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?

# Definition for a binary tree node.class TreeNode:    def __init__(self, x):        self.val = x        self.left = None        self.right = Noneclass Solution:    def kthSmallest(self, root, k):        """        :type root: TreeNode        :type k: int        :rtype: int        """        ans = []        def inorder(root):            if root.left:                inorder(root.left)            ans.append(root.val)            if root.right:                inorder(root.right)        inorder(root)        return ans[k-1]