topology - Splitting overlap between polygons into disjoint sets using shapely?

I have two overlapping shapely polygons A and B. I want to divide their intersection into two pieces, such that one part of the intersection is the set of points in A.intersection(B) (or symmetrically, B.intersection(A) to the boundary of A-B, and the other is the set of points closer to the boundary of B-A.

Is there an way to do this in shapely other than applying a brute-force mesh and checking the distance to each polygon's boundary?