  In this paper, we give a proof of homological mirror symmetry for two
variable invertible polynomials, where the symmetry group on the $B$-side is
taken to be maximal. The proof involves an explicit gluing construction of the
Milnor fibres, and as an application, we prove derived equivalences between
certain nodal stacky curves, some of whose irreducible components have
non-trivial generic stabiliser.
