{-# LANGUAGE BangPatterns #-} {-# LANGUAGE FlexibleInstances #-} {-# LANGUAGE TupleSections #-} import Control.Monad import Control.Monad.Fix import Control.Monad.State import Control.Monad.Cont import Data.IORef import qualified Data.Vector.Fusion.Stream.Monadic as VFSM import qualified Data.Vector.Unboxed as VU import qualified Data.Vector.Unboxed.Mutable as VUM main :: IO () main = do [a, b] <- map (read :: String -> Int) . words <$> getLine let cs = divisor (a + b) ans <- newIORef ((-1) :: Int) withBreak $ \break -> rep' (VU.length cs) $ \i -> do let c = cs VU.! i when (a /= c && b /= c && (b + c) `mod` a == 0 && (a + c) `mod` b == 0) $ do liftIO (writeIORef ans c) break() ret <- readIORef ans print ret divisor :: Int -> VU.Vector Int divisor n = VU.filter (/= 0) $ VU.create $ do ret <- VUM.unsafeNew 6720 -- <= 10^12 rep n $ \i -> do when (mod n i == 0) $ do flip fix 0 $ \loop !index -> do item <- VUM.unsafeRead ret index if item == 0 then VUM.unsafeWrite ret index i else loop (index + 1) when (i * i /= n) $ do flip fix 1 $ \loop !index -> do item <-VUM.unsafeRead ret index if item == 0 then VUM.unsafeWrite ret index (div n i) else loop (index + 1) return ret stream :: Monad m => Int -> Int -> VFSM.Stream m Int stream !l !r = VFSM.Stream step l where step x | x * x <= r = return $ VFSM.Yield x (x + 1) | otherwise = return $ VFSM.Done {-# INLINE [0] step #-} {-# INLINE [1] stream #-} rep :: Monad m => Int -> (Int -> m ()) -> m () rep n = flip VFSM.mapM_ (stream 1 n) {-# INLINE rep #-} stream' :: Monad m => Int -> Int -> VFSM.Stream m Int stream' !l !r = VFSM.Stream step l where step x | x < r = return $ VFSM.Yield x (x + 1) | otherwise = return $ VFSM.Done {-# INLINE [0] step #-} {-# INLINE [1] stream' #-} rep' :: Monad m => Int -> (Int -> m ()) -> m () rep' n = flip VFSM.mapM_ (stream' 0 n) {-# INLINE rep' #-} withBreak :: ((r -> ContT r IO b) -> ContT r IO r) -> IO r withBreak = flip runContT pure . callCC {-# INLINE withBreak #-}