Graph Monsters

You are given a connected, undirected graph consisting of $N$ nodes and $M$ edges. Every node has a pass value of $A_i$ and a monster with health $B_i$. Your task is to defeat all the monsters eventually. To do that, you can do the following steps: - Choose a starting node $S$ ($1 \le S \le N$) and a starting health value $H$. - Suppose your current node is $X$, you can either battle the monster