2019 Pascal Problem 22

The integer 2019 can be formed by placing two consecutive two-digit positive integers, 19 and 20, in decreasing order. What is the sum of all four-digit positive integers greater than 2019 that can be formed in this way?

\textbf{(A)}\ 476\,681\quad \textbf{(B)}\ 476\,861\quad \textbf{(C)}\ 478\,661\quad \textbf{(D)}\ 468\,671\quad \textbf{(E)}\ 468\,761

If there are no answer choices shown, enter a numerical answer.

Full credit to this problem is given to the CEMC, you may view all Pascal contests here.