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 rep(i, n) for (int i = 0; i < n; i++)
#define EPS (1e-10)
#define equals(a, b) (fabs((a) - (b)) < EPS)
const int COUNTER_CLOCKWISE = 1;
const int CLOCKWISE = -1;
const int ONLINE_BACK = 2;
const int ONLINE_FRONT = -2;
const int ON_SEGMENT = 0;

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 equals(x, p.x) && equals(y, p.y);
  }

  void print()
  {
    printf("%.10f %.10f\n", x, y);
  }
};

typedef Point Vector;

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;
}

struct Segment
{
  Point p1, p2;
};

typedef Segment Line;

class Circle
{
public:
  Point c;
  double r;
  Circle(Point c = Point(), double r = 0) : c(c), r(r) {}
};

typedef vector<Point> Polygon;

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

Point reflection(Line l, Point p)
{
  Point x = projection(l, p);
  return p + (x - p) * 2;
}

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 is_parallel(Line l1, Line l2)
{
  Vector a = l1.p2 - l1.p1, b = l2.p2 - l2.p1;
  return equals(cross(a, b), 0);
}

bool is_orthogonal(Line l1, Line l2)
{
  Vector a = l1.p2 - l1.p1, b = l2.p2 - l2.p1;
  return equals(dot(a, b), 0);
}

bool intersect(Segment s1, Segment s2)
{
  Point p0 = s1.p1, p1 = s1.p2, p2 = s2.p1, p3 = s2.p2;
  return (ccw(p0, p1, p2) * ccw(p0, p1, p3) <= 0) && (ccw(p2, p3, p0) * ccw(p2, p3, p1) <= 0);
}

Point intersection(Segment s1, Segment s2)
{
  Point p0 = s1.p1, p1 = s1.p2, p2 = s2.p1, p3 = s2.p2;
  double a0 = fabs(cross(p2 - p0, p3 - p0)), a1 = fabs(cross(p2 - p1, p3 - p1));
  return (p0 * a1 + p1 * a0) / (a0 + a1);
}

double line_distance(Line l, Point p)
{
  Point p0 = l.p1, p1 = l.p2;
  return fabs(cross(p1 - p0, p - p0)) / (p1 - p0).abs();
}

double distance(Segment s, Point p)
{
  Point p0 = s.p1, p1 = s.p2;
  if (dot(p1 - p0, p - p0) < -EPS)
  {
    return (p0 - p).abs();
  }
  if (dot(p0 - p1, p - p1) < -EPS)
  {
    return (p1 - p).abs();
  }
  return fabs(cross(p1 - p0, p - p0)) / (p1 - p0).abs();
}

double distance(Segment s1, Segment s2)
{
  if (intersect(s1, s2))
  {
    return 0;
  }
  double res = distance(s1, s2.p1);
  res = min(res, distance(s1, s2.p2));
  res = min(res, distance(s2, s1.p1));
  res = min(res, distance(s2, s1.p2));
  return res;
}

pair<Point, Point> intersection(Circle s, Line l)
{
  Point x = projection(l, s.c);
  double d = line_distance(l, s.c);
  if (equals(d, s.r))
  {
    return make_pair(x, x);
  }
  Point p0 = l.p1, p1 = l.p2;
  Vector u = p1 - p0;
  Vector v = u * (sqrt(s.r * s.r - d * d)) / u.abs();
  Point a0 = x + v, a1 = x - v;
  if (a1 < a0)
  {
    swap(a0, a1);
  }
  return make_pair(a0, a1);
}

int main()
{
  double cx, cy, r;
  cin >> cx >> cy >> r;
  Circle s = {Point{cx, cy}, r};
  int q;
  cin >> q;
  rep(i, q)
  {
    double x0, y0, x1, y1;
    cin >> x0 >> y0 >> x1 >> y1;
    Line l = {Point{x0, y0}, Point{x1, y1}};
    Point a0, a1;
    tie(a0, a1) = intersection(s, l);
    printf("%.10f %.10f %.10f %.10f\n", a0.x, a0.y, a1.x, a1.y);
  }
}