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 <complex>
#include <iomanip>
#include <iostream>

using namespace std;

typedef complex<double> Point;

Point reflection(Point a, Point b) {
  return conj(b / a) * a;
}

int main() {
  double x, y;
  cin >> x >> y;
  complex<double> p1(x, y);
  cin >> x >> y;
  complex<double> p2(x, y);
  int q;
  cin >> q;
  for (int i = 0; i < q; ++i) {
    cin >> x >> y;
    complex<double> p(x, y);
    auto refl = reflection(p2 - p1, p - p1) + p1;
    cout << fixed << setprecision(10) << refl.real() << " " << refl.imag() << endl;
  }
}