Question 73
The sets $M=\{1,2, \ldots, 27\}$ and $A=\{a_{1}, a_{2}, \ldots, a_{k}\} \subset \{1,2, \ldots, 14\}$ have the following property: every element of $M$ is either an element of $A$ or the sum of two (possibly identical) elements of $A$. Find the minimum value of $k$.