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 < (int)(n); i++)
#define repr(i, n) for (int i = (int)(n); i >= 0; i--)
#define REP(i, m, n) for (int i = (int)(m); i <= (int)(n); i++)
#define REPR(i, m, n) for (int i = (int)(m); i >= (int)(n); i--)
#define all(v) v.begin(), v.end()
template<class T> inline bool chmax(T& a, T b) { if (a < b) { a = b; return 1; } return 0; }
template<class T> inline bool chmin(T& a, T b) { if (a > b) { a = b; return 1; } return 0; }
const long long INF = (1LL<<30);

#define EPS (1e-10)
#define equals(a, b) (fabs((a)-(b)) < EPS)

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

typedef Segment Line;

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

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(Segment s, Point p){
  Vector a = s.p2 - s.p1;
  Vector b = p - s.p1;
  return s.p1 + a * (dot(a, b)/a.norm());
}

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

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;
  else if(cross(a, b) < -EPS) return CLOCKWISE;
  else if(dot(a, b) < -EPS) return ONLINE_BACK;
  else if(a.norm() < b.norm()) return ONLINE_FRONT;
  else 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 );
}

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

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

double getDistanceSP(Segment s, Point p){
  Vector a = s.p2 - s.p1;
  Vector b = p - s.p1;
  double n = dot(a, b) / a.norm();
  if(0.0 <= n && n <= 1.0) return getDistanceLP(s, p);
  else return min(getDistance(s.p1, p), getDistance(s.p2, p));
}

double getDistanceSS(Segment s1, Segment s2){
  if(intersect(s1.p1, s1.p2, s2.p1, s2.p2)) return 0.0;
  double res = INF;
  chmin(res, getDistanceSP(s1, s2.p1));
  chmin(res, getDistanceSP(s1, s2.p2));
  chmin(res, getDistanceSP(s2, s1.p1));
  chmin(res, getDistanceSP(s2, s1.p2));
  return res;
}

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

pair<Point, Point> getCrossPoints(Circle c, Line l){
  assert(getDistanceLP(l, c.c) <= c.r);
  Point pr = project(l, c.c);
  Vector a = l.p2 - l.p1;
  Vector e = a / a.abs();
  Vector vcpr = pr - c.c;
  double d = sqrt(c.r*c.r - vcpr.norm());
  return make_pair(pr+e*d, pr-e*d);
}

int main(){
  double cx, cy, r;
  cin >> cx >> cy >> r;
  Circle c = Circle(Point(cx, cy), r);

  int q;
  cin >> q;

  rep(i, q){
    double x1, y1, x2, y2;
    cin >> x1 >> y1 >> x2 >> y2;
    Point p1 = Point(x1, y1);
    Point p2 = Point(x2, y2);
    Line l = {p1, p2};
    pair<Point, Point> tmp = getCrossPoints(c, l);
    vector<Point> ans(2);
    ans[0] = tmp.first;
    ans[1] = tmp.second;
    sort(all(ans));
    cout << fixed << setprecision(10);
    cout << ans[0].x << " " << ans[0].y << " ";
    cout << ans[1].x << " " << ans[1].y << endl;
  }

  return 0;

}