Tree Master

Given is a tree with $N$ weighted vertices and $N-1$ weighted edges. The $i$-th vertex has a weight of $A_i$. The $i$-th edge has a weight of $W_i$ and connects vertices $u_i$ and $v_i$. Let $\operatorname{dist}(x,y)$ be the sum of weights of the edges in the unique [simple path](https://en.wikipedia.org/wiki/Path_(graph_theory)) connecting vertices $x$ and $y$. Let $\operatorname{V}(x,y)$ be th