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<iostream>
#include<cstdio>
#include<complex>
using namespace std;

typedef complex<double> Point;

Point project(Point a,Point b,Point c){
	c-=a; b-=a;
	double t=(c.real()*b.real()+c.imag()*b.imag())/abs(b);
	Point z=t/abs(b)*b+a;
	return z;
}

int main(){
	double x1,y1,x2,y2;
	cin>>x1>>y1>>x2>>y2;
	Point p1(x1,y1),p2(x2,y2);
	int z;
	cin>>z;
	while(z--){
		double q1,q2;
		cin>>q1>>q2;
		Point p(q1,q2);
		Point y=project( p1,p2,p);
		printf("%.10lf %.10lf\n",2*y.real()-p.real(),2*y.imag()-p.imag());
	} 
	return 0;
}