Abhijeet and his challenging race

Abhijeet and his friend Kshittiz are getting bored so, Abhijeet decided to give him a challenge. In the challenge, there is a map of a city where $N$ locations are marked and numbered from 1 to $N$. There are also $M$ bidirectional roads of length $w$ connecting the locations. It is actually a car race track and there are $K$ participants that will be participating in the race. All the participa