Improve parsing of search query for edit button.

[gety9]

1, When doing search, example "wireless keyboard amazon"
and then pressing "edit" button you get clean convenient to edit form:

2, But if we leave the page and then return to it (visit another tab) and then press edit then we get less convenient to edit form:

3, And if we tab on query form on page and then press edit, then we get even less convenient to edit form:

In situations 2 and 3 edit query should look like in situation 1 (containing only search query itself)
it will greatly improve value of edit button cause now if user is in situation 2 or 3 he is very unlikely to edit search query but is forced to open new tab and do new search.

[gety9]

p.s. by edit button i mean button "input url".

[gety9]

And this should be relatively easy to do, smg like

editInputUrl
1, If Search
(we will need parser per engine, we can do 1-2 top used engines to cover 80% of users with minimal effort)
1a, If google
(if has "google.com/search?q=" parse it and return search query)
1b, if baidu
(...)
Return query
Else return full url