Cosmo puts a golden weight of 11111 gram into the right pan of a balance. Then Fredo starts adding his bronze weights to the balance:

• first Fredo adds a bronze weight of 1 gram to one of the pans;
• then he adds a bronze weight of 2 gram to one of the pans;
• then he adds a bronze weight of 4 gram to one of the pans;
• then he adds a bronze weight of 8 gram to one of the pans;
• and so on.

Every bronze weight weighs twice as much as the preceding one. After Fredo has been doing this for some time, the two pans are in equilibrium.

(a) Is it possible that Fredo has put the 16 gram bronze weight into the left pan?
(b) Is it possible that Fredo has put the 16 gram bronze weight into the right pan?