Find k-th recipient in command propagation order

## Chain of Command (k-th Receiver in DFS-by-Child-Id Order) A company org chart forms a rooted tree with `n` people (nodes), labeled `1..n`. You are given an array `parent[1..n]` describing the tree: - `parent[i] = -1` means `i` is the root (top leader) - otherwise, `parent[i]` is the direct manager (parent) of person `i` - each node has zero or more direct reports (children) ### Command propagation rule When a person `u` issues a command, it is sent to **all subordinates** of `u` (all descendants of `u`), using this strict order: 1. Consider `u`’s direct children, sorted by increasing person id. 2. Send the command to the smallest-id child first. 3. Before sending to the next child, the command must be **fully propagated** throughout the current child’s entire subtree using the **same rule**. This defines a deterministic traversal order over the descendants of `u`: - It is equivalent to a DFS preorder over `u`’s subtree **excluding `u`**, where children are visited in ascending id. ### Task Given: - `parent[1..n]` - an issuer `u` - an integer `k` (1-indexed) Return the person id of the **k-th** subordinate who receives the command in the propagation order. If `u` has fewer than `k` descendants, return `-1`. ### Input/Output - Input: `parent[]`, `u`, `k` - Output: the person id of the k-th recipient, or `-1` ### Notes / Assumptions - The input forms a valid tree (exactly one root). - `k` is 1-indexed over recipients (descendants only; the issuer `u` is not counted). - Constraints may be large (e.g., `n` up to 2e5), so an approach better than simulating propagation step-by-step for each query is typically expected (if multiple queries are present, state how many).