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.

Example 1:


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

Example 2:


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


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?

Source: leetcode | Difficulty: MEDIUM_HARD
Tags: Tree algorithms

Graph traversal

Range queries

Starter code: # Definition for a binary tree node.
class TreeNode:
    def __init__(self, val=0, left=None, right=None):
    self.val = val
    self.left = left
    self.right = right
class Solution:
    def kthSmallest(self, root: TreeNode, k: int) -> int:
        

Solutions:
class Solution:

	def __init__(self):
		self.k = 0
		self.result = None

	def kthSmallest(self, root, k):
		if root.left and self.k < k:
			self.kthSmallest(root.left, k)
		self.k += 1
		if self.k == k:
			self.result = root.val
		if root.right and self.k < k:
			self.kthSmallest(root.right, k)
		return self.result