A particle is allowed to move in the $XY$-plane by choosing any one of the two jumps:
\begin{enumerate}
\item move two units to right and one unit up, i.e., $( a , b ) \mapsto ( a + 2 , b + 1 )$ or
\item move two units up and one unit to right, i.e., $( a , b ) \mapsto ( a + 1 , b + 2 )$.
\end{enumerate}
Let $P = ( 30,63 )$ and $Q = ( 100,100 )$. If the particle starts at the origin, then\\
(A) $P$ is reachable but not $Q$.\\
(B) $Q$ is reachable but not $P$.\\
(C) both $P$ and $Q$ are reachable.\\
(D) neither $P$ nor $Q$ is reachable.