Problem: For given a circle $c$ and a line $l$, print the coordinates of the cross points of them.

Constraints

* $p1$ and $p2$ are different
* The circle and line have at least one cross point
* $1 \leq q \leq 1,000$
* $-10,000 \leq cx, cy, x1, y1, x2, y2 \leq 10,000$
* $1 \leq r \leq 10,000$

Input

The input is given in the following format.

$cx\; cy\; r$
$q$
$Line_1$
$Line_2$
:
$Line_q$


In the first line, the center coordinate of the circle and its radius are given by $cx$, $cy$ and $r$. In the second line, the number of queries $q$ is given.

In the following $q$ lines, as queries, $Line_i$ are given ($1 \leq i \leq q$) in the following format.

$x_1\; y_1\; x_2\; y_2$

Each line is represented by two points $p1$ and $p2$ which the line crosses. The coordinate of $p1$ and $p2$ are given by ($x1$, $y1$) and ($x2$, $y2$) respectively. All input values are given in integers.

Output

For each query, print the coordinates of the cross points in the following rules.

* If there is one cross point, print two coordinates with the same values.
* Print the coordinate with smaller $x$ first. In case of a tie, print the coordinate with smaller $y$ first.



The output values should be in a decimal fraction with an error less than 0.000001.

Example

Input

2 1 1
2
0 1 4 1
3 0 3 3


Output

1.00000000 1.00000000 3.00000000 1.00000000
3.00000000 1.00000000 3.00000000 1.00000000

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;

#define EPS (1e-10)
#define equals(a,b) (fabs((a)-(b))<EPS)

class Point{
    public:
    double x,y;
    Point(double x=0,double y=0):x(x),y(y){}
    Point operator+(const Point &p){
        return Point(x+p.x,y+p.y);
    }
    Point operator-(const Point &p){
        return Point(x-p.x,y-p.y);
    }
    Point operator*(const double &a){
        return Point(a*x,a*y);
    }
    Point operator/(const double &a){
        return Point(x/a,y/a);
    }
    double abs(){
        return sqrt(norm());
    }
    double norm(){
        return x*x+y*y;
    }
    bool operator<(const Point &p){
        return x!=p.x?x<p.x:y<p.y;
    }
    bool operator==(const Point &p){
        return fabs(x-p.x)<EPS&&fabs(y-p.y)<EPS;
    }
};
typedef Point Vector;
struct Segment{
    Point p1,p2;
    Segment(){}
    Segment(Point p1,Point p2):p1(p1),p2(p2){}
};
typedef Segment Line;

class Circle{
    public:
    Point c;
    double r;
    Circle(Point c=Point(),double r=0):c(c),r(r){}
};

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;
}

bool isOrthogonal(Segment s1,Segment s2){
    return equals(dot(s1.p2-s1.p1,s2.p2-s2.p1),0.0);
}

bool isParallel(Segment s1,Segment s2){
    return equals(cross(s1.p2-s1.p1,s2.p2-s2.p1),0.0);
}

Point project(Segment s,Point p){
    Vector base=s.p2-s.p1;
    double r=dot(p-s.p1,base)/base.norm();
    return s.p1+base*r;   
}

Point reflect(Segment s,Point p){
    return p+(project(s,p)-p)*2;
}

double getDistanceLP(Line l,Point p){
    return abs(cross(l.p2-l.p1,p-l.p1))/(l.p2-l.p1).abs();
}

double getDistanceSP(Segment s,Point p){
    if(dot(s.p2-s.p1,p-s.p1)<0){
        return (p-s.p1).abs();
    }
    if(dot(s.p1-s.p2,p-s.p2)<0){
        return (p-s.p2).abs();
    }
    return getDistanceLP(s,p);
}

int ccw(Point p0,Point p1,Point p2){
    Vector a=p1-p0;
    Vector b=p2-p0;
    if(cross(a,b)>EPS) return 1;
    if(cross(a,b)<-EPS) return -1;
    if(dot(a,b)<-EPS) return 2;
    if(a.norm()<b.norm()) return -2;
    return 0;
}

bool intersect(Point p1,Point p2,Point p3,Point p4){
    return (ccw(p1,p2,p3)*ccw(p1,p2,p4)<=0&&
        ccw(p3,p4,p1)*ccw(p3,p4,p2)<=0);
}

bool intersect(Segment s1,Segment s2){
    return intersect(s1.p1,s1.p2,s2.p1,s2.p2);
}

double getDistance(Segment s1,Segment s2){
    if(intersect(s1,s2)) return 0;
    return min(min(getDistanceSP(s1,s2.p1),getDistanceSP(s1,s2.p2)),
        min(getDistanceSP(s2,s1.p1),getDistanceSP(s2,s1.p2)));
}

Point getCrossPoint(Segment s1,Segment s2){
    Vector base=s2.p2-s2.p1;
    double d1=abs(cross(base,s1.p1-s2.p1));
    double d2=abs(cross(base,s1.p2-s2.p1));
    double t=d1/(d1+d2);
    return s1.p1+(s1.p2-s1.p1)*t;
}

bool intersect(Circle c,Line l){
    double x=getDistanceLP(l,c.c);
    return (x<=c.r);    
}

pair<Point,Point> getCrossPoints(Circle c,Line l){
    assert(intersect(c,l));
    Vector pr=project(l,c.c);
    Vector e=(l.p2-l.p1)/(l.p2-l.p1).abs();
    double base=sqrt(c.r*c.r-(pr-c.c).norm());
    return make_pair(pr+e*base,pr-e*base);
}

int main(){
    double cx,cy,r,a,b,c,d;
    cin>>cx>>cy>>r;
    int q;
    cin>>q;
    Point c1,p1,p2;
    c1=Point(cx,cy);
    Circle cc(c1,r);
    for(int i=0;i<q;i++){
        cin>>a>>b>>c>>d;
        p1=Point(a,b);
        p2=Point(c,d);
        Line l(p1,p2);
        auto points=getCrossPoints(cc,l);
        if(points.first<points.second){
            printf("%.6lf %.6lf %.6lf %.6lf\n",
                points.first.x,points.first.y,
                points.second.x,points.second.y);
        }
        else{
            printf("%.6lf %.6lf %.6lf %.6lf\n",
                points.second.x,points.second.y,
                points.first.x,points.first.y);
        }
    }
}