Homological mirror symmetry for invertible polynomials in two variables

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