In a massive school which has $m$ students, and each student took at least one subject. Let $p$ be an odd prime. Given that:

(i) each student took at most $p+1$ subjects. \\
(ii) each subject is taken by at most $p$ students. \\
(iii) any pair of students has at least $1$ subject in common. \\

Find the maximum possible value of $m$.