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 <bits/stdc++.h>

using LD = long double;

struct vec2 {
	LD x, y;
	vec2(LD x = 0, LD y = 0) : x(x), y(y) {}
	vec2 operator + (const vec2 &rhs) const {
		return vec2(x + rhs.x, y + rhs.y);
	}
	vec2 operator - (const vec2 &rhs) const {
		return vec2(x - rhs.x, y - rhs.y);
	}
	LD operator * (const vec2 &rhs) const {
		return x * rhs.x + y * rhs.y;
	}
	LD operator ^ (const vec2 &rhs) const {
		return x * rhs.y - y * rhs.x;
	}
	vec2 operator * (const LD rhs) const {
		return vec2(x * rhs, y * rhs);
	}
	friend vec2 operator * (const LD lhs, const vec2 rhs) {
		return vec2(lhs * rhs.x, lhs * rhs.y);
	}
	vec2 operator / (const LD rhs) const {
		return vec2(x / rhs, y / rhs);
	}
	LD norm2() const {
		return x * x + y * y;
	}
	LD norm() const {
		return std::sqrt(norm2());
	}
	friend std::istream& operator >> (std::istream &cin, vec2 &v) {
		return cin >> v.x >> v.y;
	}
	friend std::ostream& operator << (std::ostream &cout, const vec2 v) {
		return cout << std::fixed << std::setprecision(10) << v.x << ' ' << std::fixed << std::setprecision(10) << v.y;
	}
};
int main() {
	std::ios::sync_with_stdio(0), std::cin.tie(0);
	vec2 v1, v2, v;
	std::cin >> v1 >> v2, v2 = v2 - v1, v2 = v2 / v2.norm();
	int q; std::cin >> q;
	for (int i = 1; i <= q; ++i) {
		std::cin >> v, v = v - v1;
		vec2 p = v1 + (v * v2) * v2;
		std::cout << 2 * p - (v + v1) << '\n';
	}
}