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?

/**
 * 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 {
public:
    void _get_in_order_list(TreeNode* root, vector<int> &in_list) {
        if (NULL == root) {
            return;
        }
        _get_in_order_list(root->left, in_list);
        in_list.push_back(root->val);
        _get_in_order_list(root->right, in_list);
    }
    
    int kthSmallest(TreeNode* root, int k) {
        vector<int> in_list;
        _get_in_order_list(root, in_list);
        return in_list[k - 1];
    }
};