The line $y = m x + 4$ passes through the points ( $3 , \log _ { 2 } p$ ) and ( $\log _ { 2 } p , 4$ ). What are the possible values of $p$ ?
A $p = 1$ and $p = 4$
B $p = 1$ and $p = 16$
C $\quad p = \frac { 1 } { 4 } \quad$ and $\quad p = 4$
D $\quad p = \frac { 1 } { 4 } \quad$ and $\quad p = 64$
E $\quad p = \frac { 1 } { 64 }$ and $p = 4$
F $\quad p = \frac { 1 } { 64 }$ and $p = 16$