Split And Maximize

Chef has an array $A$ of $N$ positive integers. He can perform the following operation **at most once**: - Select an index $i$ $(1 \le i \le N)$ and an integer $k\geq 1$ - Select $k$ non-negative integers $x_1, x_2,\ldots ,x_k$ such that $2^{x_1} + 2^{x_2} + \ldots + 2^{x_k} = A_i$ - Erase $A_i$ from $A$ and append $2^{x_1}, 2^{x_2}, \ldots, 2^{x_k}$ to $A$. Note that the $x_i$ need not be distin