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
#include <iostream>
#include <stdio.h>
#include <stdlib.h>
using namespace std;

int main(){
	double xx, yy, X, Y, x, y;
	int xp[2], yp[2], q;

	cin>>xp[0]>>yp[0]>>xp[1]>>yp[1];
	X = xp[1] - xp[0];
	Y = yp[1] - yp[0];

	cin>>q;
	for(int i=0;i<q;i++){
		cin>>xx>>yy;

		if(Y == 0){
			x = xx;
			y = 2*yp[0]-yy;
		}else if(X == 0){
			x = 2*xp[0]-xx;
			y = yy;
		}else{
			x = (X*X*xx-Y*Y*xx+2*X*Y*yy+2*Y*Y*xp[0]-2*X*Y*yp[0])/(X*X+Y*Y);
			y = -X/Y*(x-xx)+yy;
		}

		printf("%.10lf %.10lf\n", x, y);
	}

	return 0;
}