Bounded Spanning Tree

You are given a connected undirected edge-weighted graph with $N$ vertices and $M$ edges. There are no self-loops in this graph (that is, there is no edge which goes from a vertex to itself), but there can be multiple edges between some pairs of vertices. Your friend told you the following about this graph: - The edge weights are **distinct** integers from the range $[1, M]$. In other words, the