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>
const double 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 + (Point p){
        return Point(x + p.x, y + p.y);
    }
    Point operator - (Point p){
        return Point(x - p.x, y - p.y);
    }
    Point operator * (Point p){
        return Point(x * p.x, y * p.y);
    }
    Point operator * (double r){
        return Point(x * r, y * r);
    }
    Point operator / (Point p){
        return Point(x / p.x, y / p.y);
    }
    Point operator / (double d){
        return Point(x / d, y / d);
    }

    double abs(){
        return sqrt(norm());
    }
    double norm(){
        return x * x + y * y;
    }

    bool operator < (const Point &p) const {
        return x != p.x ? x < p.x : y < p.y;
    }
    bool operator == (const Point &p) const {
        return fabs(x - p.x) < EPS && fabs(y - p.y) < EPS;
    }
    
    
};

typedef Point Vector;

class Segment : public Point{
    public:
    Point p1, p2;
    Segment(Point p1_, Point p2_){
        p1 = p1_;
        p2 = p2_;
    }
    Segment(double a, double b, double c, double d){
        Point(a, b);
        Point(c, d);
    }
    
};

typedef Segment Line;

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

double dot(Point a, Point b){
    return a.x * b.x + a.y * b.y;
}
double cross(Point a, Point b){
    return a.x * b.y - a.y * b.x;
}
bool isOrthogonal(Point a, Point b){
    return equals(dot(a, b), 0.0);
}
bool isParallel(Point a, Point b){
    return equals(cross(a, b), 0.0);
}
bool isOrthogonal(Segment s1, Segment s2){
    return equals(dot(s1.p2 - s1.p1, s2.p2 - s1.p1), 0.0);
}
bool isParallel(Segment s1, Segment s2){
    return equals(cross(s1.p2 - s1.p1, s2.p2 - s1.p1), 0.0);
}

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

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

int ccw(Point p1, Point p2, Point p3){
    Vector a = p2 - p1;
    Vector b = p3 - p1;
    if( cross(a, b) > EPS ) return 1;
    else if( cross(a, b) < -EPS ) return -1;
    else if( dot(a, b) < -EPS ) return 2;
    else if( a.norm() < b.norm() ) return -2;
    //std::cout << std::fixed << std::setprecision(10) << ans.x << " " << ans.y << std::endl;
    else 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(Point a, Point b){
    return (a - b).abs();
}

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

/*
bool intersect(Circle c, Line l){
    double d = getDistanceLP(l, c.c);
    std::cout << d << std::endl;
    if( (c.r - d) < EPS ){
        return 1;
    }else{
        return 0;
    }
}
*/

double getDistanceSP(Segment s, Point p){
    if(dot(s.p2 - s.p1, p - s.p1) < 0.0) return (p - s.p1).abs();
    if(dot(s.p1 - s.p2, p - s.p2) < 0.0) return (p - s.p2).abs();
    return getDistanceLP(s, p);
}

double getDistance(Segment s1, Segment s2){
    if( intersect(s1, s2) ) return 0.0;
    return std::min(std::min(getDistanceSP(s1, s2.p1), getDistanceSP(s1, s2.p2)), std::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;
}

std::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 std::make_pair(pr + e * base, pr - e * base);

}

int main(void){
    Point p0, p1, p2, p3;
    Circle c;
    std::cin >> c.c.x >> c.c.y >> c.r;
    int q;
    std::cin >> q;


    for(int i = 0; i < q; i++){
        std::cin >> p1.x >> p1.y >> p2.x >> p2.y;
        Line l = Line(p1, p2);
        std::pair<Point, Point> ans;
        
        ans = getCrossPoints(c, l);
        Point ans1, ans2;
        
        if(ans.first.x > ans.second.x){
            ans1 = ans.second;
            ans2 = ans.first;
        }else if(ans.first.x == ans.second.x){
            if(ans.first.y > ans.second.y){
                ans1 = ans.second;
                ans2 = ans.first;
            }else{
                ans1 = ans.first;
                ans2 = ans.second;
            }
        }else{
            ans1 = ans.first;
            ans2 = ans.second;
        }
        
        std::cout << std::fixed << std::setprecision(10) << ans1.x << " " << ans1.y\
        << " " << ans2.x << " " << ans2.y << std::endl;
        
        
    }

    return 0;
}