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<iomanip>
using namespace std;

struct Point{
    double x;
    double y;
    Point(double x, double y) : x(x), y(y){}
    Point operator+(Point p){
        return Point(x + p.x, y + p.y);
    }
    Point operator*(double d){
        return Point(x * d, y * d);
    }
};
typedef Point Vector;
double dot(Vector v1, Vector v2){
    return v1.x * v2.x + v1.y * v2.y;
}

int main(){
    int x_p1, y_p1, x_p2, y_p2;
    cin >> x_p1 >> y_p1 >> x_p2 >> y_p2;
    Point p1(x_p1, y_p1);
    Point p2(x_p2, y_p2);
    Vector base(x_p2 - x_p1, y_p2 - y_p1);
    int q;
    cin >> q;
    for (int i = 0; i < q; i++) {
        int x_p, y_p;
        cin >> x_p >> y_p;
        Point p(x_p, y_p);
        Vector hypo(x_p - x_p1, y_p - y_p1);
        Point cross_p = p1 +
                        base * (dot(hypo, base) / dot(base, base));
        Point ans = p + Vector(cross_p.x - p.x, cross_p.y - p.y) * 2.0;
        cout << fixed << setprecision(10);
        cout << ans.x << " " << ans.y << endl;
    }
    return 0;
}