设函数 $f(x)=\left\{\begin{array}{l}-1, x < 0, \\ 1, x \geq 0,\end{array} \quad g(x)=\left\{\begin{array}{l}2-a x, x \leq-1, \\ x,-1 < x < 0, \\ x-b, x \geq 0 .\end{array}\right.\right.$
若 $f(x)+g(x)$ 在 $R$ 上连续，则
$\text{A.}$ $a=3, b=1$
$\text{B.}$ $a=3, b=2$
$\text{C.}$ $a=-3, b=1$
$\text{D.}$ $a=-3, b=2$