CMIMC 2020 Team Problem 8

[system]

Simplify

\binom{2020}{1010}\binom{1010}{1010}+\binom{2019}{1010}\binom{1011}{1010}+\cdots+\binom{1011}{1010}\binom{2019}{1010}+\binom{1010}{1010}\binom{2020}{1010}