Problem:
Reflection

For given three points p1, p2, p, find the reflection point x of p onto p1p2.

Input

xp1 yp1 xp2 yp2
q
xp0 yp0
xp1 yp1
...
xpq−1 ypq−1

In the first line, integer coordinates of p1 and p2 are given. Then, q queries are given for integer coordinates of p.

Output

For each query, print the coordinate of the reflection point x. The output values should be in a decimal fraction with an error less than 0.00000001.

Constraints

1 ≤ q ≤ 1000

-10000 ≤ xi, yi ≤ 10000

p1 and p2 are not identical.

Sample Input 1

0 0 2 0
3
-1 1
0 1
1 1

Sample Output 1

-1.0000000000 -1.0000000000
0.0000000000 -1.0000000000
1.0000000000 -1.0000000000

Sample Input 2

0 0 3 4
3
2 5
1 4
0 3

Sample Output 2

4.2400000000 3.3200000000
3.5600000000 2.0800000000
2.8800000000 0.8400000000

Solution in Haskell (judge verdict: Accepted)

import Control.Applicative ((<$>))
import Control.Monad
import Data.Complex
import Text.Printf

type Vector = Complex Double

dot :: Vector -> Vector -> Double
dot a b = realPart $ conjugate a * b

normalize :: Vector -> Vector
normalize = signum

readWords :: Read a => IO [a]
readWords = map read . words <$> getLine

main :: IO ()
main = do
  [x1,y1,x2,y2] <- readWords :: IO [Double]
  let
    p1 = x1:+y1
    p2 = x2:+y2
    d = normalize (p2-p1)

  q <- readLn

  ps <- replicateM q $ do
    [x,y] <- readWords :: IO [Double]
    return $ x:+y

  forM_ ps $ \p -> do
    let x:+y = p+(p1+((p-p1)`dot`d:+0)*d-p)*(2:+0)
    printf "%.10f %.10f\n" x y