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 {

private int n = 0;
private TreeNode re_node;

//中序遍历二叉排序树
public void InOrderTravel(TreeNode root,int k) {
if(root!=null) {
InOrderTravel(root.left,k);
n++;
if(n==k) {
this.re_node = root;
return;
}
InOrderTravel(root.right,k);
}
}

public int kthSmallest(TreeNode root, int k) {
InOrderTravel(root,k);
return this.re_node.val;
}
}