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:
#define rep(i, n) for (int i = 0; i < (int)(n); i++)
#define ALL(v) v.begin(), v.end()
typedef long long ll;

#include <bits/stdc++.h>
using namespace std;

#define EPS (1e-10)
#define equals(a,b) (fabs((a)-(b)) < EPS)

// cout<<fixed<<setprecision(15)
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;

//点またはベクトル
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);}
  
  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;
  }
};
typedef Point Vector;
//ベクトルの二乗和と絶対値
double norm(Point p){return p.x*p.x+p.y*p.y;}
double abs(Point p){return sqrt(norm(p));}
//線分または直線
struct Segment{Point p1,p2;};
typedef Segment Line;
//円
class Circle{
public:
  Point c;
  double r;
  Circle(Point c=Point(), double r=0.0): c(c), r(r) {}
};
//多角形
typedef vector<Point> Polygon;
//内積
double dot(Vector a,Vector b){return a.x*b.x+a.y*b.y;}
//外積
double cross(Vector a,Vector b){return a.x*b.y-a.y*b.x;}
//直交判定
bool isOrthgonal(Vector a,Vector b){return equals(dot(a,b), 0.0);}
//平行判定
bool isParallel(Vector a,Vector b){return equals(cross(a,b), 0.0);}
//射影
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;
}
//反射
Point reflect(Segment s,Point p){return p+(project(s,p)-p)*2.0;}
//反時計周りCounter-Clockwise
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(norm(a)<norm(b)) return ONLINE_FRONT;
  return ON_SEGMENT;
}
//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 &&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);}
//点と点の距離
double getDisPP(Point a,Point b){return abs(a-b);}
//直線と点の距離
double getDisLP(Line l,Point p){return abs(cross(l.p2-l.p1,p-l.p1))/abs(l.p2-l.p1);}
//線分と点の距離
double getDisSP(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 getDisLP(s,p);
}
//線分と線分の距離
double getDisSS(Segment s1,Segment s2){
  if(intersect(s1,s2)) return 0.0;
  return min(min(getDisSP(s1,s2.p1),getDisSP(s1,s2.p2)),
             min(getDisSP(s2,s1.p1),getDisSP(s2,s1.p2)));
}
//線分と線分の交点
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;
}
//円と直線の交点
pair<Point,Point> getCrossPoint(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 make_pair(pr+e*base,pr-e*base);
}

int main(){
  double cx,cy,r;
  cin>>cx>>cy>>r;
  Circle c;
  c.c.x=cx,c.c.y=cy,c.r=r;
  
  int q;
  cin>>q;
  
  rep(i,q){
    double x1,y1,x2,y2;
    cin>>x1>>y1>>x2>>y2;
    Line l;
    Point p1,p2;
    p1.x=x1,p1.y=y1,p2.x=x2,p2.y=y2;
    l.p1=p1,l.p2=p2;
    pair<Point,Point> p;
    Point p3,p4;
    p=getCrossPoint(c,l);
    p3=p.first,p4=p.second;
    if(p3.x<p4.x) cout<<fixed<<setprecision(7)<<p3.x<<" "<<p3.y<<" "<<p4.x<<" "<<p4.y<<endl;
    else if(p3.x==p4.x && p3.y<p4.y) cout<<fixed<<setprecision(7)<<p3.x<<" "<<p3.y<<" "<<p4.x<<" "<<p4.y<<endl;
    else cout<<fixed<<setprecision(7)<<p4.x<<" "<<p4.y<<" "<<p3.x<<" "<<p3.y<<endl;
  }
  
  return 0;
}