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 <cstring>
#include <string>
#include <vector>
#include <algorithm>
#include <tuple>
#include <queue>
#include <set>
#include <cstdio>
#include <climits>
#include <cmath>
#include <array>
#include <functional>
#include <sstream>
#include <list>
#include <iomanip>
#include <set>
const int MOD=1000000007;
const int INF=1000000000;
using namespace std;
typedef long long ll;
typedef vector<int> vi;
const double eps=1e-10;
const int inf=1e9;
typedef pair<int,int> P;
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,double y): x(x),y(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 * (double k)
  {
    return Point(x*k,y*k);
  }
  Point operator / (double k)
  {
    return Point(x/k,y/k);
  }
  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 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;
}
double norm(Point a)
{
  return a.x*a.x + a.y*a.y;
}
double abs(Vector a)
{
  return sqrt(norm(a));
}
struct Segment
{
  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,double r):  c(c),r(r){}
};

typedef vector<Point> Polygon;


bool isorthogonal(Vector a,Vector b)
{
  return fabs(dot(a,b)-0.0)<eps;
}

bool isparallel(Vector a,Vector b)
{
  return fabs(cross(a,b)-0.0)<eps;
}
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;
}
double getdistance(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);
}

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 getdistanceSS(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)
{
  //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 main(int argc,char const* argv[])
{
  double cx,cy,r;
  cin >> cx >> cy >> r;
  Point mid=Point(cx,cy);
  Circle c=Circle(mid,r);
  int q;
  cin >> q;
  for(int i=0;i<q;i++)
    {
      double p0x,p0y,p1x,p1y;
      cin >> p0x >> p0y >> p1x >> p1y;
      Point p0=Point(p0x,p0y);
      Point p1=Point(p1x,p1y);
      Line s=Segment(p0,p1);
      pair<Point,Point> ans=getcrosspoints(c,s);
      if(ans.second<ans.first)
	{
	  cout << fixed << setprecision(12) << ans.second.x << ' ' << ans.second.y << ' ' << ans.first.x << ' ' << ans.first.y << endl;
	}
      else
	{
      cout << fixed << setprecision(12) << ans.first.x << ' ' << ans.first.y << ' ' << ans.second.x << ' ' << ans.second.y << endl;
	}
    }
}