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 <iomanip>
#include <algorithm>
#include <cmath>
#include <cassert>

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

using namespace std;

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(a*x, a*y); }
	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;
	}
};

typedef Point Vector;

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

typedef Segment Line;

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


double norm(Vector a) {
	return a.norm();
}

double abs(Vector a) {
	return a.abs();
}

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 isOrthogonal(s1.p1, s1.p2, s2.p1, s2.p2);
}

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 isParallel(s1.p1, s1.p2, s2.p1, s2.p2);
}

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

Point reflect(Segment s, Point p) {
	return project(s, p)*2.0 - 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) {
	int p1p2p3, p1p2p4, p3p4p1, p3p4p2;
	p1p2p3 = ccw(p1, p2, p3);
	p1p2p4 = ccw(p1, p2, p4);
	p3p4p1 = ccw(p3, p4, p1);
	p3p4p2 = ccw(p3, p4, p2);

	if (p1p2p3 == ON_SEGMENT) return true;
	if (p1p2p4 == ON_SEGMENT) return true;
	if (p3p4p1 == ON_SEGMENT) return true;
	if (p3p4p2 == ON_SEGMENT) return true;
	if (p1p2p3 == ONLINE_FRONT && p1p2p4 == ONLINE_BACK) return true;
	if (p1p2p3 == ONLINE_BACK && p1p2p4 == ONLINE_FRONT) return true;
	if (p1p2p3 == COUNTER_CLOCKWISE && p1p2p4 == CLOCKWISE && p3p4p1 == CLOCKWISE && p3p4p2 == COUNTER_CLOCKWISE) return true;
	if (p1p2p3 == CLOCKWISE && p1p2p4 == COUNTER_CLOCKWISE && p3p4p1 == COUNTER_CLOCKWISE && p3p4p2 == CLOCKWISE) return true;
	return false;
}

bool intersect(Segment s1, Segment s2) {
	return intersect(s1.p1, s1.p2, s2.p1, s2.p2);
}

bool intersect(Circle c, Line l) {
	return (project(l, c.c) - c.c).norm() <= c.r*c.r;
}

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 (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 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 = 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 - (pr - c.c).norm());
	return make_pair(pr + e*base, pr - e*base);
}

int main() {
	double cx, cy, r;
	cin >> cx >> cy >> r;
	int q;
	cin >> q;
	Circle C;
	C.c.x = cx; C.c.y = cy; C.r = r;
	Line L;
	pair<Point, Point> crossPoints;
	double x1, y1, x2, y2;
	for (int i = 0; i < q; i++) {
		cin >> L.p1.x >> L.p1.y >> L.p2.x >> L.p2.y;
		cout << fixed << setprecision(15);
		crossPoints = getCrossPoints(C, L);
		x1 = crossPoints.first.x;
		y1 = crossPoints.first.y;
		x2 = crossPoints.second.x;
		y2 = crossPoints.second.y;
		if (x1 < x2) {
			cout << x1 << " " << y1 << " " << x2 << " " << y2 << endl;
		}
		else if (x1 > x2) {
			cout << x2 << " " << y2 << " " << x1 << " " << y1 << endl;
		}
		else {
			if (y1 < y2) {
				cout << x1 << " " << y1 << " " << x2 << " " << y2 << endl;
			}
			else if (y1 > y2) {
				cout << x2 << " " << y2 << " " << x1 << " " << y1 << endl;
			}
			else {
				cout << x1 << " " << y1 << " " << x2 << " " << y2 << endl;
			}
		}
	}

	return 0;
}