; and (II) the product of 1 minus the State-specific factor for such reform year and the beneficiary-based quarterly amount that would otherwise be determined under paragraph (1) for a State and category if the base per beneficiary, per category amount determined under paragraph (2) for the State and category were equal to 90 percent of the national average base per beneficiary, per category amount determined under subparagraph (A) for such category. (iii) High and low per beneficiary States defined In this subparagraph: (I) High per beneficiary State The term high per beneficiary State means, with respect to a category, a State for which the base per beneficiary, per category amount determined under paragraph (2) for such category is greater than 110 percent of the national average base per beneficiary, per category amount determined under subparagraph (A) for such category. (II) Low per beneficiary State The term low per beneficiary State means, with respect to a category, a State for which the base per beneficiary, per category amount determined under paragraph (2) for such category is less than 90 percent of the national average base per beneficiary, per category amount determined under subparagraph (A) for such category. (iv) State-specific factor In this subparagraph, the term State-specific factor means— (I) for the fourth reform year, 7/8 ; and (II) for a subsequent reform year, the State-specific factor under this clause for the previous reform year minus 1/8. (C) No additional expenditures (i) Determination of increase in Federal expenditures For each category for each reform year (beginning with the fourth reform year and ending with the tenth reform year), the Secretary shall determine whether the application of this paragraph— (I) to the category for the reform year will result in an aggregate increase in the aggregate Federal expenditures under subsection (a)