CONO-SUR 2013 Problem 4

Let $M$ be the set of all integers from $1$ to $2013$ . Each subset of $M$ is given one of $k$ available colors, with the only condition that if the union of two different subsets $A$ and $B$ is $M$ , then $A$ and $B$ are given different colors. What is the least possible value of $k$ ?