Rooted Minimum Spanning Tree

You are given a weighted simple undirected graph with $N$ vertices, which are numbered from $1$ to $N$. You are guaranteed that vertex $1$ is not an articulation point (which means that even after removing the vertex $1$, the remaining graph is connected) and has an edge connecting it to each of the other $N-1$ vertices. For each $K \in \{1, 2, \ldots, N-1\}$ you need to find the minimum weight o