Balls numbered $1,2,3,\dots$ are deposited in 4 bins, labeled $A,B,C,D$, using the following procedure. Ball 1 is deposited in bin $A$, and balls 2 and 3 are deposited in $B$. The next three balls are deposited in $C$, the next 4 in $D$, and the next 5 balls are deposited in bin $A$, and so on, cycling back to bin $A$ after 4 balls are deposited in bin $D$. In which bin is ball 1000 deposited?