service performed in the employ of—

(A) a school, college, or university, or

(B) an organization described in section 509(a)(3) if the organization is organized, and at all times thereafter is operated, exclusively for the benefit of, to perform the functions of, or to carry out the purposes of a school, college, or university and is operated, supervised, or controlled by or in connection with such school, college, or university, unless it is a school, college, or university of a State or a political subdivision thereof and the services performed in its employ by a student referred to in section 218(c)(5) of the Social Security Act are covered under the agreement between the Commissioner of Social Security and such State entered into pursuant to section 218 of such Act;

if such service is performed by a student who is enrolled and regularly attending classes at such school, college, or university;