Automatically Pass Search Terms to Custom Google Search on 404 Pages

Is there a simple way to pass the ‘search’ terms which landed a user on a 404 page to Custom Google Search? The Custom Google Search box is already present on the 404 page, so I would think it would just be a matter of making a few small edits to pass the terms that landed the user on the page to the plugin to run the search.

[This might also be a useful feature request.]