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;
using ll = long long;
using ull = unsigned long long;
//#define ll long long
template<class T> bool chmax(T &a, const T &b) { if (a<b) { a=b; return 1; } return 0; }
template<class T> bool chmin(T &a, const T &b) { if (a>b) { a=b; return 1; } return 0; }
#define rep(i, n) REP(i, 0, n)
#define rep_rev(i, n) for (int (i) = (int)(n) - 1 ; (i) >= 0 ; --(i))
#define ALL(v) v.begin(), v.end()
#define MSG(a) cout << #a << " " << a << endl;
#define REP(i, x, n) for(int i = x; i < n; i++)
#define all(x) (x).begin(),(x).end()
ll t1,t2;
const ll mod = 1000000007;
const int INF = 1e9;
const ll INFLONG = 1e18;
void swap(ll *x,ll *y){
  ll tmp;
  tmp = *x;
  *x = *y;
  *y = tmp;
}

#define EPS (1e-10)
#define equals(a,b) (fabs((a) - (b)) < EPS)
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():x(0),y(0){}

    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(x*a,y*a);}
    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 fabs(x - p.x) < EPS && fabs(y - p.y) < EPS;
    }

    void set(double x,double y) {
      this->x = x;
      this->y = y;
    }

    void rotateR(){
      double xt = x;
      double yt = y;
      x = yt;
      y = -xt;
    }
    void rotateL(){
      double xt = x;
      double yt = y;
      x = -yt;
      y = xt;
    }
};

struct Segment{
    Point p1,p2;
};

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



typedef Point Vector;
typedef Segment Line;

double norm(Point a){
  return a.x * a.x + a.y * a.y;
}

double abs(Point a){
  return sqrt(norm(a));
}

bool eq(Point a,Point b){
  return abs(a-b) < EPS;
}

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;
}

//直交
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);
}

//平行
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);
}

//射影
Point project(Segment s,Point p){
  Point vec1,vec2;
  vec1 = s.p2 - s.p1;
  vec2 = p - s.p1;
  return s.p1 + vec1 * dot(vec1,vec2) / vec1.norm();
}

//反射
Point reflect(Segment s,Point p){
  return p + (project(s,p) - p)* 2;
}

//位置関係(時計回りか,線分上かなど)
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);
}

//交わるか
bool intersect(Segment s1,Segment s2){
  return intersect(s1.p1,s1.p2,s2.p1,s2.p2);
}

double getDistance(Point a,Point b){
  return abs(a-b);
}

// Line : Point
double getDistanceLP(Line l,Point p){
  return abs((cross(l.p2 - l.p1,p - l.p1) / abs(l.p2 - l.p1)));
}

// Segment : Point
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;
  }
  double ans = INF;
  chmin(ans,getDistanceSP(s1,s2.p1));
  chmin(ans,getDistanceSP(s1,s2.p2));
  chmin(ans,getDistanceSP(s2,s1.p1));
  chmin(ans,getDistanceSP(s2,s1.p2));
  return ans;
}

bool intersect(Circle c,Line l){
  return c.r - getDistanceLP(l,c.c) > -EPS;
}

//円と直線の交点
pair<Point,Point> getCrossPoint(Line l,Circle c){
  assert(intersect(c,l));
  Vector pr = project(l,c.c);
  Vector e = (l.p2 - l.p1) / abs(l.p2 - l.p1);
  if(e.x < 0 || (e.x < EPS && e.y < 0)){
    e = e * -1;
  }
  double base = sqrt(c.r * c.r - norm(pr - c.c));
  return make_pair(pr - e * base,pr + e * base);
}

//円と円の交点
//pair<Point,Point> getCrossPoint(Circle c1,Circle c2){
//
//}

//int main() {
//  double cx,cy,r;
//  cin >> cx >> cy >> r;
//  Point pc1(cx,cy);
//  cin >> cx >> cy >> r;
//  Point pc2(cx,cy);
//
//  Circle c1(pc1,r),c2(pc2,r);
//}

int main() {
  double cx,cy,r;
  cin >> cx >> cy >> r;
  Point pc(cx,cy);
  Circle c(pc,r);
  ll q;
  double x, y;
  cin >> q;
  vector<Point> p(2);
  Segment s1;
  pair<Point,Point> pa;
  rep(i,q){
    rep(j,2){
      cin >> x >> y;
      p[j] = Point(x,y);
    }
    s1.p1 = p[0];
    s1.p2 = p[1];
    pa = getCrossPoint(s1,c);
    printf("%.15f %.15f ",pa.first.x,pa.first.y);
    printf("%.15f %.15f\n",pa.second.x,pa.second.y);
  }
}