer? A subsequence of an array is a sequence you obtain by deleting some