#include<cmath>
#include<iostream>
#include<iomanip>
#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(x*a, y*a); }
    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;

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

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


Point project(Point p0, Point p1, Point p2) {
    Point base = p1-p0;
    double r = dot(p2-p0, base) /norm(base);
    return p0 + base*r;
}


Point reflect(Point p0, Point p1, Point p2){
    return p2 + (project(p0,p1,p2)-p2)*2.0;
}

int main() {
    int n,i;
    
    Point p0, p1, p2,p3;
    cin >> p0.x >> p0.y >> p1.x >> p1.y;
    cin >> n;
    for(i=0;i<n;i++){
	cin >>  p2.x >> p2.y;
	p3 = reflect(p0,p1, p2);
	cout << fixed << showpoint;
	cout << setprecision(8);
	cout << p3.x <<" " << p3.y << endl;
    }
    return 0;

}
### Prompt

Please create a solution in Cpp to the following 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

### Response

```cpp
#include<cmath>
#include<iostream>
#include<iomanip>
#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(x*a, y*a); }
    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;

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

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


Point project(Point p0, Point p1, Point p2) {
    Point base = p1-p0;
    double r = dot(p2-p0, base) /norm(base);
    return p0 + base*r;
}


Point reflect(Point p0, Point p1, Point p2){
    return p2 + (project(p0,p1,p2)-p2)*2.0;
}

int main() {
    int n,i;
    
    Point p0, p1, p2,p3;
    cin >> p0.x >> p0.y >> p1.x >> p1.y;
    cin >> n;
    for(i=0;i<n;i++){
	cin >>  p2.x >> p2.y;
	p3 = reflect(p0,p1, p2);
	cout << fixed << showpoint;
	cout << setprecision(8);
	cout << p3.x <<" " << p3.y << endl;
    }
    return 0;

}
```