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 _USE_MATH_DEFINES
#include <bits/stdc++.h>
using namespace std;
#define int long long
typedef long long lint;
typedef pair<int,int> P;
const int    INF=(int)1e9;
const int    MOD=(int)1e9+7;
const double EPS=(double)1e-10;
const int    dx[]={-1,0,0,1};
const int    dy[]={0,-1,1,0};
struct Accelerate_Cin{
    Accelerate_Cin(){
        cin.tie(0);ios::sync_with_stdio(0);cout<<fixed<<setprecision(20);
    };
};

//幾何学テンプレート

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

//点
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);}

  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
typedef Point Vector;

//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;
}

//線分
struct Segment{Point p1,p2;};

//直線
typedef Segment Line;

//円
class Circle{
public:
  Point c;   //中心
  double r;  //半径
  Circle(Point c=Point(),double r=0.0):c(c),r(r){}
};

//多角形
typedef vector<Point> Polygon;


//円と直線の交点を求める。

//二つの線分の交差判定をする。
//3点の位置関係を調べる。

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);
}

//ある点から、直線/線分に対する射影を求める。
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;
}

pair<Point,Point> getCrossPoints(Circle c,Line 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);
}


signed main(){
  double cx,cy,r;cin>>cx>>cy>>r;
  Circle c={Point{cx,cy},r};
  int q;cin>>q;
  for(int i=0;i<q;i++){
    double x0,y0,x1,y1;cin>>x0>>y0>>x1>>y1;
    Point p1={x0,y0},p2={x1,y1};
    Line l={p1,p2};
    Point ans1,ans2;
    tie(ans1,ans2)=getCrossPoints(c,l);
    vector<Point>v;
    v.push_back(ans1);
    v.push_back(ans2);
    sort(v.begin(),v.end());
    cout<<fixed<<setprecision(15)<<v[0].x<<" "<<v[0].y<<" "<<v[1].x<<" "<<v[1].y<<endl;

  }

  return 0;
}