Kth Smallest Element in a BST

Given the root of a binary search tree, and an integer k, return the kth smallest value (1-indexed) of all the values of the nodes in the tree.

Example 1:

Input: root = [3,1,4,null,2], k = 1  
Output: 1

Example 2:

Input: root = [5,3,6,2,4,null,null,1], k = 3  
Output: 3

Constraints:

• The number of nodes in the tree is n.
• 1 <= k <= n <= 10^4
• 0 <= Node.val <= 10^4

Follow up:

What if the BST is modified (insert/delete operations) often and you need to find the kth smallest frequently?
How would you optimize the kthSmallest routine?