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:
//By Vlgd
#include<bits/stdc++.h>
#define EPS (1e-10)
#define equals(a,b) (fabs((a)-(b))<EPS)
using namespace std;
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);}
	double abs() {return sqrt(norm());}
	double norm() {return x*x+y*y;}
	bool operator < (const Point &p) const{
		return x!=p.x?x<p.x:y<p.y;
	}
	bool operator == (const Point &p) const{
		return fabs(x-p.x)<EPS && fabs(y-p.y)<EPS;
	}
};
typedef Point Vector;
struct Segment{
	Point p1,p2;
};
double dot(Vector a,Vector b){
	return a.x*b.x+a.y*b.y;
}
Point project(Segment s,Point p){
	Vector base=s.p1-s.p2;
	double r=dot(p-s.p1,base)/base.norm();
	return s.p1+base*r;
}
Point reflect(Segment s,Point p){
	return p+(project(s,p)-p)*2;
}
int main(){
	int x1,y1,x2,y2;
	scanf("%d%d%d%d",&x1,&y1,&x2,&y2);
	Point p1(x1,y1),p2(x2,y2);
	Segment s;
	s.p1=p1;s.p2=p2;
	int q;
	scanf("%d",&q);
	for(int i=0;i<q;i++){
		scanf("%d%d",&x1,&y1);
		Point p=reflect(s,Point(x1,y1));
		printf("%.10lf %.10lf\n",p.x,p.y);
	}	
}