KöMaL 2017 B4900

Let $K$ be a convex shape symmetric in the origin, let $e$ be a line through the origin, and let $e'$ be any line parallel to $e$. Let, furthermore $\# H$ denote the number of lattice points in a set $H$. Prove that $\# (K\cap e)+1 \ge \# (K\cap e')$.