Laravel: How to specify the number of items in pagination via route variable

I'm looking to change the number of items displayed via pagination, specified in the controller via the route below to set the amount of products to display on each page of pagination.

An example would be if the user entered http://example.com/first-category?numProducts=99 they would be shown the view 'pages.category' with 99 items in each page of the pagination. I assume I've got something wrong in the route, but need a little help please.

Routes:

//First returns single product
Route::get('/products/{cat}/{permalink}', 'ShopController@show')->name('shop.product');
//Second gets all items in category group
Route::get('/products/{cat}', 'ShopController@subIndex')->name('shop.cat');
//Third to pass variable prodNum to ShopController for paginate($prodNum)
Route::get('/products/{cat}?numProducts={prodNum}', 'ShopController@subIndexMore')

ShopController.php

The controller looks like this:

// Shows all items in category, set to 10 items per page via paginate(10)
public function subIndex($cat) {
  $category = Category::where('permalink', $cat)->first();
  $products = ProductGroup::where('category', $category->id)->orderBy('id', 'asc')->paginate(10);
  return view('pages.category',compact('products', 'category'));
}
// Shows all items in category, paginate($prodNum) determines how many items in each page
public function subIndexMore($cat, $prodNum) {
  $category = Category::where('permalink', $cat)->first();
  $products = ProductGroup::where('category', $category->id)->orderBy('id', 'asc')->paginate($prodNum);
  return view('pages.category',compact('products', 'category'));
}

via Chebli Mohamed