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:
//AOJ-CGL-7-D
#include <bits/stdc++.h>
using namespace std;
#define REP(i,a) for(int i = 0; i < (a); i++)
#define ALL(a) (a).begin(),(a).end()
typedef long long ll;
typedef pair<int, int> P;
const int INF = 1e9;
const int MOD = 1e9 + 7;

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

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 * (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;
    }
};

typedef Point Vector;

double norm(Vector a) { return a.x * a.x + a.y * a.y; }
double abs(Vector a) { return sqrt(norm(a)); }
double dot(Vector a, Vector b) { return a.x * b.x + a.y * b.y; }
double cross(Vector a, Vector b) { return a.x * b.y - a.y * b.x; }

struct Segment {
    Point p1, p2;
    Segment(Point p1 = Point(), Point p2 = Point()) : p1(p1), p2(p2) {}
};

typedef Segment Line;

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

typedef vector<Point> Polygon;

bool isOrthogonal(Vector a, Vector b) {
    return equals(dot(a, b), 0.0);
}

bool isOrthogonal(Point a1, Point a2, Point b1, Point b2) {
    return isOrthogonal(a1 - a2, b1 - b2);
}

bool isOrthogonal(Segment s1, Segment s2) {
    return equals(dot(s1.p2 - s1.p1, s2.p2 - s2.p1), 0.0);
}

bool isParallel(Vector a, Vector b) {
    return equals(cross(a, b), 0.0);
}

bool isParallel(Point a1, Point a2, Point b1, Point b2) {
    return isParallel(a1 - a2, b1 - b2);
}

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) / norm(base);
    return s.p1 + base * r;
}

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

double getDistance(Point a, Point b) {
    return abs(a - b);
}

double getDistanceLP(Line l, Point p) {
    return abs(cross(l.p2 - l.p1, p - l.p1) / abs(l.p2 - l.p1));
}

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);
}

bool intersect(Segment s1, Segment s2);

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)));
}

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;

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);
}

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) {
    // 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);
}

double arg(Vector p) { return atan2(p.y, p.x); }
Vector polar(double a, double r) { return Point(cos(r) * a, sin(r) * a); }

pair<Point, Point> getCrossPoints(Circle c1, Circle c2) {
    // assert(intersect(c1, c2));
    double d = abs(c1.c - c2.c);
    double a = acos((c1.r * c1.r + d * d - c2.r * c2.r) / (2 * c1.r * d));
    double t = arg(c2.c - c1.c);
    return make_pair(c1.c + polar(c1.r, t + a), c1.c + polar(c1.r, t - a));
}

// IN : 2, ON : 1, OUT : 0
int contains(Polygon g, Point p) {
    int n = g.size();
    bool x = false;
    for( int i = 0; i < n; i++ ) {
        Point a = g[i] - p, b = g[(i + 1) % n] - p;
        if ( abs(cross(a, b)) < EPS && dot(a, b) < EPS) return 1;
        if ( a.y > b.y ) swap(a, b);
        if ( a.y < EPS && EPS < b.y && cross(a, b) > EPS ) x = !x;
    }
    return ( x ? 2 : 0 );
}

signed main(){
    double cx, cy, r;
    int q;
    cin >> cx >> cy >> r;
    Circle c = Circle(Point(cx, cy), r);
    cin >> q;
    double x1, y1, x2, y2;
    REP(i,q){
        cin >> x1 >> y1 >> x2 >> y2;
        Line l = Line(Point(x1, y1), Point(x2, y2));
        pair<Point, Point> p = getCrossPoints(c, l);
        if(p.first.x > p.second.x || (p.first.x == p.second.x && p.first.y > p.second.y)){
            swap(p.first, p.second);
        }
        printf("%.8lf %.8lf %.8lf %.8lf\n", p.first.x, p.first.y, p.second.x, p.second.y);
    }
    return 0;
}