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<iostream>
#include<stdio.h>
#include<math.h>
using namespace std;
#define EPS (1e-15)
#define equals(a,b) (fabs((a)-(b))<EPS)

class Point {
public:
	double x, y;
	Point() {}
	Point(double xx, double yy) {
		x = xx;
		y = yy;
	}
	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 k) { return Point(x * k, y * k); }
	Point operator / (double k) { return Point(x / k, y / k); }

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

	bool operator == (const Point& p) const {
		return fabs(x - p.x) < EPS && fabs(y - p.y) < EPS;
	}
};
struct Segment {
	Point p1, p2;
};
typedef Point Vector;
typedef Segment Line;
class Circle {
public:
	Point c;
	double r;
	Circle(Point cc, double rr) {
		c = cc;
		r = rr;
	}
};

double dot(Vector a, Vector b) {
	return a.x * b.x + a.y * b.y;
}
double cross(Vector a, Vector b) {
	return a.x * b.y - a.y * b.x;
}
Point project(Segment s, Point p) {
	Vector hepo = p - s.p1;
	Vector base = s.p2 - s.p1;
	Vector t = base * (dot(p - s.p1, base) / base.norm());
	Point x = s.p1 + t;
	return x;
}
int main() {
	Point p1, p2, p, x, t;
	cin >> p1.x >> p1.y >> p2.x >> p2.y;
	Segment s;
	s.p1 = p1;
	s.p2 = p2;
	int q;
	cin >> q;
	while (q--) {
		cin >> p.x >> p.y;
		t = project(s, p);
		t = (t - p)*2;
		x = p + t;
		printf("%.9lf %.9lf\n", x.x, x.y);
	}
}