KöMaL 2006 B3950

Let $H$ be the set of integers not greater than 2006: $H$={1,2,...,2006}. Let $D$denote the number of those subsets of the set $H$ in which the number of elements divided by 32 leaves a remainder of 7, and let $S$ denote the number of those subsets of the set $H$in which the number of elements divided by 16 leaves a remainder of 14. Prove that $S$=2$D$. (Based on an OKTV (National Competition) problem)