Inverse folding is a classic instance of negative RNA design which consists of finding a sequence that uniquely folds into a target secondary structure with respect to energy minimization. A breakthrough result of Bonnet et al shows that, even in simple base pairs-based (BP) models, the decision version of a mildly constrained version of inverse folding is NP-hard. In this work, we show that inverse folding can be solved in linear time for every target structure that contains no isolated BP and no isolated stack BP. (i.e. when helices have all sizes more than $h=3$). For structures featuring shorter helices, our linear algorithm is no longer guaranteed to produce a solution, but still does so for a large proportion of instances. Our approach introduces a notion of modulo $m$-separability, generalizing a property introduced by Hales et al. Separability is a sufficient condition for the existence of a solution to the inverse folding problem. We show that, for any input secondary structure of length $n$, a modulo $m$-separated sequence can be produced in time $\mathcal{O}(n.2^m)$ anytime such a sequence exists. Meanwhile, we show that any structure such that $h=3$ is either trivially non-designable, or always admits a modulo-$2$ separated sequence ($m=2$). Solution sequences can thus be produced in linear time, and even be uniformly generated within the set of modulo-$2$ separable sequences.