2023 AMC 8 Problem 18

Greta Grasshopper sits on a long line of lily pads in a pond. From any lily pad, Greta can jump 5 pads to the right or 3 pads to the left. What is the fewest number of jumps Greta must make to reach the lily pad located 2023 pads to the right of her starting position?

\textbf{(A)} 405 \qquad \textbf{(B)} 407 \qquad \textbf{(C)} 409 \qquad \textbf{(D)} 411 \qquad \textbf{(E)} 413

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