Kth Smallest Element in a BST

Given a binary search tree, write a function

kthSmallest

to find the kth
smallest element in it.

Note:

You may assume k is always valid, 1 ≤ k ≤ BST's total elements.

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?

public class Solution {
    public int kthSmallest(TreeNode root, int k) {
        int count = countNodes(root.left);
        if (k <= count) {
            return kthSmallest(root.left, k);
        } else if (k > count + 1) {
            return kthSmallest(root.right, k-1-count); // 1 is counted as current node
        }

        return root.val;
    }

    public int countNodes(TreeNode n) {
        if (n == null) return 0;

        return 1 + countNodes(n.left) + countNodes(n.right);
    }
}