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<iostream>
#include<vector>
#include<iomanip>
#include<cmath>
#include<algorithm>
#include<cassert>
using namespace std;

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

struct Point;
typedef Point Vector;
typedef vector<Point> Polygon;
struct Circle;
struct Segment;
typedef Segment Line;
double norm(Point a);
double abs(Point a);
double dot(Vector a, Vector b);
double cross(Vector a, Vector b);
double getDistance(Point a, Point b);
double getDistanceLP(Line l, Point p);
double getDistanceSP(Segment s, Point p);
double getDistance(Segment s1, Segment s2);
bool isOrthogonal(Vector a, Vector b);
bool isOrthogonal(Point a1, Point a2, Point b1, Point b2);
bool isOrthogonal(Segment s1, Segment s2);
bool isParallel(Vector a, Vector b);
bool isParallel(Point a1, Point a2, Point b1, Point b2);
bool isParallel(Segment s1, Segment s2);
int ccw(Point p0, Point p1, Point p2);
bool intersect(Point p1, Point p2, Point p3, Point p4);
bool intersect(Segment s1, Segment s2);
bool intersect(Circle c, Line l);
Point project(Segment s, Point p);
Point reflect(Segment s, Point p);
Point getCrossPoint(Segment s1, Segment s2);
pair<Point,Point> getCrossPoints(Circle c, Line l);

struct Point{
    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 * (double a){ return Point(a*x, a*y); }
    Point operator / (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) 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;
typedef vector<Point> Polygon;

struct Circle{
    Point c;
    double r;
    Circle(Point c = Point(), double r = 0.0) : c(c), r(r) {}
};

struct Segment{
    Point p1, p2;
    Segment(Point p1, Point p2) : p1(p1), p2(p2) {}
};

typedef Segment Line;


double norm(Point a){
    return a.x * a.x + a.y * a.y;
}

double abs(Point a){
    return sqrt(norm(a));
}

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 getDistance(Point a, Point b){
    return abs(a - b);
}

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

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

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


bool isOrthogonal(Vector a, Vector b){
    return equals(dot(a, b), 0.0);
}
bool isOrthogonal(Point a1, Point a2, Point b1, Point b2){
    return isOrthogonal(a1-a2, b1-b2);
}
bool isOrthogonal(Segment s1, Segment s2){
    return equals(dot(s1.p2-s1.p1, s2.p2-s2.p1), 0.0);
}
bool isParallel(Vector a, Vector b){
    return equals(cross(a, b), 0.0);
}
bool isParallel(Point a1, Point a2, Point b1, Point b2){
    return isParallel(a1-a2, b1-b2);
}
bool isParallel(Segment s1, Segment s2){
    return equals(cross(s1.p2-s1.p1, s2.p2-s2.p1), 0.0);
}


static const int COUNTER_CLOCKWISE = 1;
static const int CLOCKWISE = -1;
static const int ONLINE_BACK = 2;   // p2->p0->p1
static const int ONLINE_FRONT = -2; // p0->p1->p2
static const int ON_SEGMENT = 0;    // p0->p2->p1

int ccw(Point p0, Point p1, Point p2){
    Vector a = p1 - p0;
    Vector b = p2 - p0;
    if(cross(a, b) > EPS)   return COUNTER_CLOCKWISE;
    if(cross(a, b) < -EPS)  return CLOCKWISE;
    if(dot(a, b) < -EPS)    return ONLINE_BACK;
    if(norm(a) < norm(b))   return ONLINE_FRONT;
    return ON_SEGMENT;
}

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);
}
bool intersect(Circle c, Line l){
    return getDistanceLP(l, c.c) < c.r+EPS; // ?
}

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

Point reflect(Segment s, Point p){
    return p + (project(s, p) - p) * 2.0;
}

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;
}

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


int main(){
    double x, y, r;
    cin >> x >> y >> r;
    Circle C(Point(x,y), r);

    int q;
    cin >> q;

    while(q-- > 0){
        double a, b, c, d;
        cin >> a >> b >> c >> d;
        pair<Point, Point> p = getCrossPoints(C, Line(Point(a,b), Point(c,d)));
        if(p.second < p.first)  swap(p.first, p.second);
        cout << fixed << setprecision(12) << p.first.x << " " << p.first.y << " " << p.second.x << " " << p.second.y << endl;
    }

    return 0;
}