Tree and Extra Edge

You have a rooted tree consisting of $n$ vertices. There are some weights on each edge of the tree denoted by $W_i$. The tree root is a vertex with number $1$. In this problem, you need to answer $Q$ queries. Each query is described by three values $u$, $v$, and $x$. It is guaranteed that subtrees of node $u$ and node $v$ are disjoint. You are allowed to add at most one edge of weight $x$ betwee