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,s,n) for (int i = (int)s; i < (int)n; i++)
#define ll long long
#define pb push_back
#define All(x) x.begin(), x.end()
#define Range(x, i, j) x.begin() + i, x.begin() + j
#define lbidx(x, y) lower_bound(x.begin(), x.end(), y) - x.begin()
#define ubidx(x, y) upper_bound(x.begin(), x.end(), y) - x.begin()
#define BiSearchRangeNum(x, y, z) lower_bound(x.begin(), x.end(), z) - lower_bound(x.begin(), x.end(), y);

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

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

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

struct Segment {
  Point p1, p2;
};

typedef Point Vector;
typedef Segment Line;

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

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

// 内積
double dot(Vector a, Vector b) {
  return a.x * b.x + a.y * b.y;
};

// 外積
double cross(Vector a, Vector b) {
  return a.x * b.y - a.y * b.x;
};

// 直交判定
bool isOrthogonal(Vector a, Vector b) {
  return equals(dot(a, b), 0.0);
};

// 並行判定
bool isParallel(Vector a, Vector b) {
  return equals(cross(a, b), 0.0);
};

// 射影
Point project(Segment s, Point p) {
  Vector base = s.p2 - s.p1;
  double r = dot(p - s.p1, base) / base.norm();
  return s.p1 + base * r;
};

// 反射
Point reflect(Segment s, Point p) {
  return p + (project(s, p) - p) * 2.0;
};

// 点と点の距離
double getDistance(Point a, Point b) {
  return abs(a - b);
};

// 点と直線の距離
double getDistanceLP(Line l, Point p) {
  return abs(cross(l.p2 - l.p1, p - l.p1) / abs(l.p2 - l.p1));
};

// 点と線分の距離
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);
};

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;

// 二つのベクトルの位置関係
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;
};

// 線分の交差判定
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);
};

// 円と直線の交差判定
bool intersect(Circle c, Line l) {
  return getDistanceLP(l, c.c) <= c.r;
};

// 線分と線分の距離
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)));
};

// 線分と線分の交点(必ず交点があり、それがどちらかの端点出ない)
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;
};

// 円cと線分lの交点
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() {
  double cx, cy, r;
  cin >> cx >> cy >> r;
  Point center = Point(cx, cy);
  Circle c = Circle(center, r);
  int q;
  cin >> q;
  Point p1, p2;
  Line l;
  rep(i, 0, q) {
    cin >> p1.x >> p1.y >> p2.x >> p2.y;
    l.p1 = p1;
    l.p2 = p2;
    pair<Point, Point> crossPs = getCrossPoints(c, l);
    if (crossPs.first.x == crossPs.second.x) {
      if (crossPs.first.y <= crossPs.second.y) {
        printf("%.10f %.10f %.10f %.10f\n", crossPs.first.x, crossPs.first.y, crossPs.second.x, crossPs.second.y);
      } else {
        printf("%.10f %.10f %.10f %.10f\n", crossPs.second.x, crossPs.second.y, crossPs.first.x, crossPs.first.y);
      }
    } else if (crossPs.first.x <= crossPs.second.x) {
      printf("%.10f %.10f %.10f %.10f\n", crossPs.first.x, crossPs.first.y, crossPs.second.x, crossPs.second.y);
    } else {
      printf("%.10f %.10f %.10f %.10f\n", crossPs.second.x, crossPs.second.y, crossPs.first.x, crossPs.first.y);
    }
  }
  return 0;
};