AMC 10 2021b Problem 16

Call a positive integer an uphill integer if every digit is strictly greater than the previous digit. For example, $1357, 89,$ and $5$ are all uphill integers, but $32, 1240,$ and $466$ are not. How many uphill integers are divisible by $15$? $\textbf{(A)} ~4 \textbf{(B)} ~5 \textbf{(C)} ~6 \textbf{(D)} ~7 \textbf{(E)} ~8$