On the table, there is a balance with two pans. The display on the balance tells the difference between the weight in the left ban and the weight in the right pan (measured in gram).
There are also $2016$ coins on the table. Cosmo tells Fredo: "There are exactly $99$ fake coins among these $2016$ coins. All genuine coins have the same weight. Some fake coins weigh one gram less than the genuine coins, and the other fake coins all weigh one gram more than the genuine coins."
Cosmo points at the leftmost coin $x$ and asks Fredo to determine whether $x$ is fake.
Question: Can Fredo decide whether coin $x$ is fake by using the balance at most twice?