2011 AIME I Problem 11

Let R be the set of all possible remainders when a number of the form 2^n, n a nonnegative integer, is divided by 1000. Let S be the sum of the elements in R. Find the remainder when S is divided by 1000.

Leading zeroes must be inputted, so if your answer is 34, then input 034

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.