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 <iostream>
#include <cstdio>
#include <cstring>
#include <algorithm>
#include <cmath>
#include <queue>
#include <vector>
#include <utility>
#define EPS 1e-10
using namespace std;
typedef long long ll;
struct Point{
	double x,y;
	Point(double x = 0.0,double y = 0.0): 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 lambda){
		return Point(x * lambda,y * lambda);
	}
	Point operator / (double lambda){
		return Point(x / lambda,y / lambda);
	}
	Point neg(){//negative.
		return Point(-x,-y);
	}
	double norm(){
		return x * x + y * y;
	}
	double abs_(){
		return sqrt(norm());
	}
	bool operator == (const Point &p)const
	{
		return abs(x - p.x) < EPS && abs(y - p.y) < EPS;
	}
	bool operator < (const Point &p)const
	{
		if(abs(x - p.x) < EPS) return y < p.y;
		else return x < p.x;
	}
};
typedef Point Vector;
struct Segment{
	Point p1,p2;
	Segment(Point p1 = Point(),Point p2 = Point()): p1(p1),p2(p2) {}
};
typedef Segment Line;
struct Circle{
	Point c;
	double r;
	Circle(Point c = Point(),double r = 0.0): c(c),r(r) {}
};
typedef vector<Point> Polygon;
double dot(Vector a,Vector b){
	return a.x * b.x + a.y * b.y;
}
double det(Vector a,Vector b){
	return a.x * b.y - b.x * a.y;
}
Vector rot(Vector a,double theta){//rotate.
	double x1 = cos(theta) * a.x - sin(theta) * a.y;
	double y1 = sin(theta) * a.x + cos(theta) * a.y;
	return Point(x1,y1);
}
vector <Point> tangent(Circle o,Point p){//make sure tangents exist.
	Vector a = p - o.c;
	double theta = acos(o.r / a.abs_());
	Vector b = a / a.abs_() * o.r;
	vector <Point> res;
	res.push_back(o.c + rot(b,theta));
	res.push_back(o.c + rot(b,-theta));
	return res;
}
int main(){
	Circle o; Point p;
	scanf("%lf%lf",&p.x,&p.y);
	scanf("%lf%lf%lf",&o.c.x,&o.c.y,&o.r);
	vector <Point> ans = tangent(o,p);
	sort(ans.begin(),ans.end());
	for(int i=0;i<(int)ans.size();i++){
		printf("%.10f %.10f\n",ans[i].x,ans[i].y);
	}
	return 0;
}