Run for beer

题意翻译

现在有 $n$ 个点，$m$ 条无向边组成的无向图，每条边有一个权值 $len$。节点编号从 $0\cdots n-1$。 已知初始速度为 $1$，每到一个点速度会变为原来的十分之一。求最少要花多少时间从 $0$ 号点到 $n-1$ 号点。 输出第一行最少时间，第二行经过的结点数，第三行输出路径。在最小化时间前提下最小化路径长度，多条最短路径任意选取。

题目描述

People in BubbleLand like to drink beer. Little do you know, beer here is so good and strong that every time you drink it your speed goes 10 times slower than before you drank it. Birko lives in city Beergrade, but wants to go to city Beerburg. You are given a road map of BubbleLand and you need to find the fastest way for him. When he starts his journey in Beergrade his speed is 1. When he comes to a new city he always tries a glass of local beer, which divides his speed by 10. The question here is what the minimal time for him to reach Beerburg is. If there are several paths with the same minimal time, pick the one that has least roads on it. If there is still more than one path, pick any. It is guaranteed that there will be at least one path from Beergrade to Beerburg.

输入输出格式

输入格式

The first line of input contains integer $ N $ — the number of cities in Bubbleland and integer $ M $ — the number of roads in this country. Cities are enumerated from 0 to $ N-1 $ , with city 0 being Beergrade, and city $ N-1 $ being Beerburg. Each of the following $ M $ lines contains three integers $ a $ , $ b $ ( $ a≠b $ ) and $ len $ . These numbers indicate that there is a bidirectional road between cities $ a $ and $ b $ with length $ len $ . - $ 2<=N<=10^{5} $ - $ 1<=M<=10^{5} $ - $ 0<=len<=9 $ - There is at most one road between two cities

输出格式

The first line of output should contain minimal time needed to go from Beergrade to Beerburg. The second line of the output should contain the number of cities on the path from Beergrade to Beerburg that takes minimal time. The third line of output should contain the numbers of cities on this path in the order they are visited, separated by spaces.

输入输出样例

输入样例 #1

8 10
0 1 1
1 2 5
2 7 6
0 3 2
3 7 3
0 4 0
4 5 0
5 7 2
0 6 0
6 7 7

输出样例 #1

32
3
0 3 7