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;

class Point {
    public:
        double x, y;
        Point(double x = 0.0, double y = 0.0): 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 k) { return Point(x * k, y * k); }
        Point operator / (double k) { return Point(x / k, y / k); }

        double friend norm(Point p) { return p.x * p.x + p.y * p.y; }
        double friend abs(Point p) { return sqrt(norm(p)); }
        double friend dot(Point p1, Point p2) { return p1.x * p2.x + p1.y * p2.y; }
};
typedef Point Vector;
struct Segment {
    Point p1, p2;
};

Point project(Segment s, Point p) {
    Vector base = s.p2 - s.p1;
    double r = dot(p - s.p1, base) / norm(base);
    return s.p1 + base * r;
}

Point reflection(Segment s, Point p) {
    Point x = project(s, p);
    return p + (x - p) * 2;
}

int main(void) {
    int q;
    Point p, ans;
    Segment s;

    cin >> s.p1.x >> s.p1.y;
    cin >> s.p2.x >> s.p2.y;
    cin >> q;
    for (int i = 0; i < q; i++) {
        cin >> p.x >> p.y;
        ans = reflection(s, p);
        printf("%.10f %.10f\n", ans.x, ans.y);
    }

    return 0;
}