How to find pair with kth largest sum?

Question

Given two sorted arrays of numbers, we want to find the pair with the kth largest possible sum. (A pair is one element from the first array and one element from the second

Answer 1

If the last two solutions were at (a1, b1), (a2, b2), then it seems to me there are only four candidate solutions (a1-1, b1) (a1, b1-1) (a2-1, b2) (a2, b2-1). This intuition could be wrong. Surely there are at most four candidates for each coordinate, and the next highest is among the 16 pairs (a in {a1,a2,a1-1,a2-1}, b in {b1,b2,b1-1,b2-1}). That's O(k).

(No it's not, still not sure whether that's possible.)