An aldopentose A can be oxidized with dilute HNO₃ to an optically active aldaric acid. A Kiliani–Fischer synthesis starting with A gives two new aldoses: B and C. Aldose B can be oxidized to an achiral, and therefore optically inactive, aldaric acid, but aldose C is oxidized to an optically active aldaric acid. Assuming the d configuration, give the structures of A, B, and C.