Problem - Interval List Intersections

Given two sorted lists of intervals, find their intersection.

Example: A = [[0,2],[5,10]], B = [[1,5],[8,12]]. Intersections: [1,2] (from [0,2] and [1,5]), [5,5] (from [5,10] and [1,5]), [8,10] (from [5,10] and [8,12]).

How would you find all intersections efficiently? Naive approach checks all $O(n \times m)$ time using $O(n + m)$ space pairs. The sorted property lets you do better.