as a coverage gap State , with respect to such year), the Secretary shall (including through contract with eligible entities (as specified by the Secretary), consistent with subsection (b)) provide for the offering to such individuals residing in such State of a health benefits plan (in this section referred to as the Federal Medicaid program or the Program ), for each quarter during the period beginning on January 1 of such year, and ending with the last day of the first quarter during which the State provides medical assistance to all such individuals under the State plan (or waiver of such plan). Under the Federal Medicaid program, the Secretary— (1) may use the Federally Facilitated Marketplace to facilitate eligibility determinations and enrollments under the Federal Medicaid Program and shall establish a set of eligibility rules to be applied under the Program in a manner consistent with section 1902(e)(14)