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)

// ???/????????????
struct Point {
  double x, y;
  Point(double x = 0.0, double y = 0.0):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(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;
  }
};
typedef Point Vector;

// ???
struct Circle {
  Point c;
  double r;
  Circle(Point c = Point(), double r = 0.0):c(c), r(r){}
};

// ????§???¢
typedef vector<Point> Polygon;

// ??????/??´???
struct Segment {
  Point p1, p2;
};
typedef Segment Line;

// ????????????????????????
double norm(Vector v)
{
  return v.x*v.x + v.y*v.y;
}
// ?????????????????§??????
double abs(Vector v)
{
  return sqrt(norm(v));
}
// ?????????????????????
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;
}
// ??´?????????
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);
}
// ????????????
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);
}
// ?°???±
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;
}
// ????°?
Point reflect(Segment s, Point p)
{
  return p + (project(s, p) - p) * 2.0;
}
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);
}
// ?????????????????¢
double getDistance(Point a, Point b)
{
  return abs(a - b);
}
// ??´?????¨?????¨????????¢
double getDistanceLP(Line l, Point p)
{
  return abs(cross(l.p2 - l.p1, p - l.p1) / abs(l.p2 - l.p1));
}
// ????????¨?????¨????????¢
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;
  return min(min(getDistanceSP(s1, s2.p1), getDistanceSP(s1, s2.p2)),
	     min(getDistanceSP(s2, s1.p1), getDistanceSP(s2, s1.p2)));
}
// ???????????????
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;
}
// ???c??¨??????l?????????
pair<Point, Point> getCrossPoints(Circle c, Line l)
{
  // assert(intersect(c, 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()
{
  Circle c;
  cin >> c.c.x >> c.c.y >> c.r;
  int q; cin >> q;
  while(q--) {
    Segment s;
    cin >> s.p1.x >> s.p1.y >> s.p2.x >> s.p2.y;
    auto ps = getCrossPoints(c, s);
    Point p, q;
    tie(p, q) = minmax(ps.first, ps.second);
    printf("%.10f %.10f %.10f %.10f\n", p.x, p.y, q.x, q.y);
  }
  return 0;
}