Chefina and Strange Tree

In Chefland, there are $N$ cities (numbered $1$ through $N$) connected by $N-1$ bidirectional roads. Each city has exactly one garden. For each valid $i$, let's denote the population of the $i$-th city by $A_i$ and the initial number of fruits in its garden by $B_i$; also, at any time, let's denote the current number of fruits in its garden by $F_i$ ($F_i = B_i$ initially). You are given a perm