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 <cmath>
#include <cstdio>

using namespace std;

struct Point {
  double x;
  double y;
};

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

Point vector_sub(Point a, Point b) {
  Point c;
  c.x = b.x - a.x;
  c.y = b.y - a.y;
  return c;
}

double distance2(Point a, Point b) {
  return pow(a.x - b.x, 2) + pow(a.y - b.y, 2);
}

Point projection_vector(Point p0, Point p1, Point p2) {
  Point pv;
  Point v10 = vector_sub(p1, p0);
  Point v12 = vector_sub(p1, p2);
  double aNorm2 = distance2(p1, p2);
  double k = dot(v10, v12) / aNorm2;
  pv.x = k * v12.x;
  pv.y = k * v12.y;
  return pv;
}

Point reflect_vector(Point p0, Point p1, Point p2) {
  Point pv = projection_vector(p0, p1, p2);
  Point v10 = vector_sub(p1, p0);
  return vector_sub(v10, pv);
}

int main(void) {
  Point p0,p1,p2;
  Point v10;
  Point pv;
  int q;
  cin >> p1.x >> p1.y >> p2.x >> p2.y;
  cin >> q;

  for(int i = 0; i < q; i++) {
    cin >> p0.x >> p0.y;
    Point rv = reflect_vector(p0, p1, p2);
    rv.x *= 2;
    rv.y *= 2;
    //printf("%.10lf %.10lf\n", p1.x + projection_vector(p0, p1, p2).x, p1.y + projection_vector(p0, p1, p2).y);
    printf("%.10lf %.10lf\n", p0.x + rv.x, p0.y + rv.y);
  }

}