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 <cmath>
#include <algorithm>
#include <vector>
#include <iomanip>
using namespace std;
#define EPS (1e-10)
#define equals(a, b) (fabs((a) - (b)) < EPS)
static const int COUNTER_CLOCKWISE = 1;
static const int CLOCKWISE = -1;
static const int ONLINE_BACK = 2;
static const int ONLINE_FRONT = -2;
static const int ON_SEGMENT = 0;

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 * (double a) { return Point(x * a, y * a); }
    Point operator / (double a) { return Point(x / a, y / a); }

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

    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;
    }
};

struct Segment {
    Point p1, p2;
};

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

typedef vector<Point> Polygon;
typedef Point Vector;
typedef Segment Line;

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(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);
}

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) * 2.0;
}

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

double getDistanceLP(Line l, Point p) {
    return fabs(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) < 0.0) 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);
}

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 ( a.norm() < b.norm() ) 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);
}

double getDistance(Segment s1, Segment s2) {
    if ( intersect(s1, s2) ) return 0.0;
    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 = fabs(cross(s1.p1 - s2.p1, base));
    double d2 = fabs(cross(s1.p2 - s2.p1, base));
    double t = d1 / (d1 + d2);
    return s1.p1 + (s1.p2 - s1.p1) * t;
}

pair<Point, Point> getCrossPoints(Circle c, Line 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()
{
    int q;
    double x1, x2, x3, y1, y2, y3, r;
    Line l;
    cin >> x1 >> y1 >> r;
    Circle c = Circle(Point(x1, y1), r);
    cin >> q;
    for (int i = 0; i != q; ++i)
    {
        cin >> x2 >> y2 >> x3 >> y3;
        l.p1 = Point(x2, y2);
        l.p2 = Point(x3, y3);
        pair<Point, Point> res = getCrossPoints(c, l);
        cout << fixed << setprecision(10);
        if (res.first < res.second)
        {
            cout << res.first.x << " " << res.first.y << " " << res.second.x << " " << res.second.y << endl;
        }
        else
        {
            cout << res.second.x << " " << res.second.y << " " << res.first.x << " " << res.first.y << endl;
        }
        
    }
    return 0;
}