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;
const double EPS = 1e-8;
const double INF = 1e12;
typedef complex<double> point;
namespace std{
    bool operator < (const point& a, const point& b) {
        return real(a) != real(b) ? real(a) < real(b) : imag(a) < imag(b);
    }
}
double cross(const point& a, const point& b) {
    return imag(conj(a)*b);
}
double dot(const point& a, const point& b) {
    return real(conj(a)*b);
}

int main()
{
    double xp1, yp1, xp2, yp2;
    scanf("%lf %lf %lf %lf", &xp1, &yp1, &xp2, &yp2);
    point p1(xp1, yp1), p2(xp2, yp2);
    int n;
    scanf("%d", &n);
    for(int i = 0; i < n; ++i) {
        double xp, yp;
        scanf("%lf %lf", &xp, &yp);
        point p(xp,yp);
        point q = dot(p-p1,p2-p1)/dot(p2-p1,p2-p1)*(p2-p1);
        point res = p + (q-(p-p1))*2.0;
        printf("%.10lf %.10lf\n", res.real(), res.imag());
    }
    return 0;
}