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<iostream>
#include<algorithm>
#include<vector>
#include<stack>
#include<queue>
#include<list>
#include<string>
#include<cstring>
#include<cstdlib>
#include<cstdio>
#include<cmath>
#include<ctime>
using namespace std;

typedef long long ll;

bool debug = false;
const int NIL = -1;
const int INF = 1000000000;
const int NUM = 100010;
const double eps = 1e-10;
clock_t START, END;

int X, Y, E;

//basic defitition
struct Point {
	double x, y;
	Point(double x = 0, double y = 0) :x(x), y(y) {}
};
typedef Point Vector;
Vector operator + (Vector A, Vector B) { return Vector(A.x + B.x, A.y + B.y); }
Vector operator - (Point A, Point B) { return Vector(A.x - B.x, A.y - B.y); }
Vector operator * (Vector A, double p) { return Vector(A.x * p, A.y * p); }
Vector operator / (Vector A, double p) { return Vector(A.x / p, A.y / p); }
bool operator < (const Point& a, const Point& b) { return a.x < b.x || (a.x == b.x && a.y < b.y); }
int dcmp(double x) { if (fabs(x) < eps)return 0; else return x < 0 ? -1 : 1; }
bool operator == (const Point& a, const Point& b) { return dcmp(a.x - b.x) == 0 && dcmp(a.y - b.y) == 0; }
struct Line {
	Point p;
	Vector v;
	Line(Point p, Vector v) :p(p), v(v) {}
	Point point(double t) { return p + v * t; }
	//Line move(double d) { return Line(p + Normal(v) * d, v); }
};
// basic operator
double Dot(Vector A, Vector B) { return A.x * B.x + A.y * B.y; }
double Length(Vector A) { return sqrt(Dot(A, A)); }
double Angle(Vector A, Vector B) { return acos(Dot(A, B) / Length(A) / Length(B)); }
double Cross(Vector A, Vector B) { return A.x * B.y - A.y * B.x; }
double Area2(Point A, Point B, Point C) { return Cross(B - A, C - A); }
Vector Rotate(Vector A, double rad) { return Vector(A.x * cos(rad) - A.y * sin(rad), A.x * sin(rad) + A.y * cos(rad)); }
Vector Normal(Vector A) { double L = Length(A); return Vector(-A.y / L, A.x / L); } //A is not zero vector
//point and line
Point GetLineIntersection(Point P, Vector v, Point Q, Vector w) {
	Vector u = P - Q;
	double t = Cross(w, u) / Cross(v, w);
	return P + v * t;
}//two lines only have one intersection and Cross(v,w) is not zero
double DistanceToLine(Point P, Point A, Point B) {
	Vector v1 = B - A, v2 = P - A;
	return fabs(Cross(v1, v2)) / Length(v1);
}
double DistanceToSegment(Point P, Point A, Point B) {
	if (A == B) return Length(P - A);
	Vector v1 = B - A, v2 = P - A, v3 = P - B;
	if (dcmp(Dot(v1, v2)) < 0) return Length(v2);
	else if (dcmp(Dot(v1, v3)) > 0) return Length(v3);
	else return fabs(Cross(v1, v2)) / Length(v1);
}
Point GetLineProjection(Point P, Point A, Point B) {
	Vector v = B - A;
	return A = v * (Dot(v, P - A) / Dot(v, v));
}
bool SegmentProperIntersection(Point a1, Point a2, Point b1, Point b2) {
	double c1 = Cross(a2 - a1, b1 - a1), c2 = Cross(a2 - a1, b2 - a1), c3 = Cross(b2 - b1, a1 - b1), c4 = Cross(b2 - b1, a2 - b1);
	return dcmp(c1) * dcmp(c2) < 0 && dcmp(c3) * dcmp(c4) < 0;
}
bool OnSegment(Point p, Point a1, Point a2) {
	return dcmp(Cross(a1 - p, a2 - p)) == 0 && dcmp(Dot(a1 - p, a2 - p)) <= 0;
}
//polygon
double ConvexPolygonArea(Point* p, int n) {
	double area = 0;
	for (int i = 1; i < n - 1; i++)
		area = Cross(p[i] - p[0], p[i + 1] - p[0]);
	return area / 2;
}
//circle
struct Circle {
	Point c;
	double r;
	Circle(Point c, double r) :c(c), r(r) {}
	Point point(double a) { return Point(c.x + cos(a) * r, c.y + sin(a) * r); }
};
int getLineCircleIntersection(Line L, Circle C, double& t1, double& t2, vector<Point>& sol) {
	double a = L.v.x, b = L.p.x - C.c.x, c = L.v.y, d = L.p.y - C.c.y;
	double e = a * a + c * c, f = 2 * (a * b + c * d), g = b * b + d * d - C.r * C.r;
	double delta = f * f - 4 * e * g;
	if (dcmp(delta) < 0)
		return 0;
	if (dcmp(delta) == 0) {
		t1 = t2 = -f / (2 * e);
		sol.push_back(L.point(t1));
		return 1;
	}
	t1 = (-f - sqrt(delta)) / (2 * e);
	sol.push_back(L.point(t1));
	t2 = (-f + sqrt(delta)) / (2 * e);
	sol.push_back(L.point(t2));
	return 2;
}


int main(void)
{
	if (debug) {
		START = clock();
		freopen("in29.txt", "r", stdin);
		freopen("out.txt", "w", stdout);
	}
	int q;
	Point A, B, O, E, F;
	vector<Point> sol;
	double r, t1, t2;
	scanf("%lf%lf%lf", &O.x, &O.y, &r);
	Circle C(O, r);
	cin >> q;
	for (int i = 0; i < q; i++) {
		scanf("%lf%lf%lf%lf", &A.x, &A.y, &B.x, &B.y);
		if (getLineCircleIntersection(Line(A, B - A), C, t1, t2, sol) == 1)
			E = F = A + (B - A) * t1;
		else {
			E = A + (B - A) * t1;
			F = A + (B - A) * t2;
			if (E.x > F.x || E.x == F.x && E.y > F.y) {
				swap(E.x, F.x);
				swap(E.y, F.y);
			}
		}
		printf("%.6lf %.6lf %.6lf %.6lf\n", E.x, E.y, F.x, F.y);
	}
	if (debug) {
		END = clock();
		double endtime = (double)(END - START) / 1000;
		printf("total time = %lf s", endtime);
	}
	return 0;
}