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;
using ll = long long;
const ll INF = 1e16;
const ll mod = 1000000007;
#define rep(i, n) for (int i = 0; i < (int)(n); i++)

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;
}
int ctoi(char c) {
  if (c >= '0' && c <= '9') {
    return c - '0';
  }
  return 0;
}
ll factorial(ll n) {
  if (n == 1) {
    return 1;
  }
  ll ans = factorial(n-1);
  return ans*n;
}
ll gcd(ll a, ll b) {
  if (b == 0) return a;
  return gcd(b, a%b);
}
ll lcm(ll a, ll b) {
  return (a/gcd(a, b))*b;
}
bool is_prime(ll n) {
  for (ll i = 2; i*i <= n; i++) {
    if (n%i == 0) return false;
  }
  return n != 1;
}
ll mod_pow(ll x, ll n, ll mod) {
  if (n == 0) return 1;
  ll res = mod_pow(x*x%mod, n/2, mod);
  if (n & 1) res = res * x % mod;
  return res;
}

#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 norm() { return x*x + y*y; }
  double abs() { return pow(norm(), 0.5); }
  bool operator < (const Point &p) const {
    return x != p.x ? x < p.x : y < p.y;
  }
};
typedef Point Vector;
struct Segment {
  Point p1, p2;
};
typedef Segment Line;
double dot(Vector a, Vector b) {
  return a.x * b.x + a.y * b.y;
}
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;
}
Point reflect(Segment s, Point p) {
  return p + (project(s, p) - p) * 2.0;
}
double cross(Point a, Point b) {
  return a.x*b.y - a.y*b.x;
}
ll ccw(Point p0, Point p1, Point p2) {
  Vector a = p1 - p0, b = p2 - p0;
  if (cross(a, b) > EPS) return 1;
  if (cross(a, b) < -EPS) return -1;
  if (dot(a, b) < -EPS) return 2;
  if (a.norm() < b.norm()) return -2;
  return 0;
}
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) {
  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;
}
class Circle {
  public:
  Point c;
  double r;
  Circle(Point c = Point(), double r = 0.0): c(c), r(r) {}
};
pair <Point, Point> getCrossPoints(Circle c, Line l) {
  Vector pr = project(l, c.c);
  Vector e = (l.p2 - l.p1) / (l.p2 - l.p1).abs();
  double base = c.r*c.r - (pr-c.c).norm();
  base = pow(base, 0.5);
  return make_pair(pr+e*base, pr-e*base);
}

int main() {
  Circle c;
  cin >> c.c.x >> c.c.y >> c.r;
  ll n;
  cin >> n;
  cout << fixed << setprecision(10);
  rep(i, n) {
    Line l;
    cin >> l.p1.x >> l.p1.y >> l.p2.x >> l.p2.y;
    pair <Point, Point> p = getCrossPoints(c, l);
    if (p.first.x > p.second.x) {
      Point tmp = p.first;
      p.first = p.second;
      p.second = tmp;
    } else if (p.first.x == p.second.x) {
      if (p.first.y > p.second.y) {
        Point tmp = p.first;
        p.first = p.second;
        p.second = tmp;
      }
    }
    cout << p.first.x << ' ' << p.first.y << ' ' << p.second.x << ' ' << p.second.y << endl;
  }
}