Binary lifting

Store up[k][v] — the 2^k-th ancestor of node v (0 for "above the root"). Building is one line per level: up[k][v] = up[k-1][up[k-1][v]]. Memory: O(n log n) — for n = 2·10^5 and LOG = 18 that is 3.6·10^6 entries, fine.

Answering "the k-th ancestor of v" decomposes k in binary:

for (int bit = 0; bit < LOG; ++bit)
    if (k >> bit & 1) v = up[bit][v];

Any per-node payload can ride along in the same table: edge weight sums become distance queries, max edge weight becomes max-edge-on-path, and combining two node states later gives path aggregates (the LCA splits the path into two upward walks).

Recognition cues: "k-th ancestor", "distance between two nodes", "path query on a tree", repeated upward walks that a plain parent loop cannot afford (a path graph forces O(n) per query — lifting makes it O(log n)).