Split Powers Of 2

Suppose that you have several powers of two, specifically, you have $A_i$ numbers equal to $2^i$ for each $1 \le i \le N$. You want to divide **all** of these numbers into two groups with equal sum. However, it's not always possible. To make it possible, in one operation you are allowed to choose any $1 \le i \le N$ and receive an extra number $2^i$ (in other words, you can increase any $A_i$ by