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 <bits/stdc++.h>
using namespace std;


typedef struct point_{
	double x,y;
	struct point_ operator-(const struct point_ & r) const{
		return {x-r.x,y-r.y};
	}
	struct point_ operator+(const struct point_ & r) const{
		return {x+r.x,y+r.y};
	}
	double norm2(){
		return x*x+y*y;
	}
} Point;

double dot(Point p1,Point p2) {
	return p1.x * p2.x + p1.y * p2.y;
}
Point c_mul(double c,Point p){
	return {c*p.x,c*p.y};
}

int main(){
	Point p1,p2,p;
	int q;
	scanf("%lf%lf%lf%lf%d",&p1.x,&p1.y,&p2.x,&p2.y,&q);
	for(int i = 0; i < q; i++){
		scanf("%lf%lf",&p.x,&p.y);
		Point v = p - p1;
		Point u = p2 - p1;
		Point p1h = c_mul(dot(u,v)/u.norm2(),u);
		Point p1q = c_mul(2,p1h) - v;
		Point ans = p1 + p1q;
		printf("%.10f %.10f\n",ans.x,ans.y);
	}
	return 0;
}