Lysine $()-($denoted by $($:$HR\}$ is an essential amino acid, and its hydrochloride salt $([H_{3}R]C{l}_2)$ exists in aqueous solution in the following equilibrium:

F

When an NaOH solution is added to a certain concentration of $[H_{3}R]C{l}_2$ solution, the distribution coefficients $(x)$ of $H_3{R}^{2+},H_2{R}^{+},HR,$ and $R^{-}$vary with $pH$ as shown on the right.

Given that $(x)=\frac{[x]}{[H_3{R}^{2+}]+[H_2{R}^{+}]+[HR]+[R^{-}]},$ which of the following statements is correct?

$($A$)\frac{K_2}{K_1}>\frac{K_3}{K_2}$

r$.$

$($B$)$ At M$,[C{I}^{-}]+[O{H}^{-}]+[R^{-}]=2[H_2{R}^{+}]+[N{a}^{+}]+[H^{+}]$

$($C$)H_2{R}^{+},[$HR$],$ and $R^{-}$cannot be in the solution at the same time.

$($D$)$ At $O,pH=\frac{-1o{g}_2-1og{K}_3}{2}$

$($E$)$ At $P,[C{l}^{-}]>[N{a}^{+}]>[O{H}^{-}]>[H^{+}]$