2020 AIME I Problem 4

Let S be the set of positive integers N with the property that the last four digits of N are 2020, and when the last four digits are removed, the result is a divisor of N. For example, 42{,}020 is in S because 4 is a divisor of 42{,}020. Find the sum of all the digits of all the numbers in S. For example, the number 42{,}020 contributes 4+2+0+2+0=8 to this total.

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.