2017 AMC 12B Problem 19

Let N=123456789101112\ldots 4344 be the 79-digit number that is formed by writing the integers from 1 to 44 in order, one after the other. What is the remainder when N is divided by 45?

\textbf{(A)}\ 1\qquad\textbf{(B)}\ 4\qquad\textbf{(C)}\ 9\qquad\textbf{(D)}\ 18\qquad\textbf{(E)}\ 44

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