Shower Soap Rack Screw Heads

[BarnaWill]

So we have a soap and shampoo rack in the bathroom. It's held to the wall by two screws and a fixing system on top.
I tried to remove it to have a good clean, but when I tried to unscrew them, they just broke off. Both screw heads have rusted clean through.
So now I have 2 screw bodies, in their rawl-plugs, with no heads at all. Both of them are flush with the wall, and they're both at the joining point of 2 largish tiles.
How on earth do I get them out? I can't drill them out like I would a messed up rawl-plug. I can't pull them out, there's nothing I can grip onto, and even if I could get a grip on something, the body of the screw is in the rawl plug and tightly screwed in. What next? Any thoughts?
Re-tiling is not an option.

Many thanks all.

[Baldric]

Leave them in situ, drill new holes ½' or so to the side, assuming old holes will be covered by rack, use Brass screws so they don't rust.

Also you could use a punch to tap them below surface and grout over

[Old_Geezer]

You can buy bits to use in a drill that'll grip and turn the screw. Name escapes me at present but try a websearch. You put the drill into reverse and slowly let it unscrew.

http://www.google.co.uk/search?client=ms-android-samsung&site=webhp&ei=ep96V9nLN8qOgAamyYHoCw&;q=grabit+screw+remover&oq=grabbit+screw+re&gs_l=mobile-gws-serp.1.0.0i10l2j0i22i30l3.11220.15436.0.17122.9.9.0.0.0.0.412.1839.0j8j4-1.9.0....0...1c.1.64.mobile-gws-serp..0.9.1835...0.5H8jp8Ge2Vg

[TonyV]

Agree with baidrics advice but worth investing in a set of these

http://www.screwfix.com/p/erbauer-tile-glass-drill-bit-set-3pcs/53634