What is the relation between Number Theory and Algebra Sets?

Let $A_{2015}$ be a set

$\large{A_{2015}=\{\ 2^{2015}-2^{k} | k \in Z, 0 \le k <2015\}\ }$

If the largest positive integer that cannot be written as the sum of one or more (not necessarily distinct) elements of $A_{2015}$ can be written as $x\times 2^{y} +1$ . Find $x+y$ if both are integers