Check Your Understanding

When counting paths of length $k$ through a centroid, you combine distances from different subtrees. For each node at distance $d$ from the centroid in subtree A, you count nodes at distance $k - d$ in other subtrees. This avoids double-counting paths within the same subtree.

Then you recurse on each subtree separately. Quiz: If the centroid has $3$ children with subtrees of sizes $10$, $15$, and $20$, how many times do you recurse after processing the centroid?