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?