Mac Mini and ATV2 - Power supply the same?

Quick question - currently have an ATV2 underneath the HDTV.

Just picked up a 2012 Mac Mini. The HDMI cable will obviously fit as is (i.e. plug out of the AT2, into the Mac Mini). What about the power cable?

Will it work - its tied up with a bunch of other cables, so would be very useful if I could simply replace the ATV2 with the Mini, without having to dig in behind the absolutely massive cabinet that everything is positioned on/behind, and swap things out...

 

Joy.

Thanks!