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;

using ld = long double;
const ld eps = 1e-8, pi = acos(-1.0);

bool eq(ld a, ld b) {
	return abs(a - b) < eps;
}

using Point = complex<ld>;

class Line {
public:
	Point a, b;
};

ld dot(Point a, Point b) {
	return real(conj(a) * b);
}

ld cross(Point a, Point b) {
	return imag(conj(a) * b);
}

int ccw(Point a, Point b, Point c) {
	b -= a, c -= a;
	if (cross(b, c) > eps) return 1;
	if (cross(b, c) < -eps) return -1;
	if (dot(b, c) < 0) return 2;
	if (norm(b) < norm(c)) return -2;
	return 0;
}

bool isis_ll(Line l, Line m) {
	return abs(cross(l.b - l.a, m.b - m.a)) > eps;
}

bool isis_ls(Line l, Line s) {
	return (cross(l.b - l.a, s.a - s.b) * cross(l.b - l.a, s.b - s.a) < eps);
}

bool isis_lp(Line l, Point p) {
	return abs(cross(l.b - p, l.a - p)) < eps;
}

bool isis_sp(Line s, Point p) {
	return abs(s.a - p) + abs(s.b - p) - abs(s.b - s.a) < eps;
}

Point proj(Line l, Point p) {
	ld t = dot(p - l.a, l.a - l.b) / norm(l.a - l.b);
	return l.a + t * (l.a - l.b);
}

int main()
{
	int q;
	ld p1x, p1y, p2x, p2y, x, y;
	cout << fixed << setprecision(9);
	cin >> p1x >> p1y >> p2x >> p2y;
	Line l = { (Point) { p1x, p1y }, (Point) { p2x, p2y } };
	cin >> q;
	while (q--) {
		cin >> x >> y;
		Point p(x, y);
		Point res = proj(l, p) * (ld)2.0 - p;
		cout << res.real() << ' ' << res.imag() << endl;
	}
	return 0;
}