2020 Cayley Problem 20

For how many pairs (m,n) with m and n integers satisfying 1 \le m \le 100 and 101 \le n \le 205 is 3^m + 7^n divisible by 10?

\textbf{(A)}\ 2600\quad \textbf{(B)}\ 2626\quad \textbf{(C)}\ 2601\quad \textbf{(D)}\ 2650\quad \textbf{(E)}\ 2625

If there are no answer choices shown, enter a numerical answer.

Full credit to this problem is given to the CEMC, you may view all Cayley contests here.