Problem: For given three points p1, p2, p, find the reflection point x of p onto p1p2.

<image>

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;

typedef long double ld;

const ld EPS = 1e-9;
const ld INF = 1e10;
const ld PI = M_PI;

struct Point{
  ld x, y;
  Point(ld x, ld y):x(x), y(y){}
  Point(){}
};

Point operator+(const Point &a, const Point &b){
  return Point(a.x + b.x, a.y + b.y);
}
Point operator-(const Point &a, const Point &b){
  return Point(a.x - b.x, a.y - b.y);
}
Point operator*(const Point &a, const ld b){
  return Point(a.x * b, a.y * b);
}
Point operator*(const Point &a, const Point &b){
  return Point(a.x*b.x-a.y*b.y, a.x*b.y+a.y*b.x);
}
Point operator/(const Point &a, const ld b){
  return Point(a.x / b, a.y / b);
}

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

ld norm(const Point &a){
  return dot(a, a);
}

struct Line:vector<Point>{
  Line(Point a = Point(0, 0), Point b = Point(0, 0)){
    this->push_back(a);
    this->push_back(b);
  }
};

Point projection(const Line &l, const Point &p){
  ld t = dot(p-l[0], l[1]-l[0]) / norm(l[0] - l[1]);
  return l[0] + (l[1] - l[0]) * t;
}

Point reflection(const Line &l ,const Point &p){
  return p + (projection(l, p) - p) * 2;
}

int main(){  
  Point p0, p1;
  cin >> p0.x >> p0.y >> p1.x >> p1.y;  
  Line base(p0, p1);
  
  int q;
  cin >> q;
  
  Point p2;
  while(q--){
    cin >> p2.x >> p2.y;
    
    Point ans = reflection(base, p2);
    printf("%.10Lf %.10Lf\n", ans.x, ans.y);
  }
  
  return 0;
}