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 <limits>
#include <cmath>
#include <cstdio>

using namespace std;

#define EPS (numeric_limits<double>::epsilon())
#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) const
    {
        return Point(x + p.x, y + p.y);
    }

    Point operator-(const Point &p) const
    {
        return Point(x - p.x, y - p.y);
    }

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

    Point operator/(const double &a) const
    {
        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 equals(x, p.x) && equals(y, p.y);
    }
};

typedef Point Vector;

struct Segment {
    Point p1, p2;
};
typedef Segment Line;

struct Circle {
    Point c;
    double 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 isParallel(Vector a, Vector b)
{
    return equals(cross(a, b), 0.0);
}

bool isParallel(Point a1, Point a2, Point b1, Point b2)
{
    return equals(cross(a2 - a1, b2 - b1), 0.0);
}

bool isOrthogonal(Vector a, Vector b)
{
    return equals(dot(a, b), 0.0);
}

bool isOrthogonal(Point a1, Point a2, Point b1, Point b2)
{
    return equals(dot(a2 - a1, b2 - b1), 0.0);
}

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

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

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();
}

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

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;

int ccw(Point p0, Point p1, Point p2)
{
    Vector a = p1 - p0;
    Vector b = p2 - p0;
    if (cross(a, b) > 0.0)
        return COUNTER_CLOCKWISE;
    else if (cross(a, b) < 0.0)
        return CLOCKWISE;
    else if (dot(a, b) < 0.0)
        return ONLINE_BACK;
    else if (a.norm() < b.norm())
        return ONLINE_FRONT;
    else
        return ON_SEGMENT;
}

bool intersect(Point p0, Point p1, Point p2, Point p3)
{
    return ccw(p0, p1, p2) * ccw(p0, p1, p3) <= 0
           && ccw(p2, p3, p0) * ccw(p2, p3, p1) <= 0;
}

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

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

int main()
{
    int cx, cy;
    double r;
    cin >> cx >> cy >> r;
    Circle circle = {Point(cx, cy), r};
    int query;
    cin >> query;
    Point p1, p2;
    for (int q = 0; q < query; q++)
    {
        cin >> p1.x >> p1.y >> p2.x >> p2.y;
        pair<Point, Point> points = CrossPoints(circle, Line{p1, p2});
        Point first, second;
        if (!equals(points.first.x, points.second.x))
        {
            if (points.first.x < points.second.x)
            {
                first = points.first;
                second = points.second;
            } else
            {
                first = points.second;
                second = points.first;
            }
        } else
        {
            if (points.first.y < points.second.y)
            {
                first = points.first;
                second = points.second;
            } else
            {
                first = points.second;
                second = points.first;
            }
        }
        printf("%.10f %.10f %.10f %.10f\n", first.x, first.y, second.x, second.y);
    }
}