general An eligible institution that is a public institution of higher education shall cover the excess costs to meet the difference between the in-State tuition, fees, and on-campus room and board at the institution and the amount awarded to the eligible student through the grant award under paragraph (3), through a combination of grant and work-study awards under this title for which the eligible student may be eligible, campus-based aid programs, State-based merit or need-based aid, or other institutional-based merit- or need-based aid. An eligible institution that is a public institution of higher education may cover, with respect to an eligible student, any amounts of the cost of attendance that are in excess of the total amount awarded to the eligible student through the grant award under paragraph (3) and the amount of excess costs provided under this subclause based on the demonstrated financial need of the student. (II) Student contribution The eligible student shall be responsible for any amounts of the cost of attendance that are in excess of the total amount awarded to the eligible student through the grant award under paragraph (3) and the amount of excess costs provided under subclause (I). The eligible student may be eligible for Federal student aid in accordance with subparagraph (B) for the remaining cost of attendance amount for which the student is responsible. (ii) Private institution (I) Matching amount (aa) In general An eligible institution that is a private, nonprofit institution of higher education shall— (AA) with respect to an eligible student described in item (bb), cover excess costs toward meeting an eligible student’s cost of attendance in an amount equal to or greater than the amount of the grant award to the eligible student described in paragraph (3)