LeetCode Kth Smallest Element in a BST

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?

Hint:

Try to utilize the property of a BST.
What if you could modify the BST node's structure?
The optimal runtime complexity is O(height of BST).
Credits:
Special thanks to @ts for adding this problem and creating all test cases.

/**
* Definition for a binary tree node.
* struct TreeNode {
*     int val;
*     TreeNode *left;
*     TreeNode *right;
*     TreeNode(int x) : val(x), left(NULL), right(NULL) {}
* };
*/
class Solution {
private:
int idx;
int value;
int K;
public:
int kthSmallest(TreeNode* root, int k) {
K = k;
idx = 0;
dfs(root);
return value;
}

void dfs(TreeNode* root) {
if (root == NULL) {
return;
}
dfs(root->left);
idx++;
if (idx == K) {
value = root->val;
return;
}
dfs(root->right);
}
};