{-# LANGUAGE BangPatterns #-} {-# LANGUAGE OverloadedStrings #-} import qualified Control.Arrow as Arrow import Data.Bits (Bits (unsafeShiftL, unsafeShiftR), FiniteBits (countTrailingZeros)) import Data.Bool (bool) import qualified Data.ByteString.Builder as BSB import qualified Data.ByteString.Char8 as BSC8 import qualified Data.List as List import qualified Data.Vector.Fusion.Stream.Monadic as MS import qualified Data.Vector.Unboxed as VU import qualified GHC.Integer.GMP.Internals as GMP import qualified System.IO as SysIO ------------------------------------------------------------------------------- main :: IO () main = do n <- readLn :: IO Int rep n $ \_ -> do p <- readLn :: IO Int BSB.hPutBuilder SysIO.stdout $ solve p solve :: Int -> BSB.Builder solve n = BSB.string8 $! show n <> (bool " 0\n" " 1\n" (isPrime n)) ------------------------------------------------------------------------------- isPrime :: Int -> Bool isPrime n | n <= 3 = n == 2 || n == 3 | even n = False | otherwise = mr n where mr k | k < 2047 = loop [2] | k < 1373653 = loop [2,3] | k < 9080191 = loop [31,73] | k < 25326001 = loop [2,3,5] | k < 4759123141 = loop [2,7,61] | k < 1122004669633 = loop [2,13,23,1662803] | k < 2152302898747 = loop [2,3,5,7,11] | k < 3474749660383 = loop [2,3,5,7,11,13] | k < 341550071728321 = loop [2,3,5,7,11,13,17] | otherwise = loop [2,325,9375,28178,450775,9780504,1795265022] where !m = k - 1 !s = countTrailingZeros m !d = m .>>. s check3 :: Int -> Bool check3 a = powModInt a d k /= 1 {-# INLINE check3 #-} check4 :: Int -> Int -> Bool check4 a i = (powModInt a (d * (1 .<<. i)) k) /= m {-# INLINE check4 #-} loop [] = True loop (a:as) | check3 a && allok = False | otherwise = loop as where allok = all (check4 a) [0..(s - 1)] ------------------------------------------------------------------------------- rep :: Monad m => Int -> (Int -> m ()) -> m () rep n = flip MS.mapM_ (stream 0 n) {-# INLINE rep #-} stream :: Monad m => Int -> Int -> MS.Stream m Int stream !l !r = MS.Stream step l where step x | x < r = return $ MS.Yield x (x + 1) | otherwise = return MS.Done {-# INLINE [0] step #-} {-# INLINE [1] stream #-} infixl 8 .>>., .<<. (.>>.) :: Bits i => i -> Int -> i (.>>.) = unsafeShiftR {-# INLINE (.>>.) #-} (.<<.) :: Bits i => i -> Int -> i (.<<.) = unsafeShiftL {-# INLINE (.<<.) #-} powModInt :: Int -> Int -> Int -> Int powModInt a n mo = fromInteger $ GMP.powModInteger (fromIntegral a) (fromIntegral n) (fromIntegral mo) {-# INLINE powModInt #-} parse1 :: IO Int parse1 = readLn {-# INLINE parse1 #-} parseN :: Int -> IO (VU.Vector Int) parseN n = VU.replicateM n parse1 {-# INLINE parseN #-}