If $f:\{1,2,3,\mathrm{....}\}\to \{0,\pm 1,\pm \mathrm{2.....}\}$ is defined by 

$f\left(n\right)=\left\{\begin{array}{cc}\begin{array}{l}n\text{/}2\\ -\left(\frac{n-1}{2}\right)\end{array}& \begin{array}{l}ifnis\text{\hspace{0.33em}}even\\ ifnis\text{\hspace{0.33em}}odd\end{array}\end{array}\right.$

then $f^{-1}\left(-100\right)$ is __________

• A

  201

• B

  301

• C

  401

• D

  101