; and (II) is not— (aa) less than $10,000; or (bb) greater than $1,500,000. (B) Improved institution described For purposes of this paragraph, an improved institution is an institution that, on the date the Secretary makes an allocation under subparagraph (A)(ii) is, with respect to— (i) the completion rate or graduation rate of Federal Pell Grant recipients at the institution, in the top 10 percent of— (I) if the institution is an institution described in any of clauses (iv) through (ix) of section 132(d)(1)(B), all such institutions participating under this part for the preceding fiscal year; or (II) if the institution is an institution described in any of clauses (i) through (iii) of section 132(d)(1)(B), all such institutions participating under this part for the preceding fiscal year