code: def make_path_unique(path, counts, new):
      
      added = False
      while any(path == c[:i] for c in counts for i in range(1, len(c)+1)):
          count = counts[path]
          counts[path] += 1
          if (not new and len(path) > 1) or added:
              path = path[:-1]
          else:
              added = True
          path = path + (int_to_roman(count),)
      if len(path) == 1:
          path = path + (int_to_roman(counts.get(path, 1)),)
      if path not in counts:
          counts[path] = 1
      return path
docs: Given a path, a list of existing paths and counts for each of the
      existing paths.