2024 AMC 10B Problem 4

Balls numbered 1, 2, 3, \ldots are deposited in 5 bins, labeled A, B, C, D, and E, using the following procedure. Ball 1 is deposited in bin A, and balls 2 and 3 are deposited in bin B. The next 3 balls are deposited in bin C, the next 4 in bin D, and so on, cycling back to bin A after balls are deposited in bin E. (For example, balls numbered 22, 23, \ldots, 28 are deposited in bin B at step 7 of this process.) In which bin is ball 2024 deposited?

\textbf{(A)} A \qquad \textbf{(B)} B \qquad \textbf{(C)} C \qquad \textbf{(D)} D \qquad \textbf{(E)} E

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