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:
// CGL_1_B.cpp
//
#include <bits/stdc++.h>
using namespace std;

const double EPS = 1e-10;
bool EQ(double a, double b){return fabs(a-b) < EPS;}
typedef complex<double> Point;
#define X real()
#define Y imag()
namespace std {
  bool operator == (const Point &a, const Point &b) {
    return EQ(a.X, b.X) && EQ(a.Y, b.Y);
  }
  bool operator < (const Point &a, const Point &b) {
    return a.X != b.X ? a.X < b.X : a.Y < b.Y;
  }
}
struct Segment {
  Point p1, p2;
  Segment(){};
  Segment(Point p1, Point p2) : p1(p1), p2(p2) {};
};
typedef Segment Line;
double dot(Point a, Point b){return real(conj(a) * b);}
double cross(Point a, Point b){return imag(conj(a) * b);}

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

Point reflect(Segment s, Point p) {
  return p + (project(s, p) - p) * 2.0;
}

int main() {
  int x1,y1,x2,y2,q,xp,yp;
  cin>>x1>>y1>>x2>>y2>>q;
  Line l(Point(x1,y1), Point(x2,y2));
  for(int i=0;i<q;++i){
    cin>>xp>>yp;
    Point p(xp,yp);
    printf("%.10f %.10f\n", reflect(l,p).X, reflect(l,p).Y);
  }

  return 0;
}