若函数 $f\left(x\right)=\{\begin{array}{c}{x}^2+1,x\le 1\\ \frac{2}{x},x>1\end{array}$，则 $f\left(f\right(10\left)\right)=$(   )

A．

$lg101$

B．

$b$

C．

$1$

D．

$0$