C seems more appropriate Looking ahead $"a"$ so $S \rightarrow Aa$ will take care and looking ahead "$b$"$A \rightarrow Ab$ will take care.
Drawing DFA productions will be like :
$S' \rightarrow.S ,\$\\ S\rightarrow.Aa,\$\\A\rightarrow .Ab,a/b\\A\rightarrow .c,a/b$