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)
//点を表す構造体
class Point {
  public:
  double x,y;
  Point(double x=0,double y=0): x(x),y(y){}

  //各種演算
  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 abs() { return sqrt(norm()); }
  double norm() { return x*x+y*y; }

  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;
  }
};

//ベクトルを表す構造体
typedef Point Vector;

//線分を表す構造体
struct Segment{
  Segment(Point p1 = Point(), Point p2 = Point()) : p1(p1), p2(p2) {}
  Point p1,p2;
};

//直線を表す構造体
typedef Segment Line;

//円を表すクラス
class Circle{
  public:
  //円の中心
  Point c;
  //半径
  double r;
  Circle(Point c=Point(),double r=0.0): c(c),r(r) {}
};

//多角形の表現
typedef vector<Point> Polygon;

//ベクトルaとbの内積
double dot(Vector a,Vector b){
  return a.x*b.x+a.y*b.y;
}

//ベクトルaとbの外積
double cross(Vector a,Vector b){
  return a.x*b.y-a.y*b.x;
}

//ベクトルaとbの直交判定
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);
}

//ベクトルaとbの平行判定
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を対称軸とした点pの線対称の点
Point reflect(Segment s,Point p){
  return p+(project(s,p)-p)*2.0;
}


//反時計回りCCW
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;
//反時計回りCCW
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p1p2と線分p3p4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 &&
          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);
}


//点aと点bの距離
double getDistace(Point a,Point b){
  return (a-b).abs();
}
//直線lと点pの距離
double getDistaceLP(Line l,Point p){
  return abs(cross(l.p2-l.p1,p-l.p1)/(l.p2-l.p1).abs());
} 
//線分sと点pの距離
double getDistaceSP(Segment s,Point p){
  if(dot(s.p2-s.p1,p-s.p1)<0.0) return (p-s.p1).abs();
  if(dot(s.p1-s.p2,p-s.p2)<0.0) return (p-s.p2).abs();
  return getDistaceLP(s,p);
}
//線分s1と線分s2の距離
double getDistace(Segment s1,Segment s2){
  if(intersect(s1,s2)) return 0.0;
  return min(min(getDistaceSP(s1,s2.p1),getDistaceSP(s1,s2.p2))
  ,min(getDistaceSP(s2,s1.p1),getDistaceSP(s2,s1.p2)));
}

//線分s1と線分s2の交点
Point getCrossPoint(Segment s1,Segment s2){
  Vector base=s1.p2-s1.p1;
  double d1=abs(cross(base,s2.p2-s2.p1));
  double d2=abs(cross(base,s1.p2-s2.p1));
  if(equals(fabs(d1),0.0) && equals(fabs(d2),0.0)) return s2.p1;
  return s2.p1+(s2.p2-s2.p1)*d2/d1;
}

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

int main(){
  cin.tie(nullptr);
  ios_base::sync_with_stdio(false);
  int cx,cy,r;
  cin>>cx>>cy>>r;
  Point p(cx,cy);
  Circle c(p,r);
  int q;
  cin>>q;
  for(int i=0;i<q;i++){
    int x0,x1,y0,y1;
    cin>>x0>>y0>>x1>>y1;
    Point p1(x0,y0),p2(x1,y1);
    Line s1(p1,p2);
    auto p=getCrossPoints(c,s1);
    tie(p1,p2)=p;
    if(p1>p2){
      swap(p1,p2);
    }
    cout<<fixed<<setprecision(15)<<p1.x<<' '<<p1.y<<' '<<p2.x<<' '<<p2.y<<'\n';
  }
  return(0);
}