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;
typedef complex<double> Point;
using Circle = struct{Point c; double r;};
typedef vector<Point> Polygon;
typedef Point Vector;
typedef pair<Point, Point> Segment;
typedef Segment Line;
constexpr double EPS = (1e-9L);
enum CCW { ONLINE_FRONT = -2, CLOCKWISE, ON_SEGMENT, COUNTER_CLOCKWISE, ONLINE_BACK };
double dot(const Point& p1, const Point& p2) { return (conj(p1) * p2).real(); }
double cross(const Point& p1, const Point& p2) { return (conj(p1) * p2).imag(); }
constexpr bool eq(double a) { return abs(a) < EPS; }
Point project(Segment s, Point p) {
	Vector base = s.fi - s.se;
	double r = dot(p - s.fi, base) / norm(base);
	return s.fi + base * r;
}
Point reflect(Segment s, Point p) { return p + (project(s, p) - p) * 2.0; }
int ccw(const Point& p1, const Point& p2, const Point& p3) {
	Point a = p2 - p1, b = p3 - p1;
	if (cross(a, b) > EPS) return 1;
	if (cross(a, b) < -EPS) return -1;
	if (dot(a, b) < -EPS) return 2;
	if (norm(a) < norm(b)) 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.fi, s1.se, s2.fi, s2.se);
}
double getDistance(Point &a, Point &b) { return abs(a - b); }
double getDistanceLP(Line &l, Point &p) {
	return abs(cross(l.se - l.fi, p - l.fi) / abs(l.se - l.fi));
}
double getDistanceSP(Segment &s, Point &p) {
	if(dot(s.se - s.fi, p - s.fi) < 0.0) return abs(p - s.fi);
	if(dot(s.fi - s.se, p - s.se) < 0.0) return abs(p - s.se);
	return getDistanceLP(s, p);
}
double getDistance(Segment &s1, Segment &s2) {
	if(intersect(s1, s2)) return 0.0;
	return min(min(getDistanceSP(s1, s2.fi), getDistanceSP(s1, s2.se)),
				min(getDistanceSP(s2, s1.fi), getDistanceSP(s2, s1.se)));
}
Point getCrossPoint(Segment s1, Segment s2) {
	Vector base = s2.se - s2.fi;
	double d1 = abs(cross(base, s1.fi - s2.fi));
	double d2 = abs(cross(base, s1.se - s2.fi));
	double t = d1 / (d1 + d2);
	return s1.fi + (s1.se - s1.fi) * t;
}
pair<Point, Point> getCrossPoints(Circle c, Line l) {
	Vector pr = project(l, c.c);
	Vector e = (l.se - l.fi) / abs(l.se - l.fi);
	double base = sqrt(c.r * c.r - norm(pr - c.c));
	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(Point(x1, y1), Point(x2, y2)));
		if(ppp.se.real() < ppp.fi.real() || (ppp.se.real() == ppp.fi.real() && ppp.se.imag() < ppp.fi.imag()))
			swap(ppp.fi, ppp.se);
		cout << ppp.fi.real() << " " << ppp.fi.imag() << " " << ppp.se.real() << " " << ppp.se.imag() << "\n";
	}
	return 0;
}