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

<image>

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>           // printf(), scanf()

static const double EPS = 1e-10;
class Point
{
public:
	double x, y;

	Point(double x = 0, double y = 0): x(x), y(y) {}
	Point operator + (Point p) { return Point(x + p.x, y + p.y); }
	Point operator - (Point p) { return Point(x - p.x, y - p.y); }
	Point operator * (double a) { return Point(a * x, a * y); }
	Point operator / (double a) { return Point(x / a, y / a); }
};

struct Segment
{
	Point p1, p2;
};

typedef Point Vector;
typedef Segment Line;

double
norm(Vector a)
{
	return a.x * a.x + a.y * a.y;
}

double
dot(Vector a, Vector b)
{
	return a.x * b.x + a.y * b.y;
}

Point
project(Segment s, Point p)
{
	Vector base = s.p2 - s.p1;
	double r = dot(p - s.p1, base) / norm(base);
	return s.p1 + base * r;
}

Point
reflect(Segment s, Point p)
{
	return p + (project(s, p) - p) * 2.0;
}

int
main(int argc, char** argv)
{
	Segment s;
	Point p, a;
	int q;
	int x, y;
	int x1, y1, x2, y2;
	int i;

	scanf("%d %d %d %d", &x1, &y1, &x2, &y2);
	s.p1.x = x1, s.p1.y = y1;
	s.p2.x = x2, s.p2.y = y2;

	scanf("%d", &q);
	for (i = 0; i < q; ++i)
	{
		scanf("%d %d", &x, &y);
		p.x = x, p.y = y;

		a = reflect(s, p);
		printf("%.10f %.10f\n", a.x, a.y);
	}

	return 0;
}