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 CPP):

Solution:
//http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=CGL_1_B
#include <iostream>
#include <cmath>
#include <cstdio>

using namespace std;

class Point{
private:
    double x;
    double y;
public:
    double getX(){return x;};
    double getY(){return y;};
    void setPoint(double inX, double inY){x = inX; y = inY;};
    void disp(){printf("%.12f %.12f\n", x,y);}
};


int main(){
    int n;
    double inX, inY;
    Point P, P1, P2, Output;
    cin >> inX >> inY;
    P1.setPoint(inX, inY);
    cin >> inX >> inY;
    P2.setPoint(inX, inY);
    cin >> n;
    double ax = P2.getX() - P1.getX();
    double ay = P2.getY() - P1.getY();
    double length = ax*ax + ay*ay;
    for(int i=0; i<n; i++){
        cin >> inX >> inY;
        P.setPoint(inX, inY);
        double bx = P.getX() - P1.getX();
        double by = P.getY() - P1.getY();
        double dot = ax*bx + ay*by;

        double outX = ax * dot/length + P1.getX();
        double outY = ay * dot/length + P1.getY();

        bx = outX - inX;
        by = outY - inY;
        outX += bx;
        outY += by;

        Output.setPoint(outX, outY);
        Output.disp();
    }
    return 0;
}