How many non-empty subsets S of {1,2,3,…,15} have the following two properties?
(1) No two consecutive integers belong to S.
(2) If S contains k elements, then S contains no number less than k.
<spanclass=′latex−bold′>(A)</span>277<spanclass=′latex−bold′>(B)</span>311<spanclass=′latex−bold′>(C)</span>376<spanclass=′latex−bold′>(D)</span>377<spanclass=′latex−bold′>(E)</span>405