Generate split-stay pairs efficiently

Given N Airbnb listings, each with available days as integers, and an inclusive requested date range [L, R], return all ordered pairs (X, Y) of distinct listings such that there exists a split day s in [L, R−1] where X is available for every day in [L, s] and Y is available for every day in [s+1, R]. Availability for each stay segment must be contiguous. Design an algorithm that improves on the naive O(N^2 · R) approach: describe data structures, core steps, and time/space complexity. Discuss how to handle sparse availability and large ranges. For the example A=[1,2,3,6,7,10,11], B=[3,4,5,6,8,9,10,13], C=[7,8,9,10,11] with [L, R]=[3, 11], the valid result is [(B, C)].