### 230. Kth Smallest Element in a BST

Given a binary search tree, write a function kthSmallest to find the kth smallest element in it.

Example 1:

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

Example 2:

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

Constraints:

The number of elements of the BST is between 1 to 10^4. You may assume k is always valid, 1 ≤ k ≤ BST's total elements.

### Analyze

/** * Definition for a binary tree node. * function TreeNode(val, left, right) { *     this.val = (val===undefined ? 0 : val) *     this.left = (left===undefined ? null : left) *     this.right = (right===undefined ? null : right) * } *//** * @param {TreeNode} root * @param {number} k * @return {number} */var kthSmallest = function(root, k) {  const countResult = { value: 0 }  return analyzeCount(root, k, countResult)}
var analyzeCount = function(node, k, count) {  if (!node) return null  const pickLeft = analyzeCount(node.left, k, count)  if (typeof pickLeft === 'number') return pickLeft  count.value = count.value + 1  if (k === count.value) {    return node.val  }  const pickRight = analyzeCount(node.right, k, count)  if (typeof pickRight === 'number') return pickRight}