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<bitset>
#include<cassert>
#include<cctype>
#include<cmath>
#include<cstdio>
#include<cstring>
#include<functional>
#include<limits>
#include<list>
#include<map>
#include<set>
#include<stack>
#include<string>
#include<sstream>
#include<queue>
#include<vector>
using namespace std;

#define MOD 1000000007
#define INF 0x3f3f3f3f
#define INFL 0x3f3f3f3f3f3f3f3fLL

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

//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); }
	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; }

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

};

//1?¬?
typedef Point Vector;

class Segment {
public:
	Point p1, p2;
	Segment(Point p1 = Point(), Point p2 = Point(1, 1)) :p1(p1), p2(p2) {}
};
typedef Segment Line;

//2?¬?
class Circle {
public:
	Point c; //center
	double r; //radius
	Circle(Point c = Point(), double r = 0.0) :c(c), r(r) {}
};
typedef vector<Point> Polygon;

//????§? argument
double arg(Vector p) { return atan2(p.y, p.x); }
//?\???¢??? polar form
Vector polar(double r, double a) { return Point(cos(a)*r, sin(a)*r); }

//?????? dot product
double dot(Vector a, Vector b) { return a.x*b.x + a.y*b.y; }
//?????? cross product
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; }

//??????(p0,p1)????????????p2???????????¢???
enum { ONLINE_FRONT = -2, CLOCKWISE, ON_SEGMENT, COUNTER_CLOCKWISE, ONLINE_BACK };
int ccw(Point p0, Point p1, Point p2) {
	Vector a = p1 - p0, 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); }

//2??????????????¢
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))
	);
}

//?????¨??´??????????????????
bool intersect(Circle c, Line l) { return getDistanceLP(l, c.c) <= c.r; }
//?????¨??????????????????
bool intersect(Circle c1, Circle c2) { return getDistance(c1.c, c2.c) <= c1.r + c2.r; }

//????????¨???????????????
Point getCrossPoint(Segment s1, Segment s2) {
	Vector base = s2.p2 - s2.p1;
	double a1 = abs(cross(base, s1.p1 - s2.p1)); //area1
	double a2 = abs(cross(base, s1.p2 - s2.p1)); //area2
	double t = a1 / (a1 + a2);
	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) / (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);
}
//?????¨????????????
pair<Point, Point> getCrossPoints(Circle c1, Circle c2) {
	assert(intersect(c1, c2));
	double d = (c1.c - c2.c).abs();
	double a = acos((c1.r*c1.r + d*d - c2.r*c2.r) / (2 * c1.r*d));
	double t = arg(c2.c - c1.c);
	return make_pair(c1.c + polar(c1.r, t + a), c1.c + polar(c1.r, t - a));
}

int main() {
	Circle c;
	cin >> c.c.x >> c.c.y >> c.r;
	int q; cin >> q;
	for (int i = 0; i < q; i++) {
		Line l;
		scanf("%lf%lf%lf%lf", &l.p1.x, &l.p1.y, &l.p2.x, &l.p2.y);

		pair<Point, Point> points = getCrossPoints(c, l);
		Point a = points.first;
		Point b = points.second;
		if (b < a)swap(a, b);
		printf("%.10f %.10f %.10f %.10f\n", a.x, a.y, b.x, b.y);
	}

	return 0;
}