; and (4) by adding at the end the following new paragraph: (9) Distribution of additional residency positions (A) Additional residency positions (i) In general For each of fiscal years 2019 through 2023 (and succeeding fiscal years if the Secretary determines that there are additional residency positions available to distribute under clause (iv)(II)), the Secretary shall, subject to clause (ii) and subparagraph (D), increase the otherwise applicable resident limit for each qualifying hospital that submits a timely application under this subparagraph by such number as the Secretary may approve for portions of cost reporting periods occurring on or after July 1 of the fiscal year of the increase. (ii) Number available for distribution For each such fiscal year, the Secretary shall determine the total number of additional residency positions available for distribution under clause (i) in accordance with the following: (I) Allocation to hospitals already operating over resident limit One-third of such number shall be available for distribution only to hospitals described in subparagraph (B). (II) Aggregate limitation Except as provided in clause (iv)(I), the aggregate number of increases in the otherwise applicable resident limit under this subparagraph shall be equal to 3,000 in each such year. (iii) Process for distributing positions (I) Rounds of applications The Secretary shall initiate 5 separate rounds of applications for an increase under clause (i), 1 round with respect to each of fiscal years 2019 through 2023. (II) Number available In each of such rounds, the aggregate number of positions available for distribution in the fiscal year under clause (ii) shall be distributed, plus any additional positions available under clause (iv). (III) Timing The Secretary shall notify hospitals of the number of positions distributed to the hospital under this paragraph as a result of an increase in the otherwise applicable resident limit by January 1 of the fiscal year of the increase. Such increase shall be effective