Lowest Common Ancestor of a BST

Write `lowest_common_ancestor(root, p, q)` returning the deepest node that is an ancestor of both. Nodes are node objects, both present in the tree, and a node counts as its own ancestor. In a general binary tree this needs a search of both subtrees. In a BST it does not: walk down, and the first node whose value lies between the two targets is the answer, because that is where their paths diverge. Using a general-tree algorithm here is a correct answer that misses the point of the question.