Problem: Find the tangent lines between a point $p$ and a circle $c$.

Constraints

* $-1,000 \leq px, py, cx, cy \leq 1,000$
* $1 \leq r \leq 1,000$
* Distance between $p$ and the center of $c$ is greater than the radius of $c$.

Input

The input is given in the following format.

$px \; py$
$cx \; cy \; r$

$px$ and $py$ represents the coordinate of the point $p$. $cx$, $cy$ and $r$ represents the center coordinate and radius of the circle $c$ respectively. All input values are given in integers.

Output

Print coordinates of the tangent points on the circle $c$ based on the following rules.

* 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 0.00001.

Examples

Input

0 0
2 2 2


Output

0.0000000000 2.0000000000
2.0000000000 0.0000000000


Input

-3 0
2 2 2


Output

0.6206896552 3.4482758621
2.0000000000 0.0000000000

Solution (in CPP):

Solution:
#include <bits/stdc++.h>

using namespace std;

#define TemplateVersion "3.4.0"
// Useful Marcos
//====================START=====================
// Compile use C++11 and above
#ifdef LOCAL
#define debug(args...)                           \
    {                                            \
        string _s = #args;                       \
        replace(_s.begin(), _s.end(), ',', ' '); \
        stringstream _ss(_s);                    \
        istream_iterator<string> _it(_ss);       \
        err(_it, args);                          \
    }
void err(istream_iterator<string> it)
{
}
template <typename T, typename... Args>
void err(istream_iterator<string> it, T a, Args... args)
{
    cerr << *it << " = " << a << endl;
    err(++it, args...);
}
#define MSG cout << "Finished" << endl
#else
#define debug(args...)
#define MSG
#endif
#if __cplusplus >= 201703L
template <typename... Args>
void readln(Args &... args)
{
    ((cin >> args), ...);
}
template <typename... Args>
void writeln(Args... args)
{
    ((cout << args << " "), ...);
    cout << endl;
}
#elif __cplusplus >= 201103L
void readln()
{
}
template <typename T, typename... Args>
void readln(T &a, Args &... args)
{
    cin >> a;
    readln(args...);
}
void writeln()
{
    cout << endl;
}
template <typename T, typename... Args>
void writeln(T a, Args... args)
{
    cout << a << " ";
    writeln(args...);
}
#endif
#if __cplusplus >= 201103L
#define FOR(_i, _begin, _end) for (auto _i = _begin; _i < _end; _i++)
#define FORR(_i, _begin, _end) for (auto _i = _begin; _i > _end; _i--)
#else
#define FOR(_i, _begin, _end) for (int _i = (int)_begin; _i < (int)_end; _i++)
#define FORR(_i, _begin, _end) for (int _i = (int)_begin; _i > (int)_end; _i--)
#define nullptr NULL
#endif
#if __cplusplus >= 201103L
#define VIS(_kind, _name, _size) \
    vector<_kind> _name(_size);  \
    for (auto &i : _name)        \
        cin >> i;
#else
#define VIS(_kind, _name, _size)    \
    vector<_kind> _name;            \
    _name.resize(_size);            \
    for (int i = 0; i < _size; i++) \
        cin >> _name[i];
#endif
// alias
#define mp make_pair
#define pb push_back
#define eb emplace_back
#define all(x) (x).begin(), (x).end()
#define tcase() \
    int T;      \
    cin >> T;   \
    FOR(kase, 1, T + 1)
// Swap max/min
template <typename T>
bool smax(T &a, const T &b)
{
    if (a > b)
        return false;
    a = b;
    return true;
}
template <typename T>
bool smin(T &a, const T &b)
{
    if (a < b)
        return false;
    a = b;
    return true;
}
// ceil divide
template <typename T>
T cd(T a, T b)
{
    return (a + b - 1) / b;
}
// min exchange
template <typename T>
bool se(T &a, T &b)
{
    if (a < b)
        return false;
    swap(a, b);
    return true;
}
// A better MAX choice
const int INF = 0x3f3f3f3f;

typedef long long ll;
typedef unsigned long long ull;
typedef pair<int, int> pii;
typedef vector<int> vi;
typedef vector<ll> vll;
typedef set<int> si;
typedef vector<string> cb;
//====================END=====================

// Constants here
const double EPS = 1e-8;
const double PI = acos(-1);
const double FAC = 1e-18;

typedef double db;

int sgn(db x)
{
    if (abs(x) < EPS)
        return 0;
    if (x < 0)
        return -1;
    return 1;
}

inline db sqr(db x) { return x * x; }

// Point/Vector
struct Point
{
    db x, y;

    Point() : x(0.0), y(0.0) {}

    Point(db _x, db _y) : x(_x), y(_y) {}

    bool operator==(const Point &p)
    {
        return sgn(x - p.x) == 0 && sgn(y - p.y) == 0;
    }

    bool operator<(const Point &p)
    {
        int c = sgn(x - p.x);
        if (c)
            return c == -1;
        return sgn(y - p.y) == -1;
    }

    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*(db d) { return Point(x * d, y * d); }
    Point operator/(db d) { return Point(x / d, y / d); }

    db operator^(const Point &p) { return x * p.y - y * p.x; }
    db operator*(const Point &p) { return x * p.x + y * p.y; }

    db dis(const Point &p) { return (*this - p).len(); }
    db alpha() { return atan2(y, x); }

    Point unit() { return *this / len(); }
    Point scale(db r) { return unit() * r; }

    Point rotCC() { return Point(-y, x); }
    Point rotCL() { return Point(y, -x); }

    Point rot(Point p, db angle)
    {
        Point v = *this - p;
        db c = cos(angle), s = sin(angle);
        return Point(p.x + v.x * c - v.y * s, p.y + v.x * s + v.y * c);
    }

    db len() { return hypot(x, y); }
    db len2() { return x * x + y * y; }

    db rad(Point a, Point b)
    {
        Point ap = a - *this, bp = b - *this;
        return abs(atan2(abs(ap ^ bp), ap * bp));
    }

    void read() { cin >> x >> y; }
    void write() { cout << x << ' ' << y; }
    void Debug() { cerr << "Point: (" << x << ", " << y << ")\n"; }
};

// Line
struct Line
{
    Point s, e;

    Line(){};

    Line(Point _s, Point _e) : s(_s), e(_e) {}

    Line(Point p, db angle)
    {
        s = p;
        if (sgn(angle - PI / 2))
            e = (s + Point(1, tan(angle)));
        else
            e = (s + Point(0, 1));
    }

    //ax+by+c=0
    Line(db a, db b, db c)
    {
        if (sgn(a) == 0)
        {
            s = Point(0, -c / b);
            e = Point(1, -c / b);
        }
        else if (sgn(b) == 0)
        {
            s = Point(-c / a, 0);
            e = Point(-c / a, 1);
        }
        else
        {
            s = Point(0, -c / b);
            e = Point(1, -(c + a) / b);
        }
    }

    db len() { return s.dis(e); }
    db angle()
    {
        db ans = atan2(e.y - s.y, e.x - s.x);
        if (sgn(ans) == -1)
            ans += PI;
        if (sgn(ans - PI) == 0)
            ans -= PI;
        return ans;
    }

    // 1 -> On Counter-clockwise
    // 2 -> On Clockwise
    // 3 -> On Line BUT MAY NOT ON THE SEGMENT!
    int relation(Point p)
    {
        int c = sgn((p - s) ^ (e - s));
        if (c < 0)
            return 1;
        else if (c > 0)
            return 2;
        return 3;
    }

    bool checkOn(Point p) { return relation(p) == 3 && sgn((p - s) ^ (p - e)) <= 0; }

    bool parallel(Line l) { return sgn((e - s) ^ (l.e - l.s)) == 0; }

    // 0 -> Not Intersect
    // 1 -> Informal
    // 2 -> Formal Intersection
    int crossSS(Line l)
    {
        int d1 = sgn((e - s) ^ (l.s - s));
        int d2 = sgn((e - s) ^ (l.e - s));
        int d3 = sgn((l.e - l.s) ^ (s - l.s));
        int d4 = sgn((l.e - l.s) ^ (e - l.s));
        if ((d1 ^ d2) == -2 && (d3 ^ d4) == -2)
            return 2;
        return (d1 == 0 && sgn((l.s - s) * (l.s - e)) <= 0) ||
               (d2 == 0 && sgn((l.e - s) * (l.e - e)) <= 0) ||
               (d3 == 0 && sgn((s - l.s) * (s - l.e)) <= 0) ||
               (d4 == 0 && sgn((e - l.s) * (e - l.e)) <= 0);
    }

    // 0 -> Not Intersect
    // 1 -> Informal
    // 2 -> Formal Intersection
    int crossLS(Line l)
    {
        int d1 = sgn((e - s) ^ (l.s - s));
        int d2 = sgn((e - s) ^ (l.e - s));
        if ((d1 ^ d2) == -2)
            return 2;
        return (d1 == 0 || d2 == 0);
    }

    // 0 -> Parallel
    // 1 -> Same
    // 2 -> Intersect
    int crossLL(Line l)
    {
        if (this->parallel(l))
            return l.relation(s) == 3;
        return 2;
    }

    Point intersec(Line l)
    {
        db a1 = (l.e - l.s) ^ (s - l.s);
        db a2 = (l.e - l.s) ^ (e - l.s);
        return Point((s.x * a2 - e.x * a1) / (a2 - a1), (s.y * a2 - e.y * a1) / (a2 - a1));
    }

    db disPL(Point p) { return abs((p - s) ^ (e - s)) / len(); }
    db disPS(Point p)
    {
        if (sgn((p - s) * (e - s)) < 0 || sgn((p - e) * (s - e)) < 0)
            return min(p.dis(s), p.dis(e));
        return disPL(p);
    }
    db disSS(Line l) { return min(min(disPS(l.s), disPS(l.e)), min(l.disPS(s), l.disPS(e))); }

    Point proj(Point p) { return s + ((e - s) * ((e - s) * (p - s))) / ((e - s).len2()); }
    Point refl(Point p)
    {
        Point q = proj(p);
        return Point(2 * q.x - p.x, 2 * q.y - p.y);
    }

    bool operator==(Line l) { return s == l.s && e == l.e; }

    void adjust()
    {
        if (e < s)
            swap(s, e);
    }

    void read()
    {
        s.read();
        e.read();
    }

    void Debug() { cerr << "Line: Start: (" << s.x << ", " << s.y << ") End: (" << e.x << ", " << e.y << ")\n"; }
};

// Circle
struct Circle
{
    Point p;
    db r;

    Circle(){};

    Circle(Point _p, db _r) : p(_p), r(_r) {}

    Circle(db x, db y, db _r) : p({x, y}), r(_r) {}

    Circle(Point a, Point b, Point c, bool in = false)
    {
        if (!in)
        {
            Line u = Line((a + b) / 2, (a + b) / 2 + (b - a).rotCC());
            Line v = Line((b + c) / 2, (b + c) / 2 + (c - b).rotCC());
            p = u.intersec(v);
            r = p.dis(a);
        }
        else
        {
            Line u, v;
            db m = atan2(b.y - a.y, b.x - a.x), n = atan2(c.y - a.y, c.x - a.x);
            u.s = a;
            u.e = a + Point(cos((n + m) / 2), sin((n + m) / 2));
            v.s = b;
            m = atan2(a.y - b.y, a.x - b.x), n = atan2(c.y - b.y, c.x - b.x);
            v.e = b + Point(cos((n + m) / 2), sin((n + m) / 2));
            p = u.intersec(v);
            r = Line(a, b).disPS(p);
        }
    }

    bool operator==(const Circle &c) { return p == c.p && sgn(r - c.r) == 0; }

    bool operator<(const Circle &c) { return (p < c.p) || (p == c.p && sgn(r - c.r) < 0); }

    db area() { return PI * r * r; }

    db cir() { return 2 * PI * r; }

    // 0 -> Outside
    // 1 -> On
    // 2 -> Inside
    int relationP(Point v)
    {
        db dis = v.dis(p);
        if (sgn(dis - r) < 0)
            return 2;
        else if (sgn(dis - r) == 0)
            return 1;
        return 0;
    }

    // The number of intersections
    int relationS(Line l)
    {
        db dis = l.disPS(p);
        if (sgn(dis - r) < 0)
            return 2;
        else if (sgn(dis - r) == 0)
            return 1;
        return 0;
    }

    // The number of intersections
    int relationL(Line l)
    {
        db dis = l.disPL(p);
        if (sgn(dis - r) < 0)
            return 2;
        else if (sgn(dis - r) == 0)
            return 1;
        return 0;
    }

    // 1 -> Inside
    // 2 -> Internally-tangent
    // 3 -> Intersect
    // 4 -> Externally-tangent
    // 5 -> Disjoint
    int relationC(Circle c)
    {
        db d = p.dis(c.p);
        if (sgn(d - r - c.r) > 0)
            return 5;
        if (sgn(d - r - c.r) == 0)
            return 4;
        db l = abs(r - c.r);
        if (sgn(d - r - c.r) < 0 && sgn(d - l) > 0)
            return 3;
        if (sgn(d - l) == 0)
            return 2;
        // TODO: Check if this one is necessary
        // if (sgn(d - l) < 0)
        return 1;
    }

    // The return value is the number of intersections
    int crossC(Circle c, Point &p1, Point &p2)
    {
        int re = relationC(c);
        if (re == 1 || re == 5)
            return 0;
        db d = p.dis(c.p), l = (d * d + r * r - c.r * c.r) / (2.0 * d), h = sqrt(r * r - l * l);
        Point tmp = p + (c.p - p).scale(l);
        p1 = tmp + (c.p - p).rotCC().scale(h);
        p2 = tmp + (c.p - p).rotCL().scale(h);
        if (re == 2 || re == 4)
            return 1;
        return 2;
    }

    // Same as above
    int crossL(Line l, Point &p1, Point &p2)
    {
        if (!this->relationL(l))
            return 0;
        Point a = l.proj(p);
        db d = l.disPL(p);
        d = sqrt(r * r - d * d);
        if (sgn(d) == 0)
        {
            p1 = a;
            p2 = a;
            return 1;
        }
        p1 = a + (l.e - l.s).scale(d);
        p2 = a - (l.e - l.s).scale(d);
        return 2;
    }

    int tangent(Point q, Line &u, Line &v)
    {
        int x = relationP(q);
        if (x == 2)
            return 0;
        if (x == 1)
        {
            u = Line(q, q + (q - p).rotCC());
            v = u;
            return 1;
        }
        db d = p.dis(q);
        db l = r * r / d;
        db h = sqrt(r * r - l * l);
        u = Line(q, p + ((q - p).scale(l) + (q - p).rotCC().scale(h)));
        v = Line(q, p + ((q - p).scale(l) + (q - p).rotCL().scale(h)));
        return 2;
    }

    // The area of intersecting space
    // With circle c
    db area(Circle c)
    {
        int re = relationC(c);
        if (re >= 4)
            return 0;
        if (re <= 2)
            return min(area(), c.area());
        db d = p.dis(c.p);
        db hf = (r + c.r + d) / 2.0;
        db ss = 2 * sqrt(hf * (hf - r) * (hf - c.r) * (hf - d));
        db a1 = acos((r * r + d * d - c.r * c.r) / (2.0 * r * d));
        a1 = a1 * r * r;
        db a2 = acos((c.r * c.r + d * d - r * r) / (2.0 * c.r * d));
        a2 = a2 * c.r * c.r;
        return a1 + a2 - ss;
    }

    // The area of intersecting space
    // With triangle PAB
    db area(Point a, Point b)
    {
        if (sgn((p - a) ^ (p - b)) == 0)
            return 0.0;
        Point q[5];
        int len = 0;
        q[len++] = a;
        Line l(a, b);
        Point p1, p2;
        if (crossL(l, q[1], q[2]) == 2)
        {
            if (sgn((a - q[1]) * (b - q[1])) < 0)
                q[len++] = q[1];
            if (sgn((a - q[2]) * (b - q[2])) < 0)
                q[len++] = q[2];
        }
        q[len++] = b;
        if (len == 4 && sgn((q[0] - q[1]) * (q[2] - q[1])) > 0)
            swap(q[1], q[2]);
        double res = 0;
        for (int i = 0; i < len - 1; i++)
        {
            if (relationP(q[i]) == 0 || relationP(q[i + 1]) == 0)
            {
                double arg = p.rad(q[i], q[i + 1]);
                res += r * r * arg / 2.0;
            }
            else
                res += fabs((q[i] - p) ^ (q[i + 1] - p)) / 2.0;
        }
        return res;
    }

    // Two circle whose center are a and b respectivelly
    static int GetCircle(Point a, Point b, db r, Circle &c1, Circle &c2)
    {
        Circle x(a, r), y(b, r);
        int t = x.crossC(y, c1.p, c2.p);
        if (!t)
            return 0;
        c1.r = c2.r = r;
        return t;
    }

    // The circle which tangent is l and point p on it
    static int GetCircle(Line l, Point p, db r, Circle &c1, Circle &c2)
    {
        db dis = l.disPL(p);
        if (sgn(dis - r * 2) > 0)
            return 0;
        if (sgn(dis) == 0)
        {
            c1.p = p + ((l.e - l.s).rotCC().scale(r));
            c2.p = p + ((l.e - l.s).rotCL().scale(r));
            c1.r = c2.r = r;
            return 2;
        }
        Line u1 = Line((l.s + (l.e - l.s).rotCC().scale(r)), (l.e + (l.e - l.s).rotCC().scale(r)));
        Line u2 = Line((l.s + (l.e - l.s).rotCL().scale(r)), (l.e + (l.e - l.s).rotCL().scale(r)));
        Circle cc(p, r);
        Point p1, p2;
        if (!cc.crossL(u1, p1, p2))
            cc.crossL(u2, p1, p2);
        c1 = Circle(p1, r);
        if (p1 == p2)
        {
            c2 = c1;
            return 1;
        }
        c2 = Circle(p2, r);
        return 2;
    }

    // u and v are the common tangent of the four circles
    static int GetCircle(Line u, Line v, db r, Circle &c1, Circle &c2, Circle &c3, Circle &c4)
    {
        if (u.parallel(v))
            return 0;
        Line u1 = Line(u.s + (u.e - u.s).rotCC().scale(r), u.e + (u.e - u.s).rotCC().scale(r));
        Line u2 = Line(u.s + (u.e - u.s).rotCL().scale(r), u.e + (u.e - u.s).rotCL().scale(r));
        Line v1 = Line(v.s + (v.e - v.s).rotCC().scale(r), v.e + (v.e - v.s).rotCC().scale(r));
        Line v2 = Line(v.s + (v.e - v.s).rotCL().scale(r), v.e + (v.e - v.s).rotCL().scale(r));
        c1.r = c2.r = c3.r = c4.r = r;
        c1.p = u1.intersec(v1);
        c2.p = u1.intersec(v2);
        c3.p = u2.intersec(v1);
        c4.p = u2.intersec(v2);
        return 4;
    }

    // Tangent with circle cx and cy
    static int GetCircle(Circle cx, Circle cy, db r, Circle &c1, Circle &c2)
    {
        Circle x(cx.p, r + cx.r), y(cy.p, r + cy.r);
        int t = x.crossC(y, c1.p, c2.p);
        if (!t)
            return 0;
        c1.r = c2.r = r;
        return t;
    }

    void read()
    {
        p.read();
        cin >> r;
    }

    void Debug() { cerr << "Circle: Center: (" << p.x << ", " << p.y << ") Radius: " << r << '\n'; }
};

// Pre-Build Function
inline void build()
{
}

// Actual Solver
inline void solve()
{
    cout << fixed << setprecision(10);
    Point p;
    Circle c;
    p.read();
    c.read();
    Line u, v;
    c.tangent(p, u, v);
    Point p1 = u.s == p ? u.e : u.s;
    Point p2 = v.s == p ? v.e : v.s;
    se(p1, p2);
    p1.write();
    cout << '\n';
    p2.write();
    cout << '\n';
}

int main()
{
    ios::sync_with_stdio(false);
    cin.tie(nullptr);
    cout.tie(nullptr);

#ifdef LOCAL
    clock_t _begin = clock();
#endif

    build();
    solve();

#ifdef LOCAL
    cerr << "Time elapsed: " << (double)(clock() - _begin) * 1000 / CLOCKS_PER_SEC << "ms." << endl;
#endif

    return 0;
}