How can I jump to Firefox’s search field when browsing on github.com?

If I am browsing on github.com and hit CTRL + K, using the browser’s search will not work.

Hitting CTRL+K the first time opens up some spotlight-/albert-like search in the middle of the screen, except it’s just for the site.
Hitting CTRL+K the second time puts the focus in the upper left field.

Is it possible to “escape”, for the lack of a better, term github.com in order to jump to FF’s search field directly?