Problem: Kth Smallest Element in a BST

Statement

Given the root of a binary search tree and an integer k, return the $k^{th}$ smallest value ($1$-indexed) among all node values in the tree.

Note: If the BST is modified frequently (i.e., with insert and delete operations) and you need to find the $k^{th}$ smallest element repeatedly, how would you optimize your approach?

Constraints:

• The number of nodes in the tree is n.

• $1 \leq$ k $\leq$ n $\leq 10^4$ ...