Problems - Path Queries II - Read Statement

You are given a tree with $n$ nodes, each with a value. Process $q$ queries of two types: update node $s$ to value $x$, or find the maximum value on the path from node $a$ to node $b$. Constraints: $1 \leq n, q \leq 200000$. The tree is given as edges.

Values can be up to $10^9$. The tree is connected and has exactly $n-1$ edges. This is a direct application of HLD with a max segment tree. The queries are online, so you must answer each query before seeing the next. Read the full problem at CSES.