You want to travel from Syrjälä to Lehmälä by plane using a minimum-price route. Which cities will you certainly visit?
The first input line contains two integers $n$ and $m$ : the number of cities and the number of flights. The cities are numbered $1,2,\ldots,n$ . City 1 is Syrjälä, and city $n$ is Lehmälä.
After this, there are $m$ lines describing the flights. Each line has three integers $a$ , $b$ , and $c$ : there is a flight from city $a$ to city $b$ with price $c$ . All flights are one-way flights.
You may assume that there is a route from Syrjälä to Lehmälä.
First print an integer $k$ : the number of cities that are certainly in the route. After this, print the $k$ cities sorted in increasing order.
5 6 1 2 3 1 3 4 2 3 1 2 4 5 3 4 1 4 5 8· \n · · \n · · \n · · \n · · \n · · \n · · \n
4 1 3 4 5\n · · · \n