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 namespace std;

struct Vector{
    double x,y;
    Vector(double x=0,double y=0):x(x),y(y){}
};
typedef Vector Point;

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

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

double abs(Vector a){
    return sqrt(a.x*a.x+a.y*a.y);
}

int main(){
    Point a,b;
    cin>>a.x>>a.y>>b.x>>b.y;
    int q;
    cin>>q;
    while(q--){
        Point t;
        cin>>t.x>>t.y;
        Vector p1(b.x-a.x,b.y-a.y),p2(t.x-a.x,t.y-a.y);
        double s1=dot(p1,p2);
        double s2=abs(p1);
        double k=s1/(s2*s2);
        Vector p3(k*p1.x,k*p1.y);
        Point d(p3.x+a.x,p3.y+a.y);
        Vector p4(d.x-t.x,d.y-t.y);
        Vector p5(2*p4.x,2*p4.y);
        Point ans(p5.x+t.x,p5.y+t.y);
        printf("%.10lf %.10lf\n",ans.x,ans.y);

    }
}