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

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Constraints

* 1 ≤ q ≤ 1000
* -10000 ≤ xi, yi ≤ 10000
* p1 and p2 are not identical.

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.

Examples

Input

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


Output

-1.0000000000 -1.0000000000
0.0000000000 -1.0000000000
1.0000000000 -1.0000000000


Input

0 0 3 4
3
2 5
1 4
0 3


Output

4.2400000000 3.3200000000
3.5600000000 2.0800000000
2.8800000000 0.8400000000

Solution (in JAVA):

Solution:
import java.io.*;
import java.util.Scanner;

public class Main{
    public static void main(String args[]){
        Scanner scan = new Scanner(System.in);
        
        double x = scan.nextDouble();
        double y = scan.nextDouble();
        double xx = scan.nextDouble();
        double yy = scan.nextDouble();
        int qer = scan.nextInt();
                    
        double xxx = 0;
        double yyy = 0;
        xxx = xx - x;
        yyy = yy - y;
        
        double xp[] = new double[qer];
        double yp[] = new double[qer];
        double ansx[] = new double[qer];
        double ansy[] = new double[qer];
        for(int i = 0; i < qer; i++){
            xp[i] = scan.nextDouble();
            yp[i] = scan.nextDouble();
            double xxxx = x - xp[i];
            double yyyy = y - yp[i];
            ansx[i] = x - xxx * (xxxx * xxx + yyyy * yyy) / (xxx * xxx + yyy * yyy);
            ansy[i] = y - yyy * (xxxx * xxx + yyyy * yyy) / (xxx * xxx + yyy * yyy);
            ansx[i] = 2 * ansx[i] - xp[i];
            ansy[i] = 2 * ansy[i] - yp[i];
            System.out.println(ansx[i] + " " + ansy[i]);
        }

    }

}