设连续可偏导的函数 $f(x, y)$ 满足 $\lim _{\substack{x \rightarrow 1 \\ y \rightarrow 0}} \frac{f(x, y)-2 x-y+1}{(x-1)^2+y^2}=-1$ ，则 $\lim _{x \rightarrow 0}\left[f\left( e ^{2 x^2}, x \tan 2 x\right)\right]^{\frac{1}{\sqrt{1+x}-\sqrt{1+\ln (1+x)}}}=(\quad)$ ．
A. $e ^6$
B. $e^{12}$
C. $e^{18}$
D. $e ^{24}$