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 <string>
#include <stack>
#include <queue>
#include <vector>
#include <list>
#include <set>
#include <map>
#include <algorithm>
#include <cmath>

#include <cstdio>

using namespace std;
#define rep(i, n) for (int i = 0; i < (n); i++)
#define repc(i, s, n) for (int i = (s); i <= (n); i++)
#define rrep(i, n) for (int i = (n) - 1; i >= 0; i--)
#define rrepc(i, s, n) for (int i = (s); i >= (n); i--)
typedef long long ll;
typedef unsigned long long ull;

/*================================================
	Geometry
================================================*/
#define EPS (1e-10)
#define equals(a, b) (fabs((a) - (b)) < EPS)

const int COUNTER_CLOCKWISE = 1;
const int CLOCKWISE = -1;
const int ONLINE_BACK = 2;
const int ONLINE_FRONT = -2;
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 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;
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;

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; }

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) { 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); }

double Distance_PP(Point a, Point b) { return (a - b).abs(); }
double Distance_PL(Point p, Line l) { return abs(cross(l.p2 - l.p1, p - l.p1)) / (l.p2 - l.p1).abs(); }
double Distance_PS(Point p, Segment s) {
	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 Distance_PL(p, s);
}
double Distance_SS(Segment s1, Segment s2) {
	double op1, op2, op3, op4, distance;

	if (intersect(s1, s2)) return 0.0;

	op1 = Distance_PS(s1.p1, s2);
	op2 = Distance_PS(s1.p2, s2);
	op3 = Distance_PS(s2.p1, s1);
	op4 = Distance_PS(s2.p2, s1);

	distance = min(op1, op2);
	distance = min(distance, op3);
	distance = min(distance, op4);

	return distance;
}
Point CrossPoint(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;
}
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;
}
pair<Point, Point> CrossPoint(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()
{
	int q;
	pair<Point, Point> ans;
	Circle c;
	Line l;

	cin >> c.c.x >> c.c.y >> c.r;
	cin >> q;
	rep(i, q) {
		cin >> l.p1.x >> l.p1.y >> l.p2.x >> l.p2.y;
		ans = CrossPoint(c, l);
		if (ans.first.x < ans.second.x ||
			(ans.first.x == ans.second.x) && (ans.first.y < ans.second.y)) {
			printf("%.10lf %.10lf %.10lf %.10lf\n", ans.first.x, ans.first.y, ans.second.x, ans.second.y);
		}
		else printf("%.10lf %.10lf %.10lf %.10lf\n", ans.second.x, ans.second.y, ans.first.x, ans.first.y);
	}

	return 0;
}