Need help with this problem in organising an event at my org. Please help or give any hint :)

There are T teachers who can each have a maximum of S students. Each student can have a maximum of S teachers. There are S time slots for the student and teacher to meet.

In each slot a teacher will teach one of its student and then teacher gets another student while the student goes to another teacher.

For S = 3

Expected Teachers — 150 Expected Students — 250 Expected S — 3 Time limit doesnt matter until the solution comes under 15 mins

Input:

Teacher 1 — Student 1, Student 2

Teacher 2 — Student 2, Student 3

Teacher 3 — Student 1, Student 3

Teacher 4 — Student 1, Student 3, Student 2

Expected Solution (Attached Image)

Tried this, but it's for a single Teacher and its mentee and can be used to check if it's possible to assign the students to the current teacher or not, but otherwise it doesnt provide the optimal way of scheduling so that there is no conflict in the future.