Leetcode 3609. Minimum Moves to Reach Target in Grid

Given start (sx,sy) and target (tx,ty) on an infinite grid where each move adds m = max(x,y) to either x or y, determine the minimum number of such monotone increases to reach (tx,ty) (or return -1 if unreachable). Constraints up to 1e9 force a mathematical/greedy reasoning about reachability and step counts rather than brute force.