BALKAN-SL 2014 C2

Let $M=\{1,2,...,2013\}$ and let $\Gamma$ be a circle. For every nonempty subset $B$ of the set $M$ , denote by $S(B)$ sum of elements of the set $B$ , and define $S(\varnothing)=0$ ( $\varnothing$ is the empty set ). Is it possible to join every subset $B$ of $M$ with some point $A$ on the circle $\Gamma$ so that following conditions are fulfilled: $1$ . Different subsets are joined with different points; $2$ . All joined points are vertices of a regular polygon; $3$ . If $A_1,A_2,...,A_k$ are some of the joined points, $k>2$ , such that $A_1A_2...A_k$ is a regular $k-gon$ , then $2014$ divides $S(B_1)+S(B_2)+...+S(B_k)$ ?