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 <iostream>
#include <math.h>
using namespace std;

typedef struct point{
    double x;
    double y;
}vect;

double dot(vect a,vect b){
    return a.x*b.x+a.y*b.y;
}

double cross(vect a,vect b){
    return a.x*b.y-a.y*b.x;
}

double norm(vect a){
    return a.x*a.x+a.y*a.y;
}

double ab(vect a){
    return sqrt(norm(a));
}

point project(point p1,point p2,point p){
    vect v1,v2;
    point px;
    v1.x=p.x-p1.x;
    v1.y=p.y-p1.y;

    v2.x=p2.x-p1.x;
    v2.y=p2.y-p1.y;

    double t=dot(v1,v2)/norm(v2);

    px.x=p1.x+t*v2.x;
    px.y=p1.y+t*v2.y;
    return px;
}

point reflect(point p1,point p2,point p){
    point px=project(p1,p2,p);

    vect ppx,ppx_2;
    ppx.x=px.x-p.x;
    ppx.y=px.y-p.y;

    ppx_2.x=2*ppx.x;
    ppx_2.y=2*ppx.y;

    point pr;
    pr.x=ppx_2.x+p.x;
    pr.y=ppx_2.y+p.y;

    return pr;
}

int main() {
    int q;
    point p1,p2,p,pr;
    cin>>p1.x>>p1.y>>p2.x>>p2.y;
    cin>>q;
    for (int i = 0; i < q; ++i) {
        cin>>p.x>>p.y;
        pr=reflect(p1,p2,p);
        printf("%.8lf %.8lf\n",pr.x,pr.y);
    }
    return 0;
}