Minimal Travel Time

Chef's college is starting next week. There are $S$ subjects in total, and he needs to choose $K$ of them to attend each day, to fulfill the required number of credits to pass the semester. There are $N + 1$ buildings. His hostel is in building number $0$. Subject $i$ is taught in building $A_i$. After each subject, there is a break, during which he goes back to his hostel. There are $M$ bidirecti