Google Adsense search on your page. How do I show the query in the AdSense for search form?

Situation:
Google Adsense for search with results on your page.
For convenience, another Google Adsense search form is added to the results page.
After the search, the form that appears on the results page is empty and if the user wants to refine the request, he has to re-enter it completely.
The solution to the issue - Google Adsense search on your page. How to show a request in the form of AdSense for search ? ..