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 <iostream>
#include <cstdio>
#include<cmath>
using namespace std;

int main(){
    double x1, y1, x2, y2, x, y, dx, dy, X, Y, k;
    int q;
    cin >> x1 >> y1 >> x2 >> y2 >> q;
    while (q--){
      cin >> x >> y;
      k=((x1-x2)*(x1-x)+(y1-y2)*(y1-y))/(pow(x1-x2,2)+pow(y1-y2,2));
      X = 2*(x1+k*(x2-x1))-x;
      Y = 2*(y1+k*(y2-y1))-y;
  		printf("%.10lf %.10lf\n",X,Y);
    }
}