c# fill everything but GraphicsPath

Question

I have some code that looks like that:

GraphicsPath p = new GraphicsPath();
// Add some elements to p ...
// ...

g.FillPath(bgBrush, p);
// where g : Graphics and bgBrush : Brush

Which results in something that looks like this:

### |
  ##|
 ## |

How can I fill the exact complement of the path?

Desired output:

   #|
##  |
#  #|