Fix bing page numbering, add sc to parameter, minor refactor

Bing page numbering doesn't increase by 10 each time. The first page returns 10 results, and all pages thereafter return 14 results. This means we need to update the page numbering

Next, the 'sc' parameter, whatever it means, needs to be present in order to not return the same results.

Finally, the code to check the page had some duplicate checks, so I refactored the code in this section which is low-risk.

searx/engines/bing.py

@@ -72,7 +72,16 @@ base_url = 'https://www.bing.com/search'
 
 
 def _page_offset(pageno):
-    return (int(pageno) - 1) * 10 + 1
+    """
+    Page 1 => 1 (returns 10 results)
+    Page 2 => 11 (returns 14 results)
+    Page 3 => 25 (returns 14 results)
+    Page 4 => 39 (returns 14 results)
+    """
+    pageno_int = int(pageno)
+    if pageno_int <= 1:
+        return 1
+    return 11 + (pageno_int - 2) * 14
 
 
 def set_bing_cookies(params, engine_language, engine_region):
@@ -95,18 +104,19 @@ def request(query, params):
         # don't ask why it is only sometimes / its M$ and they have never been
         # deterministic ;)
         'pq': query,
+        # Unsure meaning of sc, but breaks bing if not present
+        'sc': '0-0',
     }
 
     # To get correct page, arg first and this arg FORM is needed, the value PERE
     # is on page 2, on page 3 its PERE1 and on page 4 its PERE2 .. and so forth.
     # The 'first' arg should never send on page 1.
-
     if page > 1:
         query_params['first'] = _page_offset(page)  # see also arg FORM
-    if page == 2:
-        query_params['FORM'] = 'PERE'
-    elif page > 2:
-        query_params['FORM'] = 'PERE%s' % (page - 2)
+        if page == 2:
+            query_params['FORM'] = 'PERE'
+        else:  # page > 2:
+            query_params['FORM'] = 'PERE%s' % (page - 2)
 
     params['url'] = f'{base_url}?{urlencode(query_params)}'