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<cmath>
#include<cstdio>
#include<vector>
#define f first
#define s second
#define mp make_pair
#define eps (1e-11)
#define equals(a,b) (fabs((a)-(b))<eps)
using namespace std;

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

  double abs(){ return sqrt(norm());}
  double norm(){ return (x*x+y*y);}
};
typedef Point Vector;
typedef vector<Point> Polygon;

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){}
};

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);}

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;
}

bool isOrthogonal(Vector a,Vector b){
  return equals(dot(a,b),0.0);
}

bool isParallel(Vector a,Vector b){
  return equals(cross(a,b),0.0);
}

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;

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);
}

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 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)));
}

pair<Point,Point> getCrossPoints(Circle c,Line 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 mp(pr+e*base,pr-e*base);
}

int main()
{
  Point A,B;
  int q,a,b;
  Circle C;

  cin>>C.c.x>>C.c.y>>C.r;
  cin>>q;
  for(int i=0;i<q;i++){
    cin>>A.x>>A.y>>B.x>>B.y;
    pair<Point,Point> PP=getCrossPoints(C,Line(A,B));
    if((PP.s.x-PP.f.x)>eps)
      printf("%.10f %.10f %.10f %.10f\n",PP.f.x,PP.f.y,PP.s.x,PP.s.y);
    else if((PP.s.x-PP.f.x)<-eps)
      printf("%.10f %.10f %.10f %.10f\n",PP.s.x,PP.s.y,PP.f.x,PP.f.y);
    else {
      if((PP.s.y-PP.f.y)>eps)
	printf("%.10f %.10f %.10f %.10f\n",PP.f.x,PP.f.y,PP.s.x,PP.s.y);
      else 
	printf("%.10f %.10f %.10f %.10f\n",PP.s.x,PP.s.y,PP.f.x,PP.f.y);
    }
  }
  return 0;
}