Oleg and (the ghost of) Erdös play the following game. Oleg chooses a non- negative integer a1 with at most 1000 digits.

In Round i the following happens:
Oleg tells the number a_i to Erdös, who then chooses a non negative integer b_i, and then Oleg defines a_i+1 = |a_i-b_i| or a_i+1 = a_i + b_i.
Erdös wins if a₂₀ is a power of 10, otherwise Oleg wins.

Who is the winner, Oleg or Erdös?