设 $m,n\in R$,若直线 $\left(m+1\right)x+\left(n+1\right)y-2=0$与圆 ${\left(x-1\right)}^2+{\left(y-1\right)}^2=1$相切,则 $m+n$的取值范围是（）

A．	$\left[1-\sqrt{3},1+\sqrt{3}\right]$	B．	$(-\infty ,1-\sqrt{3})\cup [1+\sqrt{3},+\infty )$
C．	$\left[2-2\sqrt{2},2+2\sqrt{2}\right]$	D．	$(-\infty ,2-2\sqrt{2}]\cup [2+2\sqrt{2},+\infty )$