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>

#define reint register int
#define coint const int

using namespace std;

struct Vector {
    double x, y;

    inline Vector operator+(const Vector &v) const {
        return (Vector){ x + v.x, y + v.y };
    }

    inline double dot(const Vector &v) const { return x * v.x + y * v.y; }
    inline double cross(const Vector &v) const { return x * v.y - y * v.x; }
    inline double length(void) const { return sqrt(x * x + y * y); }

    inline Vector operator*(const double a) const {
        return (Vector){ x * a, y * a };
    }
};

struct Point {
    double x, y;

    inline Vector operator-(const Point &p) const {
        return (Vector){ x - p.x, y - p.y };
    }

    inline Point operator+(const Vector &v) const {
        return (Point){ x + v.x, y + v.y };
    }
};

int main(void) {
    Point p1, p2;
    scanf("%lf%lf%lf%lf", &p1.x, &p1.y, &p2.x, &p2.y);
    const Vector vecP1P2 = p2 - p1;
    const double lenP1P2 = vecP1P2.length();
    int q;
    scanf("%d", &q);
    for (reint i = 1; i <= q; ++i) {
        Point p;
        scanf("%lf%lf", &p.x, &p.y);
        const Vector vecP1P = p - p1;
        const double lenP1H = vecP1P.dot(vecP1P2) / lenP1P2;
        const Vector vecP1H = vecP1P2 * (lenP1H / lenP1P2);
        const Point h = p1 + vecP1H;
        const Point x = (Point){ h.x * 2 - p.x, h.y * 2 - p.y };
        printf("%.12f %.12f\n", x.x, x.y);
    }

    return 0;
}