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:
/*
w2sc
2019/12/19
19:14:17
*/
#include <bits/stdc++.h>
#define ull unsigned long long
#define ll long long
using namespace std;
struct Point{
    double x,y;
    Point(){}
    Point(double xx,double yy){x=xx,y=yy;}
    Point operator +(Point A){return Point(x+A.x,y+A.y);}
    Point operator -(Point A){return Point(x-A.x,y-A.y);}
    Point operator *(double k){return Point(k*x,k*y);}
    double operator *(Point A){return x*A.x+y*A.y;}
    double operator ^(Point A){return x*A.y-y*A.x;}
    double len(){return sqrt(x*x+y*y);}
};
typedef Point Vec;
struct Line{
    Point A,B;
    Line(){}
    Line(Point AA,Point BB){A=AA,B=BB;}
};
int main()
{
    Line l;
    Point p;
    scanf("%lf%lf%lf%lf",&l.A.x,&l.A.y,&l.B.x,&l.B.y);
    int q;
    scanf("%d",&q);
    while(q--)
    {
        scanf("%lf%lf",&p.x,&p.y);
        Vec v=p-l.A,u=(l.B-l.A);
        u=u*(u*v/u.len()/u.len());
        Point re=p+(u-v)*2;
        printf("%.10f %.10f\n",re.x,re.y);
    }
    return 0;
}