write a go solution for Description:
You are given a weighted undirected connected graph consisting of n vertices and m edges. It is guaranteed that there are no self-loops or multiple edges in the given graph.

Let's define the weight of the path consisting of k edges with indices e_1,e_2,...,e_k as sumlimits_i=1^kw_e_i-maxlimits_i=1^kw_e_i+minlimits_i=1^kw_e_i, where w_i — weight of the i-th edge in the graph.

Your task is to find the minimum weight of the path from the 1-st vertex to the i-th vertex for each i (2<=i<=n).

Input Format:
The first line contains two integers n and m (2<=n<=2*10^5; 1<=m<=2*10^5) — the number of vertices and the number of edges in the graph.

Following m lines contains three integers v_i,u_i,w_i (1<=v_i,u_i<=n; 1<=w_i<=10^9; v_inequ_i) — endpoints of the i-th edge and its weight respectively.

Output Format:
Print n-1 integers — the minimum weight of the path from 1-st vertex to the i-th vertex for each i (2<=i<=n).

Note:
None. Output only the code with no comments, explanation, or additional text.