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<cmath>
#include<vector>
#include<algorithm>
#include<cassert>

using namespace std;

const double EPS = 1e-10;
bool equals(double a, double b){ return (fabs(a) - fabs(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;

static const int NOTCROSS = 4;
static const int CIRCUMSCRIBED = 3; 
static const int INTERSECT = 2;
static const int INSCRIBED = 1;
static const int INCLUDE = 0;

class Point{
public:
	double x, y;
	
	Point(double x = 0, double y = 0): x(x), y(y) {}
	Point(const Point &p) { x = p.x; y = p.y;};
	
	Point operator + (const Point &p) { return Point(x + p.x, y + p.y); }
	Point operator - (const Point &p) { return Point(x - p.x, y - p.y); }
	Point operator * (const double &a) { return Point(x * a, y * a); }
	Point operator / (const double &a) { return Point(x / a, y / a); }
	
	Point & operator = (const Point& p) {x = p.x; y = p.y; return *this;};
	Point & operator += (const Point& p) {x += p.x; y += p.y; return *this;};
	Point & operator -= (const Point& p) {x -= p.x; y -= p.y; return *this;};
	Point & operator *= (const Point& p) {x *= p.x; y *= p.y; return *this;};
	Point & operator /= (const Point& p) {x /= p.x; y /= p.y; return *this;};
	
	bool operator < (const Point &p) const {
		return x != p.x ? x < p.x : y < p.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;
	}
	
	double abs() { return sqrt(norm()); };
	double norm() { return x * x + y * y;};
};

typedef Point Vector;


double norm(Vector a){
	return a.x * a.x + a.y * a.y;
}

double abs(Vector a){
	return sqrt(norm(a));
}

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;
}

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;



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 isPrallel(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) / norm(base);
	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 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);
}



int intersect(Circle c1, Circle c2){
	double dis = abs(c1.c - c2.c);
	
	if(dis > c1.r + c2.r + EPS) return NOTCROSS;
	if(fabs(dis - c1.r - c2.r) < EPS) return CIRCUMSCRIBED;
	if(dis > fabs(c1.r - c2.r) + EPS) return INTERSECT;
	if(fabs(dis - fabs(c1.r - c2.r)) < EPS) return INSCRIBED;
	return INCLUDE;
}

double getDistace(Point a, Point b){
	return abs(a - b);
}

double getDistanceLP(Line l, Point p){
	return abs(cross(l.p2 - l.p1, p - l.p1)) / abs(l.p2 - l.p1);
}

double getDistanceSP(Segment s, Point p){
	if(dot(s.p2 - s.p1, p - s.p1) < 0.0) return abs(p - s.p1);
	if(dot(s.p1 - s.p2, p - s.p2) < 0.0) return abs(p - s.p2);
	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)));
}

Point getCrosPoint(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;
}

bool intersect(Circle c, Line l){
	return getDistanceLP(l, c.c) < c.r + EPS;
}

pair<Point, Point> getCrossPoint(Circle c, Line l){
	assert(intersect(c,l));
	Vector pr = project(l, c.c);
	Vector e = (l.p2 - l.p1) / abs(l.p2 - l.p1);
	double base = sqrt(c.r * c.r - norm(pr - c.c));
	return make_pair(pr + e * base, pr - e *base);
}

// int getCrosPoint(Circle c1, Circle c2, Point &res1, Point &res2){
	// int ins = intersect(c1, c2);
	// if(ins == NOTCROSS || ins == INCLUDE) return 0;
	// if(ins == CIRCUMSCRIBED){
		// Vector v = c2.c - c1.c;
		// res1 = v*c1.r/(c1.r + c2.r) + c1.c;
		// return 1;
	// }
	// if(ins == INSCRIBED) {
		
		// if(fabs(c1.r - c2.r) < EPS){
			// return -1;// infinity
		// }
		
		// if(c1.r > c2.r){
			// swap(c1, c2);
		// }
		
		// Vector v = c1.c - c2.c;
		// res1 = v*(c2.r - c1.r)/c1.r + c2.c;
		
		// return 1;
	// }
// }




signed main(){
	cin.tie(0);
	ios::sync_with_stdio(false);
	cout<<fixed<<setprecision(10);
	
	Circle c;
	Line L;
	int ans, q;
	
	cin>>c.c.x>>c.c.y>>c.r;
	
	cin>>q;
	
	for(int i = 0; i < q; i++){
		pair<Point,Point> ans;
		cin>>L.p1.x>>L.p1.y>>L.p2.x>>L.p2.y;
		
		ans = getCrossPoint(c,L);
		
		if(ans.first > ans.second) swap(ans.first, ans.second);
		
		cout<<ans.first.x<<" "<<ans.first.y<<" "<<ans.second.x<<" "<<ans.second.y<<endl;
	}
	
	return 0;
}