2021 Fall AMC 10B Problem 3

The expression \frac{2021}{2020} - \frac{2020}{2021} is equal to the fraction \frac{p}{q} in which p and q are positive integers whose greatest common divisor is { }1. What is p?

\textbf{(A)}\: 1\qquad\textbf{(B)} \: 9\qquad\textbf{(C)} \: 2020\qquad\textbf{(D)} \: 2021\qquad\textbf{(E)} \: 4041

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