Sticky Notes

You are given a tree with $N$ vertices (numbered $1$ through $N$). Its edges are numbered $1$ through $N-1$. For each valid $i$, there is an integer $a_i$ written on the $i$-th vertex. Also, for each valid $i$, there is an integer $b_i$ written on the $i$-th edge. You want the following condition to be satisfied: for each vertex $v$ and each edge $e$ adjacent to $v$, $a_v \ge b_e$. In order to