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 FOR(i, a, n) for(ll i = (ll)a; i < (ll)n; i++)
#define rep(i, n) FOR(i, 0, n)
#define ALL(x) (x).begin(), (x).end()
using namespace std;
typedef long long ll;

constexpr ll mod = 1e9 + 7;

template <class T> inline bool chmax(T &a, const T b) {
    if(a >= b) return false;
    a = b;
    return true;
}
template <class T> inline bool chmin(T &a, const T b) {
    if(a <= b) return false;
    a = b;
    return true;
}

/*-------------------------------------------*/

struct Point {
    double x, y;
    Point(double x = 0, double y = 0) : x(x), y(y) {}
    Point operator+(const Point &p) { return Point{x + p.x, y + p.y}; }
    Point operator-(const Point &p) { return Point{x - p.x, y - p.y}; }
    Point operator*(const double k) { return Point{x * k, y * k}; }
    Point operator/(const double k) { return Point{x / k, y / k}; }

    double norm() { return x * x + y * y; }
    double abs() { return sqrt(norm()); }
};
typedef Point Vector;
struct Segment {
    Point p1, p2;
};
typedef Segment Line;
struct Circle {
    Point c;
    double r;
    Circle(Point c = Point(), double r = 0) : c(c), r(r) {}
};
typedef vector<Point> Polygon;

double norm(Vector v) { return v.x * v.x + v.y * v.y; }
double abs(Vector v) { return sqrt(norm(v)); }

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; }

bool isOrthogonal(Vector a, Vector b) { return dot(a, b) == 0; }
bool isOrthogonal(Point a1, Point a2, Point b1, Point b2) {
    return isOrthogonal(a1 - a2, b1 - b2);
}
bool isOrthogonal(Line l1, Line l2) {
    return isOrthogonal(l1.p2, l1.p1, l2.p2, l2.p1);
}

bool isParallel(Vector a, Vector b) { return cross(a, b) == 0; }
bool isParallel(Point a1, Point a2, Point b1, Point b2) {
    return isParallel(a1 - a2, b1 - b2);
}
bool isParallel(Line l1, Line l2) {
    return isParallel(l1.p1, l1.p2, l2.p1, l2.p2);
}

Point project(Line l, Point p) {
    Vector base = l.p2 - l.p1;
    double r = dot(p - l.p1, base) / base.norm();
    return l.p1 + base * r;
}
Point reflect(Line l, Point p) { return p + (project(l, p) - p) * 2; }

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) > 0) return COUNTER_CLOCKWISE;
    if(cross(a, b) < 0) return CLOCKWISE;
    if(dot(a, b) < 0) 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 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) return abs(p - s.p1);
    if(dot(s.p1 - s.p2, p - s.p2) < 0) return abs(p - s.p2);
    return getDistanceLP(s, p);
}
double getDistance(Segment s1, Segment s2) {
    if(intersect(s1, s2)) return 0;
    return min({getDistanceSP(s1, s2.p1), getDistanceSP(s1, s2.p2),
                getDistanceSP(s2, s1.p1), getDistanceSP(s2, s1.p2)});
}

Point getCrossPoint(Line l1, Line l2) {
    Vector base = l2.p2 - l2.p1;
    double d1 = abs(cross(base, l1.p1 - l2.p1));
    double d2 = abs(cross(base, l1.p2 - l2.p1));
    double t = d1 / (d1 + d2);
    return l1.p1 + (l1.p2 - l1.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() {
    Circle c;
    cin >> c.c.x >> c.c.y >> c.r;
    int n;
    cin >> n;
    while(n--) {
        Line l;
        cin >> l.p1.x >> l.p1.y >> l.p2.x >> l.p2.y;
        pair<Point, Point> ret = getCrossPoints(c, l);
        Point a = ret.first, b = ret.second;
        if(a.x == b.x ? a.y > b.y : a.x > b.x) swap(a, b);
        printf("%.10f %.10f %.10f %.10f\n", a.x, a.y, b.x, b.y);
    }
}