binarySearch :: Integral a => (a -> Ordering) -> (a, a) -> Maybe a
binarySearch p (low, high)
   | high < low = Nothing
   | otherwise =
     let mid = (low + high) `div` 2
     in case p mid of
          LT -> binarySearch p (low, mid - 1)
          GT -> binarySearch p (mid + 1, high)
          EQ -> Just mid