AMC 8 2007 Problem 18

The product of the two $99$-digit numbers $303,030,303,...,030,303$ and $505,050,505,...,050,505$ has thousands digit $A$ and units digit $B$. What is the sum of $A$ and $B$? $\mathrm{(A)}\ 3 \mathrm{(B)}\ 5 \mathrm{(C)}\ 6 \mathrm{(D)}\ 8 \mathrm{(E)}\ 10$