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 + (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;

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;
}

struct Segment {
    Point p1, p2;
};

typedef Segment Line;

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

typedef vector<Point> Polygon;

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

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

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) {
    Point projection = project(s, p);
    Vector toReflection = (projection - p) * 2.0;
    return p + toReflection; 
}

int ccw(Point p0, Point p1, Point p2) {
    Vector v1 = p1 - p0;
    Vector v2 = p2 - p0;

    // 反時計
    if (cross(v1, v2) > 0.0) return 1;
    // 時計
    if (cross(v1, v2) < 0.0) return -1;

    // p1, p2 が逆方向
    if (dot(v1, v2) < 0.0) return 2;

    // p1, p2 が同方向
    if (v1.abs() < v2.abs()) return -2;
    return 0;
}

bool intersect(Segment s1, Segment s2) {
    return (ccw(s1.p1, s1.p2, s2.p1) * ccw(s1.p1, s1.p2, s2.p2) <= 0
            && ccw(s2.p1, s2.p2, s1.p1) * ccw(s2.p1, s2.p2, s1.p2) <= 0);
}

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);
}

double getDistanceSS(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))
    );
}

double getDistancePP(Point p1, Point p2) {
    return (p2 - p1).abs();
}

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));

    Vector hypo = s1.p2 - s1.p1;
    return s1.p1 + hypo * (d1 / (d1 + d2));
}

pair<Point, Point> getCircleSegmentCrossPoint(Circle c, Segment s) {
    Point projection = project(s, c.c);
    double dist = sqrt(c.r * c.r - (c.c - projection).norm());
    Vector base = s.p2 - s.p1;
    base = base / base.abs();
    Point a = projection + (base * dist);
    return make_pair(projection + (base * dist), projection - (base * dist));
}

void printPoints(Point p1, Point p2) {
    cout << p1.x << " " << p1.y << " " << p2.x << " " << p2.y << endl;
}

int main() {
    cout << fixed << setprecision(11);
    double cx, cy, r;
    cin >> cx >> cy >> r;
    Point c = {cx, cy};
    Circle circle = {c, r};

    int q;
    cin >> q;
    double x1, y1, x2, y2;
    for (int i = 0; i < q; i++) {
        cin >> x1 >> y1 >> x2 >> y2;
        Point p1 = {x1, y1};
        Point p2 = {x2, y2};
        Segment s = {p1, p2};

        pair<Point, Point> crossPoints = getCircleSegmentCrossPoint(circle, s);
        Point first = crossPoints.first;
        Point second = crossPoints.second;
        if (first.x < second.x) {
            printPoints(first, second);
        } else if (first.x > second.x) {
            printPoints(second, first);
        } else {
            if (first.y <= second.y) {
                printPoints(first, second);
            } else {
                printPoints(second, first);
            }
        }
    }

    return 0;
}