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;
struct cww{cww(){ios::sync_with_stdio(false);cin.tie(0);}}star;
#define P(x) cout << (x) << "\n"
#define p(x) cout << (x)
#define all(c) (c).begin(), (c).end()
#define rall(c) (c).rbegin(), (c).rend()
#define vv(type, c, m, n, i) vector<vector<type>> c(m, vector<type>(n, i));
#define rep(i,a,n) for(int i=(a), i##_len=(n); i<i##_len; ++i)
#define rrep(i,a,n) for(int i=(a), i##_len=(n); i>i##_len; --i)
#define len(x) ((int)(x).size())
#define mp make_pair
#define eb emplace_back
#define fi first
#define se second
typedef long long ll;
typedef long double ld;
typedef vector<int> vi;
typedef vector<double> vd;
typedef vector<long long> vll;
typedef vector<string> vs;
typedef vector<bool> vb;
#define EPS (1e-10)
#define equals(a, b) (fabs((a) - (b)) < EPS)
enum CCW { ONLINE_FRONT = -2, CLOCKWISE, ON_SEGMENT, COUNTER_CLOCKWISE, ONLINE_BACK };
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 * (Point p) { return Point(x * p.x, y * p.y); }
	Point operator * (double p) { return Point(x * p, y * p); }
	Point operator / (Point p) { return Point(x / p.x, y / p.y); }
	Point operator / (double p) { return Point(x / p, y / p); }
	void insert(double a, double b) { x = a; y = b; }
	double norm() { return x * x + y * y; }
	double abs() { return sqrt(norm()); }
	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 {
	Vector p1, p2;
	Segment(double x1 = 0.0, double y1 = 0.0, double x2 = 0.0, double y2 = 0.0):
		p1(x1, y1), p2(x2, y2) {}
	Segment(Point a1, Point a2) : p1(a1), p2(a2) {}
	void insert(Vector a1, Vector a2) { p1 = a1; p2 = a2; }
};
typedef Segment Line;
inline double dot(Vector a, Vector b) { return a.x * b.x + a.y * b.y; }
inline double cross(Vector a, Vector b) { return a.x * b.y - a.y * b.x; }
inline bool isOrthogonal(Vector a, Vector b) { return equals(dot(a, b), 0.0); }
inline bool isOrthogonal(Vector a1, Vector a2, Vector b1, Vector b2) {
	return isOrthogonal(a1 - a2, b1 - b2);
}
inline bool isOrthogonal(Segment s1, Segment s2) {
	return equals(dot(s1.p2 - s1.p1, s2.p2 - s2.p1), 0.0);
}
inline bool isParallel(Vector a, Vector b) { return equals(cross(a, b), 0.0); }
inline bool isParallel(Vector a1, Vector a2, Vector b1, Vector b2) {
	return isParallel(a1 - a2, b1 - b2);
}
inline 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) / base.norm();
	return s.p1 + base * r;
}
Point reflect(Segment s, Point p) {
	return p + (project(s, p) - p) * 2.0;
}
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 (a - b).abs(); }
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;
}
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 = sqrt(c.r * c.r - (pr - c.c).norm());
	return mp(pr + e * base, pr - e * base);
}
int main() {
	cout << setprecision(10) << fixed;
	double x, y, r; cin >> x >>  y >> r;
	Circle ci(Point(x, y), r);
	int q; cin >> q;
	double x1, y1, x2, y2;
	pair<Point, Point> ppp;
	rep(i, 0, q) {
		cin >> x1 >> y1 >> x2 >> y2;
		ppp = getCrossPoints(ci, Line(x1, y1, x2, y2));
		if(ppp.se < ppp.fi) swap(ppp.fi, ppp.se);
		cout << ppp.fi.x << " " << ppp.fi.y << " " << ppp.se.x << " " << ppp.se.y << "\n";
	}
	return 0;
}