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<cstdio>
#include<complex>

typedef std::complex<double> point;

double InnerProd(point x,point y);
point projection(point x,point y);
point reflection(point x,point y,point z);
int main(){
        point p1,p2,p,ans;
        double x1,y1,x2,y2;
        int q;
        scanf("%lf%lf%lf%lf",&x1,&y1,&x2,&y2);
        p1=point(x1,y1);
        p2=point(x2,y2);
        scanf("%d",&q);
        for(int i=0;i<q;i++){
                scanf("%lf%lf",&x1,&y1);
                p=point(x1,y1);
                ans=reflection(p1,p2,p);
                printf("%.10lf %.10lf\n",ans.real(),ans.imag());
        }
        return 0;
}

double InnerProd(point x,point y){
        return (std::conj(x)*y).real();
}

/*x??????y???????°???±*/
point projection(point x,point y){
        return y/std::norm(y)*InnerProd(x,y);
}

/*xy????????????????????¨??????z???????§°???*/
point reflection(point x,point y,point z){
        return 2.0*(projection(z-x,y-x)-(z-x))+z;
}