In Occidentalia there are $20$ different companies, each looking to hire $15$ new employees. A group of $300$ applicants interview each of the companies. Each company qualifies each applicant as suitable or not suitable to work in it, in such a way that each of them finds exactly $p$ suitable applicants, with $p > 15$. and each applicant is found suitable by at least one company. What is the smallest of $p $f or which it is always possible to assign $15$ applicants to each company, given that each company is assigned only applicants that it considers appropriate, and that each of the $300$ applicants is assigned to a company?