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 <sstream>
#include <regex>
#include <cstdio>
#include <cmath>
#include <cctype>
#include <string>
#include <vector>
#include <list>
#include <set>
#include <map>
#include <queue>
#include <stack>
#include <algorithm>
#include <functional>
#include <iomanip>

using namespace std;
using ll = long long int;
#define rep(i,n) for(int i = 0; i < n; i++)
#define FOR(i, a, b)  for(int i = (a); i < (b) ; i++)
#define pb push_back
#define SORT(v,n) sort(v, v+n)
#define ALL(x) (x).begin(),(x).end()
#define debug(x) cerr << #x << ": " << x << '\n'
#define elif else if
#define int ll
//const int INF = 100100100;
const int INF = (1LL << 32);
const int MOD = (int)1e9 + 7;
const double EPS = 1e-9;
int dx[8] = { 1, 0, -1, 0, 1, -1, -1, 1 };
int dy[8] = { 0, 1, 0, -1, 1, 1, -1, -1 };
typedef vector<vector<int>> vvi;
typedef vector<vector<vector<int>>> vvvi;
#define equals(a,b) (fabs((a) - (b)) < EPS)

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 and fabs(y - p.y) < EPS;
	}
};

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;
}

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

typedef Segment Line;

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

//直交判定
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);
}

//平行判定
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);
}

//線分sに対する点pの射影
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;
}

//線分ｓに対する点ｐの反射
Point refrect(Segment s, Point p) {
	return p + (project(s, p) - p) * 2.0;
}

//2点間の距離
double getDistance(Point a, Point b) {
	Point res = a - b;
	return res.abs();
}
//点と直線の距離
double getDistanceLP(Line l, Point p) {
	return abs(cross(l.p2 - l.p1, p - l.p1) / Vector(l.p2 - l.p1).abs());
}

//線分ｓと点ｐの距離
double getDistanceSP(Segment s, Point p) {
	if (dot(s.p2 - s.p1, p - s.p1) < 0.0) {
		Point r = p - s.p1;
		return r.abs();
	}
	if (dot(s.p1 - s.p2, p - s.p2) < 0.0) {
		Point r = p - s.p2;
		return r.abs();
	}
	return getDistanceLP(s, p);
}

//counter clock wise
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;
}

//線分と線分の交差判定
bool intersect(Point p1, Point p2, Point p3, Point p4) {
	return (ccw(p1, p2, p3) * ccw(p1, p2, p4) <= 0 and
		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);
}

//線分と線分の距離
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))
	);
}

//線分s1と線分s2の交点
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;
}

//円ｃと線分ｌの交差判定
bool intersect(Circle c, Line l) {
	return getDistanceSP(l, c.c) <= c.r;
}

//円ｃと線分ｌの交点
pair<Point, Point> getCrossPoints(Circle c, Line l) {
	Vector pr = project(l, c.c);
	Vector e = (l.p2 - l.p1) / Vector(l.p2 - l.p1).abs();
	double base = sqrt(c.r * c.r - Vector(pr - c.c).norm());
	return make_pair(pr + e * base, pr - e * base);
}

signed main() {
	ios::sync_with_stdio(false);
	int cx, cy, r;
	cin >> cx >> cy >> r;
	Circle c = Circle(Point(cx, cy), r);
	int q; 
	cin >> q;
	rep(i, q) {
		int x1, y1, x2, y2;
		cin >> x1 >> y1 >> x2 >> y2;
		Line l = Line(Point(x1, y1), Point(x2, y2));
		auto r = getCrossPoints(c, l);
		cout << fixed << setprecision(10);
		if (r.first.x > r.second.x) {
			cout << r.second.x << ' ' << r.second.y << ' ';
			cout << r.first.x << ' ' << r.first.y << endl;
		}elif(r.first.x < r.second.x) {
			cout << r.first.x << ' ' << r.first.y << ' ';
			cout << r.second.x << ' ' << r.second.y << endl;
		}elif(r.first.y < r.second.y) {
			cout << r.first.x << ' ' << r.first.y << " ";
			cout << r.second.x << ' ' << r.second.y << endl;
		}
		else {
			cout << r.second.x << ' ' << r.second.y << " ";
			cout << r.first.x << ' ' << r.first.y << endl;
		}
	}
	return 0;
}