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))
#define SQR(n) ((n) * (n))

#define COUNTER_CLOCKWISE (1)
#define CLOCKWISE (-1)
#define ONLINE_BACK (2)
#define ONLINE_FRONT (-2)
#define ON_SEGMENT (0)

struct Point 
{
  double x, y;
  
  Point() {}
  
  Point(double x, double y) : x(x), y(y) {}
  
  void input() { scanf("%lf %lf", &x, &y); }
  void output() { printf("%.10f %.10f", x, y); }
  void outputspace() { output(); putchar(' '); }
  void outputln() { output(); putchar('\n'); }
  
  double abs() { return (sqrt(norm())); }
  double norm() { return (x * x + y * y); }
  
  Point operator + (Point d) { return (Point(x + d.x, y + d.y)); }
  Point operator - (Point d) { return (Point(x - d.x, y - d.y)); }
  Point operator - () { return (Point(-x, -y)); }
  Point operator * (double a) { return (Point(x * a, y * a)); }
  Point operator / (double a) { return (Point(x / a, y / a)); }
  
  bool operator < (Point d) {
    if(x < d.x) return (true);
    if(x > d.x) return (false);
    return (y < d.y);
  }

};

struct Segment
{
  Point p1, p2;
  
  Segment() {}
  Segment(Point p1, Point p2) : p1(p1), p2(p2) {}

  void input() { p1.input(); p2.input(); }
  
};

struct Circle
{
  Point c;
  double r;
  Circle() {}
  Circle(Point c, double r) : c(c), r(r) {}
  
  void inputcr() { c.input(); scanf("%lf", &r); }
  
};

typedef pair < Point, Point > TwoPoint;
typedef Point Vector;
typedef vector < Point > Polygon;
typedef Segment Line;

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);
}

Point project(Line l, Point p)
{
  Vector base = l.p2 - l.p1;
  return (l.p1 + base * (dot(p - l.p1, base) / base.norm()));
}

Point reflect(Line l, Point p)
{
  return (-p + project(l, p) * 2.0);
}


int ccw(Point p0, Point p1, Point p2)
{
  Vector a = p1 - p0, 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));
}


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

double getDistanceSP(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 (getDistanceLP(s, p));
}

double getDistance(Segment s1, Segment s2)
{
  double ans;

  if(intersect(s1, s2)) {
    ans = 0.0;
  } else {
    ans = min(getDistanceSP(s2, s1.p1), getDistanceSP(s2, s1.p2));
    ans = min(ans, min(getDistanceSP(s1, s2.p1), getDistanceSP(s1, s2.p2)));
  }

  return (ans);
}

Point getCrossPoint(Segment s1, Segment s2)
{
  double d1 = getDistanceLP(s2, s1.p1);
  double d2 = getDistanceLP(s2, s1.p2);
  
  return (s1.p1 + (s1.p2 - s1.p1) * (d1 / (d1 + d2)));
}

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

TwoPoint getCrossPoints(Circle c, Line l)
{
  Vector pr, e;
  double base;
  if(intersect(c, l)) abort();
  
  pr = project(l, c.c);
  base = sqrt(SQR(c.r) - (pr - c.c).norm());
  e = (l.p2 - l.p1) / (l.p2 - l.p1).abs();
  
  return (make_pair(pr + (e * base), pr - (e * base)));
}

int main()
{
  int n;
  Circle c;
  
  c.inputcr(); cin >> n;
  for(int i = 0; i < n; i++) {
    Line l;
    TwoPoint tp;
    
    l.input();
    tp = getCrossPoints(c, l);

    if(tp.second < tp.first) swap(tp.first, tp.second);
    tp.first.outputspace(); tp.second.outputln();
  }

  return (0);
}