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 = 0.0, double y = 0.0) :
			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 k) {
		return Point(x * k, y * k);
	}
	Point operator /(double k) {
		return Point(x / k, y / k);
	}

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

	bool operator <(Point p) {
		return x != p.x ? x < p.x : y < p.y;
	}
	bool operator ==(Point p) {
		return equals(x, p.x) && equals(y, p.y);
	}
};
typedef Point Vector;

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

double dot(Vector v1, Vector v2) {
	return v1.x * v2.x + v1.y * v2.y;
}
double cross(Vector v1, Vector v2) {
	return v1.x * v2.y - v1.y * v2.x;
}
Vector unitVector(Vector v) {
	return v / v.abs();
}
bool isOrthogonal(Vector v1, Vector v2) {
	return equals(dot(v1, v2), 0.0);
}
bool isOrthogonal(Segment s1, Segment s2) {
	return equals(dot(s1.p2 - s1.p1, s2.p2 - s2.p1), 0.0);
}
bool isOrthogonal(Point l1, Point l2, Point m1, Point m2) {
	return isOrthogonal(l2 - l1, m2 - m1);
}
bool isParallel(Vector v1, Vector v2) {
	return equals(cross(v1, v2), 0.0);
}
bool isParallel(Segment s1, Segment s2) {
	return equals(cross(s1.p2 - s1.p1, s2.p2 - s2.p1), 0.0);
}
bool isParallel(Point l1, Point l2, Point m1, Point m2) {
	return isParallel(l1 - l2, m1 - m2);
}

enum PositionSP {
	COUNTER_CLOCKWISE = -1,
	CLOCKWISE = 1,
	ONLINE_BACK = 2,
	ONLINE_FRONT = -2,
	ON_SEGMENT = 0
};
PositionSP ccw(Point p1, Point p2, Point p) {
	Vector a = p2 - p1, b = p - p1;
	if (cross(a, b) > EPS)
		return COUNTER_CLOCKWISE;
	else if (cross(a, b) < -EPS)
		return CLOCKWISE;
	else if (dot(a, b) < -EPS)
		return ONLINE_BACK;
	else if (a.norm() < b.norm())
		return ONLINE_FRONT;
	else
		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);
}
Point intersection(Segment s1, Segment s2) {
	double d1 = abs(cross(s2.p2 - s2.p1, s1.p1 - s2.p1));
	double d2 = abs(cross(s2.p1 - s2.p2, s1.p2 - s2.p2));
	return s1.p1 + (s1.p2 - s1.p1) * d1 / (d1 + d2);
}
Point projection(Segment s, Point p) {
	Vector base = s.p2 - s.p1;
	double r = dot(p - s.p1, base) / base.norm();
	return s.p1 + base * r;
}

double distancePP(Point p1, Point p2) {
	return (p1 - p2).abs();
}
double distanceLP(Line l, Point p) {
	return abs(cross(l.p2 - l.p1, p - l.p1) / distancePP(l.p2, l.p1));
}
double distanceSP(Segment s, Point p) {
	if (dot(s.p2 - s.p1, p - s.p1) < 0.0)
		return distancePP(s.p1, p);
	else if (dot(s.p1 - s.p2, p - s.p2) < 0.0)
		return distancePP(s.p2, p);
	else
		return distanceLP(s, p);
}
double distanceSS(Segment s1, Segment s2) {
	if (intersect(s1, s2))
		return 0.0;
	else {
		return min(min(distanceSP(s1, s2.p1), distanceSP(s1, s2.p2)),
				min(distanceSP(s2, s1.p1), distanceSP(s2, s1.p2)));
	}
}

class Circle {
public:
	Point c;
	double r;
	Circle(Point c = Point(), double r = 0.0) :
			c(c), r(r) {
	}
};
pair<Point, Point> intersection(Circle c, Line l) {
	Point pr = projection(l, c.c);
	double base = sqrt(c.r * c.r - (pr - c.c).norm());
	Vector e = unitVector(l.p2 - l.p1);
	return make_pair(pr + e * base, pr - e * base);
}

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;
		cin >> l.p1.x >> l.p1.y;
		cin >> l.p2.x >> l.p2.y;
		pair<Point, Point> x = intersection(C, l);
		if (x.first < x.second) {
			cout << fixed << setprecision (10) << x.first.x << " " << x.first.y << " ";
			cout << x.second.x << " " << x.second.y << endl;
		} else {
			cout << fixed << setprecision (10) << x.second.x << " " << x.second.y << " ";
			cout << x.first.x << " " << x.first.y << endl;
		}
	}
	return 0;
}