# Time:  O(max(h, k))
# Space: O(h)

# 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.
# class TreeNode:
#     def __init__(self, x):
#         self.val = x
#         self.left = None
#         self.right = None

class Solution:
    # @param {TreeNode} root
    # @param {integer} k
    # @return {integer}
    def kthSmallest(self, root, k):
        s, cur, rank = [], root, 0

        while s or cur:
            if cur:
                s.append(cur)
                cur = cur.left
            else:
                cur = s.pop()
                rank += 1
                if rank == k:
                    return cur.val
                cur = cur.right

        return float("-inf")
