Largest value shared by two BSTs

You are given the roots of two binary search trees, a and b, holding integer values. Return the largest integer that appears in both trees. If the trees share no value, return -1.

Implement:

def largest_common_value(a: TreeNode | None, b: TreeNode | None) -> int: ...

where TreeNode has val, left and right.

Constraints

• Each tree has between 1 and 10^5 nodes.
• Every node value is between -10^9 and 10^9.
• Both inputs are valid BSTs: every value in a node's left subtree is smaller than the node's value, and every value in its right subtree is larger.
• Trees may be unbalanced, so the height can be as large as the node count.

Aim for better than O(n) extra memory by using the BST ordering.

Example 1

Tree a values: 1, 3, 6, 8, 10, 12, 15
Tree b values: 2, 4, 6, 7, 10, 11, 14
Output: 10

Both 6 and 10 appear in both trees. 10 is the larger one.

Example 2

Tree a values: 2, 5, 9
Tree b values: 1, 4, 7
Output: -1

No value appears in both trees.

Reconstructed from the reported question; details may differ from what interviewers ask.