Selecting Edges

You are given an undirected graph $G$ with $N$ vertices (numbered $1$ through $N$) and $M$ edges (numbered $1$ through $M$). $G$ does not contain any self-loops, but it may contain parallel edges. For each valid $i$, the $i$-th vertex has a non-negative integer weight $A_i$. Also, for each valid $i$, the $i$-th edge has a non-negative integer weight $B_i$. Let $E = \{1, 2, \ldots, M\}$ denote t