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:
#include<cstdio>
#include<cmath>
struct Point {double x, y;};

double inner(double x1, double y1, double x2, double y2){
    return x1*x2 + y1*y2;
}

double cross(double x1, double y1, double x2, double y2){
    return x1*y2 - y1*x2;
}

double abs(Point x){
    return sqrt(x.x*x.x + x.y*x.y);
}

int main(int argc, char const *argv[])
{
    Point p0, p1, p2;
    Point a, b, x;
    
    int q;
    scanf("%lf %lf %lf %lf", &p1.x, &p1.y, &p2.x, &p2.y);
    a.x = p2.x - p1.x;
    a.y = p2.y - p1.y;

    scanf("%d", &q);
    for(int i=0; i<q; i++){
        scanf("%lf %lf", &p0.x, &p0.y);
        b.x = p0.x - p1.x;
        b.y = p0.y - p1.y;
        if(abs(b)==0){
            printf("%.10lf %.10lf\n", b.x, b.y);
        }
        else{
            double sine = cross(a.x, a.y, b.x, b.y)/(abs(a)*abs(b));
            double cosine = inner(a.x, a.y, b.x, b.y)/(abs(a)*abs(b)); 

            x.x = (2*cosine*cosine-1)*b.x + (2*cosine*sine)*b.y;
            x.y = -(2*cosine*sine)*b.x + (2*cosine*cosine-1)*b.y;
            
            printf("%.10lf %.10lf\n", x.x+p1.x, x.y+p1.y);
        }
    }
    return 0;
}