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?

/**
 * Definition for a binary tree node.
 * public class TreeNode {
 *     int val;
 *     TreeNode left;
 *     TreeNode right;
 *     TreeNode(int x) { val = x; }
 * }
 */
public class Solution {
   
    int mK = 0;
    int val = 0;
   
    public int kthSmallest(TreeNode root, int k) {
        mK = k;
        visit(root);
        return val;
    }
   
    private void visit(TreeNode root) {
        if (root.left != null) {
            visit(root.left);
        }
        if (mK == 1) {
            val = root.val;
        }
        mK--;
        if (mK > 0 && root.right != null) {
            visit(root.right);
        }
    }
}