1. Find centroid c of the current tree using the algorithm from the previous problem.
2. DFS from c to get distances to all nodes. Count pairs with distance sum k using a frequency map.
3. For each child subtree, DFS again and subtract pairs where both nodes are in that subtree.
4. Remove c and recursively process each component.
Time: O(nlogn) because each node is processed O(logn) times and each processing is O(1) or O(logn).
Space complexity is O(n) for the data structures used.