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:
#pragma GCC optimize("Ofast")
#include <bits/stdc++.h>
using namespace std;
#define rep(i, n) for(int i = 0; i < (int)(n); i++)
#define all(x) x.begin(),x.end()
const long double PI = acos(-1.0L);
const long long MOD = 1000000007LL;
// const long long MOD = 998244353LL;
typedef long long ll;
typedef pair<int, int> pii;
typedef pair<long long, long long> pll;
template<class T> inline bool chmax(T &a, T b) { if (a < b) { a = b; return true;} return false; }
template<class T> inline bool chmin(T &a, T b) { if (a > b) { a = b; return true;} return false; }
///////////////////////////////////////////////////////////////////////////////////////////////////

using DD = double; // 精度が足りないときはlong double
#define EPS (1e-10)
#define equals(a, b) (fabs((a) - (b)) < EPS)

//点
struct Point {
    DD x, y;
    Point (DD x = 0, DD y = 0): x(x), y(y) {}

    Point& operator+=(const Point &p) { x += p.x; y += p.y; return *this;}
    Point operator+(const Point &p) const { return Point(*this) += p;}
    Point& operator-=(const Point &p) { x -= p.x; y -= p.y; return *this;}
    Point operator-(const Point &p) const { return Point(*this) -= p;}
    Point& operator*=(DD a) { x *= a; y *= a; return *this;}
    Point operator*(DD a) const { return Point(*this) *= a;}
    Point& operator/=(DD a) { x /= a; y /= a; return *this;}
    Point operator/(DD a) const { return Point(*this) /= a;}
    bool operator== (const Point &p) const { return fabs(x - p.x) < EPS && fabs(y - p.y) < EPS;}
    friend istream& operator >>(istream& is, Point& p) { is >> p.x >> p.y; return is;}
    friend ostream& operator <<(ostream& os, const Point& p) { os<<p.x<<" "<<p.y; return os;}
};
typedef Point Vector; //ベクトル

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

//線分
struct Segment {
    Point p1,p2;
    Segment(Point p1 = Point(), Point p2 = Point()): p1(p1),p2(p2) {}
};
typedef Segment Line; //直線

struct Circle {
    Point c;
    DD r;
    Circle(Point c = Point(), DD r = 0): c(c), r(r) {}
};

typedef vector<Point> Polygon; //多角形

//射影
Point project(const Segment &s, const Point &p) {
    Vector base = s.p2 - s.p1;
    DD r = dot(p - s.p1, base) / norm(base);
    return s.p1 + base * r;
}
inline Point reflect(const Segment &s, const Point &p) {return p + (project(s,p) - p) * (DD)2;} //線対称

int ccw(const Point &p0, const Point &p1, const Point &p2) {
    Vector a = p1 - p0;
    Vector b = p2 - p0;
    if (cross(a,b) > EPS) return 1; //p0,p1から見てp2は左側(反時計回り)
    if (cross(a,b) < -EPS) return -1; //p0,p1から見てp2は右側(時計回り)
    if (dot(a,b) < -EPS) return 2; //p2-p0-p1の順に一直線上
    if (norm(a) < norm(b)) return -2; //p0-p1-p2の順に一直線上
    return 0; //p0-p2-p1の順に一直線上
}
//線分p1,p2とp3,p4の交差判定
inline bool intersect(const Point &p1, const Point &p2, const Point &p3, const Point &p4) { return (ccw(p1, p2, p3) * ccw(p1, p2, p4) <= 0 && ccw(p3, p4, p1) * ccw(p3, p4, p2) <= 0);}
inline bool intersect(const Segment &s1, const Segment &s2) { return intersect(s1.p1, s1.p2, s2.p1, s2.p2);}
inline DD getDistance(const Point &a, const Point &b) { return abs(a - b);}
inline DD getDistanceLP(const Line &l, const Point &p) { return abs(cross(l.p2 - l.p1,p - l.p1) / abs(l.p2 - l.p1));}
DD getDistanceSP(const Segment &s, const 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);
}
DD getDistance(const Segment &s1, const Segment &s2) {
    if (intersect(s1, s2)) return (DD)0;
    return min({getDistanceSP(s1, s2.p1), getDistanceSP(s1, s2.p2), getDistanceSP(s2, s1.p1), getDistanceSP(s2, s1.p2)});
}

//線分と線分の交点
Point getCrossPoint(const Segment &s1, const Segment &s2) {
    Vector base = s2.p2 - s2.p1;
    DD d1 = abs(cross(base, s1.p1 - s2.p1));
    DD d2 = abs(cross(base, s1.p2 - s2.p1));
    DD t = d1 / (d1 + d2);
    return s1.p1 + (s1.p2 - s1.p1) * t;
}

//円と直線の交差判定
inline bool intersect(const Circle &c, const Line &l) { return getDistanceLP(l, c.c) - c.r < EPS;}

//円と線分の交点
pair<Point, Point> getCrossPoints(const Circle &c, const Line &l) {
    assert(intersect(c,l));
    Vector pr = project(l, c.c);
    Vector e = (l.p2 - l.p1) / abs(l.p2 - l.p1);
    DD base = sqrt(c.r * c.r - norm(pr - c.c));
    return make_pair(pr + e * base, pr - e * base);
}

int ort(const Point &a) { //象限
    if (norm(a) < EPS) return 0;
    if (a.y > 0) return a.x > 0 ? 1 : 2;
    return a.x > 0 ? 4 : 3;
}

bool xsort(const Point &a, const Point &b) {
    if (equals(a.x, b.x)) return a.y < b.y;
    return a.x < b.x;
}

bool ysort(const Point &a, const Point &b) {
    if (equals(a.y, b.y)) return a.x < b.x;
    return a.y < b.y;
}

bool argsortcross(const Point &a, const Point &b) {
    int ao = ort(a), bo = ort(b);
    if (ao != bo) return ao < bo;
    return cross(a,b) > 0;
}

bool argsortatan2(const Point &a, const Point &b) {
    return atan2(a.y, a.x) < atan2(b.y, b.x);
}

int main() {
    ios::sync_with_stdio(false); cin.tie(nullptr);
    Circle C; cin >> C.c >> C.r;
    int Q; cin >> Q;
    while (Q--) {
        Segment s; cin >> s.p1 >> s.p2;
        vector<Point> p(2);
        tie(p[0],p[1]) = getCrossPoints(C,s);
        sort(all(p),xsort);
        cout << fixed << setprecision(10) << p[0] << " " << p[1] << endl;
    }
}