If a parabola has the focus at $\left(0,-1\right)$ and a directrix line $y=1$, find the standard equation for the parabola.

• A. $4y=x^2$
• B. $4\left(y-1\right)=x^2$
• C. $-4y=x^2$
• D. $-4\left(y+1\right)=x^2$