Question
You maintain a dynamic set of integers in a BST and must answer order-statistic queries efficiently. Given a list of operations, process them in order: ['insert', x] adds x to the set (duplicates are ignored), and ['kth', k] asks for the k-th smallest value currently in the set (1-indexed; if k exceeds the set size, the answer is -1). Return the list of answers, one per 'kth' query, in order. Your solution must support each operation in average time better than O(size) by augmenting the BST with subtree sizes.
dynamic_kth_smallest(ops: list[list]) → list[int][[["insert",5],["insert",3],["insert",8],["kth",1],["kth",2],["kth",3]]]out[3,5,8]State your approach and its time/space complexity out loud before you optimize. Handle the edge cases (empty input, duplicates, overflow), and say why you chose this over the brute force. Green tests are the floor, not the grade.
Vibe coding: describe the solution in plain language (or narrate it) and the coach grades your approach. Generating runnable code from your description is coming next.