A line $L : y = m x + 3$ meets $y$-axis at $E ( 0,3 )$ and the arc of the parabola $y ^ { 2 } = 16 x$, $0 \leq y \leq 6$ at the point $F \left( x _ { 0 } , y _ { 0 } \right)$. The tangent to the parabola at $F \left( x _ { 0 } , y _ { 0 } \right)$ intersects the $y$-axis at $G \left( 0 , y _ { 1 } \right)$. The slope $m$ of the line $L$ is chosen such that the area of the triangle $E F G$ has a local maximum.

Match List I with List II and select the correct answer using the code given below the lists:

\textbf{List I}
\begin{itemize}
  \item[P.] $m =$
  \item[Q.] Maximum area of $\triangle EFG$ is
  \item[R.] $y_0 =$
  \item[S.] $y_1 =$
\end{itemize}

\textbf{List II}
\begin{enumerate}
  \item $\frac{1}{2}$
  \item $4$
  \item $2$
  \item $1$
\end{enumerate}

\textbf{Codes:}
\begin{tabular}{ l l l l l }
 & P & Q & R & S \\
(A) & 4 & 1 & 2 & 3 \\
(B) & 3 & 4 & 1 & 2 \\
(C) & 1 & 3 & 2 & 4 \\
(D) & 1 & 3 & 4 & 2 \\
\end{tabular}