AMC 12 2024a Problem 9

Let $M$ be the greatest integer such that both $M + 1213$ and $M + 3773$ are perfect squares. What is the units digit of $M$?

$\textbf{(A) }1 \textbf{(B) }2 \textbf{(C) }3 \textbf{(D) }6 \textbf{(E) }8$