How to sort items after search items

Hi all,

I'm doing a ecommerce website that can search item, and after that i need to add in sort option in it. But i dun know how to add in previous request input to sort function.

In my view i have two form

<form action="{{ url('shop/'.$cat.'/search') }}" method="GET">
    <div id="price_range" class="noUi-target noUi-ltr noUi-horizontal noUi-background">
    </div>
                  <input style="width: 30%; margin-right: 10px;" type="number" readonly="true" name="lowerprice" id="price-value-lower" value="0" class="example-val">
                  <input style="width: 30%;" type="number" readonly="true" name="upperprice" id="price-value-upper" value="100" class="example-val">
    </div>              
        <button class="aa-filter-btn" type="submit">Filter</button>
</form>

 <form action="{{ url('shop/'.$cat.'/search') }}" method="GET">
                  <label for="">Sort by</label>
                  <select name="" onchange="this.form.submit()">
                    <option value="1" selected="Default">Default</option>
                    <option value="2">Name</option>
                    <option value="3">Price</option>
                    <option value="4">Date</option>
                  </select>
</form>

And in my item views i have include paginate link which is something like this

<div class="aa-product-catg-pagination">
  {{ $data->appends(request()->input())->links() }}
</div>

my shopController

$data = product::where('ori_price','>',$request->lowerprice)->where('ori_price','<',$request->upperprice)->where('status',0)->paginate(1);

return view('interface.shop', compact('cat','data','totalItem'));

Is there anyway to pass previous request to sort form? or i need to join two form to one single form? Thanks