2022 Fermat Problem 15

A positive integer a is input into a machine. If a is odd, the output is a+3. If a is even, the output is a+5. This process can be repeated using each successive output as the next input. For example, if the input is a=1 and the machine is used three times, the final output is 12. If the input is a=15 and the machine is used 51 times, the final output is

\textbf{(A)}\ 213\quad \textbf{(B)}\ 218\quad \textbf{(C)}\ 212\quad \textbf{(D)}\ 220\quad \textbf{(E)}\ 215

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 Fermat contests here.