The provisions of Kan. Stat. Ann. § 25-205, and amendments thereto, shall not apply to the offices of governor and lieutenant governor. The names of candidates for governor and lieutenant governor shall be printed upon the official primary ballot when each pair thereof shall have qualified to become candidates in one or the other of the following methods:

(a) Nomination petitions shall be filed on their behalf, not later than 12 noon, June 1, prior to such primary election, or if such date falls on Saturday, Sunday or a legal holiday, then before 12 noon the following business day, as provided for in Kan. Stat. Ann. § 25-4005, and amendments thereto; or

(b) such persons shall have filed not later than the time for filing nomination petitions, as provided in paragraph (a), with the secretary of state, a declaration of intention to become candidates accompanied by a fee as provided in Kan. Stat. Ann. § 25-4006, and amendments thereto.