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

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