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>
#define f first
#define s second
#define mp make_pair
#define pi M_PI
#define inf 1<<30
#define eps (1e-11)
#define equals(a,b) (fabs((a)-(b))<eps)
using namespace std;

class Point{
public:
  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 k){ return Point(x*k,y*k);}
  Point operator/(double k){ return Point(x/k,y/k);}
  bool operator<(Point p)const{ return (x!=p.x ? x<p.x : y<p.y);}
  bool operator==(Point p)const{ return fabs(x-p.x)<eps && fabs(y-p.y)<eps;}

  double abs(){ return sqrt(norm());}
  double norm(){ return (x*x+y*y);}
};
typedef Point Vector;
typedef vector<Point> Polygon;

class Segment{
public:
  Point p1,p2;
  Segment(Point p1=Point(),Point p2=Point()):p1(p1),p2(p2){}
};
typedef Segment Line;

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

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);}

Point rotate(Point base,Point a,double r){
  Point b=a-base;
  a.x=b.x*cos((r/180)*M_PI)-b.y*sin((r/180)*M_PI);
  a.y=b.x*sin((r/180)*M_PI)+b.y*cos((r/180)*M_PI);
  a=a+base;
  return a;
}

pair<Point,Point> getTangent(Circle c,Point p){
  Vector v=p-c.c;
  double r=acos(c.r/abs(v))*360/(2*pi);
  v=v*c.r/abs(v);
  Point p1=rotate(c.c,c.c+v,r);
  Point p2=rotate(c.c,c.c+v,360-r);
  return mp(p1,p2);
}

int main()
{
  int x,y,r;

  cin>>x>>y;
  Point p(x,y);
  cin>>x>>y>>r;
  Circle c(Point(x,y),r);

  pair<Point,Point> pp=getTangent(c,p);
  if(pp.s<pp.f)swap(pp.f,pp.s);
  printf("%.10f %.10f\n",pp.f.x,pp.f.y);
  printf("%.10f %.10f\n",pp.s.x,pp.s.y);
  return 0;
}