#include <iostream>
#include <fstream>
#include <string>
#include <iomanip>
#include <math.h>
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; }
};

typedef Point Vector;


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;
}

int main(){
    //cinの入力元をテキストファイルに(テスト用)
    #if 0
    std::ifstream in("input.txt");
    std::cin.rdbuf(in.rdbuf());
    #endif

    Point p1, p2;
    int q;

    //標準入力
    cin >> p1.x;
    cin >> p1.y;
    cin >> p2.x;
    cin >> p2.y;
    cin >> q;

    Vector v12 = p2 - p1;
    double norm = v12.norm();

    for(int i=0; i<q; i++){
        Point p;
        cin >> p.x;
        cin >> p.y;

        double uvdot = dot(v12, p-p1);
        Vector th = v12 * (uvdot/norm);
        Vector tv = th - (p - p1);
        Vector t = p1 + th + tv;

        std::cout << setprecision(14) << t.x << " " << t.y << "\n";
    }

    return 0;
}


### Prompt

Please provide a CPP coded solution to the problem described below:

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 <iostream>
#include <fstream>
#include <string>
#include <iomanip>
#include <math.h>
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; }
};

typedef Point Vector;


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;
}

int main(){
    //cinの入力元をテキストファイルに(テスト用)
    #if 0
    std::ifstream in("input.txt");
    std::cin.rdbuf(in.rdbuf());
    #endif

    Point p1, p2;
    int q;

    //標準入力
    cin >> p1.x;
    cin >> p1.y;
    cin >> p2.x;
    cin >> p2.y;
    cin >> q;

    Vector v12 = p2 - p1;
    double norm = v12.norm();

    for(int i=0; i<q; i++){
        Point p;
        cin >> p.x;
        cin >> p.y;

        double uvdot = dot(v12, p-p1);
        Vector th = v12 * (uvdot/norm);
        Vector tv = th - (p - p1);
        Vector t = p1 + th + tv;

        std::cout << setprecision(14) << t.x << " " << t.y << "\n";
    }

    return 0;
}


```