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<algorithm>
#include<vector>
#include<stack>
#include<queue>
#include<list>
#include<string>
#include<cstring>
#include<cstdlib>
#include<cstdio>
#include<cmath>
#include<ctime>
using namespace std;

typedef long long ll;

bool debug = false;
const int NIL = -1;
const int INF = 1000000000;
const int NUM = 100010;
const double eps = 1e-10;
const double PI = 3.1415926535;
clock_t START, END;

int X, Y, E;

//basic defitition
struct Point {
	double x, y;
	Point(double x = 0, double y = 0) :x(x), y(y) {}
};
typedef Point Vector;
Vector operator + (Vector A, Vector B) { return Vector(A.x + B.x, A.y + B.y); }
Vector operator - (Point A, Point B) { return Vector(A.x - B.x, A.y - B.y); }
Vector operator * (Vector A, double p) { return Vector(A.x * p, A.y * p); }
Vector operator / (Vector A, double p) { return Vector(A.x / p, A.y / p); }
bool operator < (const Point& a, const Point& b) { return a.x < b.x || (a.x == b.x && a.y < b.y); }
int dcmp(double x) { if (fabs(x) < eps)return 0; else return x < 0 ? -1 : 1; }
bool operator == (const Point& a, const Point& b) { return dcmp(a.x - b.x) == 0 && dcmp(a.y - b.y) == 0; }
struct Line {
	Point p;
	Vector v;
	Line(Point p, Vector v) :p(p), v(v) {}
	Point point(double t) { return p + v * t; }
	//Line move(double d) { return Line(p + Normal(v) * d, v); }
};
// basic operator
double Dot(Vector A, Vector B) { return A.x * B.x + A.y * B.y; }
double Length(Vector A) { return sqrt(Dot(A, A)); }
double Angle(Vector A, Vector B) { return acos(Dot(A, B) / Length(A) / Length(B)); }
double Cross(Vector A, Vector B) { return A.x * B.y - A.y * B.x; }
double Area2(Point A, Point B, Point C) { return Cross(B - A, C - A); }
Vector Rotate(Vector A, double rad) { return Vector(A.x * cos(rad) - A.y * sin(rad), A.x * sin(rad) + A.y * cos(rad)); }
Vector Normal(Vector A) { double L = Length(A); return Vector(-A.y / L, A.x / L); } //A is not zero vector
//point and line
Point GetLineIntersection(Point P, Vector v, Point Q, Vector w) {
	Vector u = P - Q;
	double t = Cross(w, u) / Cross(v, w);
	return P + v * t;
}//two lines only have one intersection and Cross(v,w) is not zero
double DistanceToLine(Point P, Point A, Point B) {
	Vector v1 = B - A, v2 = P - A;
	return fabs(Cross(v1, v2)) / Length(v1);
}
double DistanceToSegment(Point P, Point A, Point B) {
	if (A == B) return Length(P - A);
	Vector v1 = B - A, v2 = P - A, v3 = P - B;
	if (dcmp(Dot(v1, v2)) < 0) return Length(v2);
	else if (dcmp(Dot(v1, v3)) > 0) return Length(v3);
	else return fabs(Cross(v1, v2)) / Length(v1);
}
Point GetLineProjection(Point P, Point A, Point B) {
	Vector v = B - A;
	return A = v * (Dot(v, P - A) / Dot(v, v));
}
bool SegmentProperIntersection(Point a1, Point a2, Point b1, Point b2) {
	double c1 = Cross(a2 - a1, b1 - a1), c2 = Cross(a2 - a1, b2 - a1), c3 = Cross(b2 - b1, a1 - b1), c4 = Cross(b2 - b1, a2 - b1);
	return dcmp(c1) * dcmp(c2) < 0 && dcmp(c3) * dcmp(c4) < 0;
}
bool OnSegment(Point p, Point a1, Point a2) {
	return dcmp(Cross(a1 - p, a2 - p)) == 0 && dcmp(Dot(a1 - p, a2 - p)) <= 0;
}
double angle(Vector v) { return atan2(v.y, v.x); }
//polygon
double ConvexPolygonArea(Point* p, int n) {
	double area = 0;
	for (int i = 1; i < n - 1; i++)
		area = Cross(p[i] - p[0], p[i + 1] - p[0]);
	return area / 2;
}
//circle
struct Circle {
	Point c;
	double r;
	Circle(Point c, double r) :c(c), r(r) {}
	Point point(double a) { return Point(c.x + cos(a) * r, c.y + sin(a) * r); }
};
int getTangents(Point p, Circle C, Vector* v) {
	Vector u = C.c - p;
	double dist = Length(u);
	if (dist < C.r)
		return 0;
	else if (dcmp(dist - C.r) == 0) {
		v[0] = Rotate(u, PI / 2);
		return 1;
	}
	else {
		double ang = asin(C.r / dist);
		double l = sqrt(dist * dist - C.r * C.r);
		//u = u / dist * l;
		v[0] = Rotate(u, -ang);
		v[0] = p + v[0] / sqrt(v[0].x * v[0].x + v[0].y * v[0].y) * l;
		v[1] = Rotate(u, ang);
		v[1] = p + v[1] / sqrt(v[1].x * v[1].x + v[1].y * v[1].y) * l;
		return 2;
	}
}

int main(void)
{
	if (debug) {
		START = clock();
		freopen("in29.txt", "r", stdin);
		freopen("out.txt", "w", stdout);
	}
	Point v[2];
	Point O, P;
	double r;
	scanf("%lf%lf", &P.x, &P.y);
	scanf("%lf%lf%lf", &O.x, &O.y, &r);
	Circle C2(O, r);
	getTangents(P, C2, v);
	if (v[0].x == v[1].x) {
		if (v[0].y > v[1].y)
			swap(v[0], v[1]);
	}
	else if (v[0].x > v[1].x)
		swap(v[0], v[1]);
	printf("%.10lf %.10lf\n%.10lf %.10lf\n", v[0].x, v[0].y, v[1].x, v[1].y);
	if (debug) {
		END = clock();
		double endtime = (double)(END - START) / 1000;
		printf("total time = %lf s", endtime);
	}
	return 0;
}