CGMO 2006 Problem 6

Let $M= \{ 1, 2, \cdots, 19 \}$ and $A = \{ a_{1}, a_{2}, \cdots, a_{k}\}\subseteq M$ . Find the least $k$ so that for any $b \in M$ , there exist $a_{i}, a_{j}\in A$ , satisfying $b=a_{i}$ or $b=a_{i}\pm a_{i}$ ( $a_{i}$ and $a_{j}$ do not have to be different) .