Interactive MST

There is a hidden **undirected connected** graph $G$ with $n$ nodes and $m$ edges numbered $0, 1, \ldots m - 1$, and a hidden permutation $p_0, p_1, \ldots, p_{m-1}$ of edges. The graph doesn't contain any self loops or multiple edges. You only know the value of $n$ and $m$. You can ask queries. In one query, you give the judge a vector $w = [w_0, w_1, \ldots, w_{m-1}]$ of size $m$ consisting o