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<cstdio>
#include<cmath>
#include<vector>
#include<iomanip>
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;

#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;
		}
};

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 Point Vector;
typedef vector<Point> Polygon;

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;
}

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;
}
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 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);
}

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);
}

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;
}

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)));
}

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(void){
	Circle c;
	int q;
	Line l;
	Point p_1, p_2;
	cin >> c.c.x >> c.c.y >> c.r;
	cin >> q;
	for(int i = 1; i <= q; i++){
		cin >> l.p1.x >> l.p1.y >> l.p2.x >> l.p2.y;
		p_1 = getCrossPoints(c, l).first;
		p_2 = getCrossPoints(c, l).second;
		if(abs(p_1.x - p_2.x) < EPS){
			if(p_1.y < p_2.y) cout << fixed << setprecision(6) << p_1.x << " " << p_1.y << " " << p_2.x << " " << p_2.y << endl;
			else cout << fixed << setprecision(6) << p_2.x << " " << p_2.y << " " << p_1.x << " " << p_1.y << endl;
		}else{
			if(p_1.x < p_2.x) cout << fixed << setprecision(6) << p_1.x << " " << p_1.y << " " << p_2.x << " " << p_2.y << endl;
			else cout << fixed << setprecision(6) << p_2.x << " " << p_2.y << " " << p_1.x << " " << p_1.y << endl;
		}
	}
	return 0;
}