Laravel: how to send text input as route parameter?

view

<form method="GET" action="" >
    <input id="q" name="q" type="text" />
    <button type="submit" id="submitButton" class="btn btn-primary">Go</button>
</form>

Route

Route::get('product/search/{page}/{q?}','ProductController@search')->name('searchproduct');

Controller

public function search(Request $request)
    {
        //processing

        return view('products',['products'=> $search_results]);
    }

after submitting the form, the url looks like this:

example.com/appname/public/product/search/1?q=search+this

I want it always to look like this:

example.com/appname/public/product/search/1/search+this

via Chebli Mohamed