Design an algorithm and write code to find the first common ancestor of two nodes in a binary tree. Avoid storing additional nodes in a data structure. NOTE: This is not necessarily a binary search tree.

For example, Given the following tree: root = [3,5,1,6,2,0,8,null,null,7,4]


    3

   / \

  5   1

 / \ / \

6  2 0  8

  / \

 7   4

Example 1:


Input: root = [3,5,1,6,2,0,8,null,null,7,4], p = 5, q = 1

Input: 3

Explanation: The first common ancestor of node 5 and node 1 is node 3.

Example 2:


Input: root = [3,5,1,6,2,0,8,null,null,7,4], p = 5, q = 4

Output: 5

Explanation: The first common ancestor of node 5 and node 4 is node 5.

Notes: