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>
#define ll long long
#define rep(i,n) for(ll i=0;i<n;i++)
using namespace std;
const double pi = acos(-1);
const double eps = 1e-10;

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;


template<class T>
bool equals(T a,T b){ return fabs((a)-(b)) < eps; }

struct Point{
    double x, y;
    Point(){}
    Point(double x, double y) : 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(x*a, y*a); }
    Point operator / (double a) { return Point(x/a, y/a); }
    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 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;
    }
};

bool sort_x(Point a, Point b){ return !equals(a.x,b.x)?a.x<b.x:a.y<b.y; }
bool sort_y(Point a, Point b){ return !equals(a.y,b.y)?a.y<b.y:a.x<b.x; }

typedef Point Vector;
typedef vector<Point> Polygon;
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(){}
    Segment(Point p1, Point p2):p1(p1),p2(p2){}
};
typedef Segment Line;

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

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);
}

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);
}
double getDistanceSS(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)/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);
}

int main(){
    cin.tie(0);
    ios::sync_with_stdio(false);
    cout << fixed << setprecision(15);
    double c0,c1,r;
    cin>>c0>>c1>>r;
    Circle c(Point(c0,c1),r);
    ll q;cin>>q;
    rep(Q,q){
        double x0,y0,x1,y1;
        cin>>x0>>y0>>x1>>y1;
        Point p0(x0,y0),p1(x1,y1);
        Line l(p0,p1);
        pair<Point,Point> p=getCrossPoints(c,l);
        if(p.first>p.second) swap(p.first,p.second);
        cout<<p.first.x<<" "<<p.first.y<<" ";
        cout<<p.second.x<<" "<<p.second.y<<endl;
    }
    return 0;
}