Subjecting $\mathrm{D}-(-)$ -threose to a Kiliani-Fischer synthesis yields two other epimeric aldopentoses, $\mathrm{D}-(+)$ -xylose and $\mathrm{D}-(-)$ -lyxose. $\mathrm{D}-(+)$ - Xylose can be oxidized (with nitric acid) to an optically inactive aldaric acid, while similar oxidation of $\mathrm{D}-(-)$ -lyxose gives an optically active product. What are the structures of $\mathrm{D}-(+)$ -xylose and $\mathrm{D}-(-)$ -lyxose?