Count Number of Possible Root Nodes

Given an undirected tree and a set of directed parent guesses (each guess orients an existing edge u→v), count how many choices of root make at least k guesses true. The core challenge is to evaluate correctness for all possible roots efficiently (n, guesses ≤ 1e5) by computing the count for one root via DFS and then using a rerooting technique to update the count in O(1) per edge.