Graph and Minimum Spanning Tree

You are given a connected, undirected, weighted graph $G$ with $N$ vertices and $M$ edges. $G$ has no self-loops, and at most one edge joins any pair of vertices.

For each edge $(u, v)$, compute the total weight of a minimum spanning tree that is forced to contain that edge.

The first line contains the number of vertices $N$ and the number of edges $M$ ($2 \le N \le 200000$, $N-1 \le M \le 200000$).

Each of the next $M$ lines contains the edge information $u$, $v$, $w$, meaning that the edge joining vertex $u$ and vertex $v$ has weight $w$ ($1 \le u, v \le N$, $u \ne v$, $1 \le w \le 10^9$).

For each edge, print the total weight of a minimum spanning tree containing that edge, one per line. Print the answers in the order the edges are given in the input.