IrMO 2012 Problem 1

Let $$C=\{1,22,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20\}$$ and let $$S=\{4,5,9,14,23,37\}$$ Find two sets $A$ and $B$ with the properties (a) $A\cap B=\emptyset$ . (b) $A\cup B=C$ . (c) The sum of two distinct elements of $A$ is not in $S$ . (d) The sum of two distinct elements of $B$ is not in $S$ .