iterative solution
# Definition for a binary tree node.
# class TreeNode(object):
#     def __init__(self, x):
#         self.val = x
#         self.left = None
#         self.right = None

class Solution(object):
    def kthSmallest(self, root, k):
        """
        :type root: TreeNode
        :type k: int
        :rtype: int
        """
        stack,cur,rank=[],root,0 
        while stack or cur:
            if cur:
                stack.append(cur)
                cur=cur.left
            else: 
                cur=stack.pop()
                rank+=1
                if rank==k:
                    return cur.val
                cur=cur.right

recursion
# Definition for a binary tree node.
# class TreeNode(object):
#     def __init__(self, x):
#         self.val = x
#         self.left = None
#         self.right = None

class Solution(object):
    def kthSmallest(self, root, k):
        """
        :type root: TreeNode
        :type k: int
        :rtype: int
        """
        return self.recursion(root,k)
    def sizeOfTree(self,root):
        if root is None:return 0 
        size=self.sizeOfTree(root.left)+self.sizeOfTree(root.right)+1 
        return size 
    def recursion(self,root,k):
        leftSize=self.sizeOfTree(root.left)
        if leftSize==k-1:return root.val 
        elif leftSize<k-1: return self.recursion(root.right,k-leftSize-1)
        else:return self.recursion(root.left,k)