OMCPLP 2020 Problem 1

In certain country, the coins have the following values: $2^0, 2^1, 2^2,\dots 2^{10}$ . A cash machine has $1000$ coins of each value and give the money using each coin(of each value) at most once. The customers order all the positive integers: $1,2,3,4,5,\dots$ (in this order) in coins. a) Determine the first integer, such that the cash machine cannot provide. b) In the moment that the first customer can not be attended, by the lack of coins, what are the coins which are not available in the cash machine?