CMO 2015 Problem 3

Let $n \geq 5$ be a positive integer and let $A$ and $B$ be sets of integers satisfying the following conditions:

i) $|A| = n$ , $|B| = m$ and $A$ is a subset of $B$ ii) For any distinct $x,y \in B$ , $x+y \in B$ iff $x,y \in A$ Determine the minimum value of $m$ .