Go: package main

import (
	"bufio"
	"os"
	"math"
	"strings"
	"strconv"
	"fmt"
)

var scanner = bufio.NewScanner(os.Stdin)

const (
	INF = 0x7FFFFFFF
	EPS = 1e-10
)

type Point struct {
	x, y float64
}
func (p *Point) plus(q *Point) *Point {
	return &Point{p.x + q.x, p.y + q.y}
}
func (p *Point) minus(q *Point) *Point {
	return &Point{p.x - q.x, p.y - q.y}
}
func (p *Point) multi(a float64) *Point {
	return &Point{p.x * a, p.y * a}
}
func (p *Point) div(a float64) *Point {
	return &Point{p.x / a, p.y / a}
}
func (p *Point) abs() float64 {
	return math.Sqrt(p.norm())
}
func (p *Point) norm() float64 {
	return p.x*p.x + p.y*p.y
}
func (p *Point) isLessThan(q *Point) bool {
	if p.x != q.x {
		return p.x < q.x && p.y < q.y
	}
	return true
}
func (p *Point) isEqual(q *Point) bool {
	return math.Abs(p.x - q.x) < EPS && math.Abs(p.y - q.y) < EPS
}

type Segment struct {
	p1, p2 *Point
}
func (s *Segment) norm() float64 {
	return (s.p2.x - s.p1.x)*(s.p2.x - s.p1.x) +
		(s.p2.y - s.p1.y)*(s.p2.y - s.p1.y)
}
func (s *Segment) abs() float64 {
	return math.Sqrt(s.norm())
}

func norm(a *Point) float64 {
	return a.x*a.x + a.y*a.y
}

func abs(a *Point) float64 {
	return math.Sqrt(norm(a))
}

func polar(a, r float64) *Point {
	return &Point{math.Cos(r)*a, math.Sin(r)*a}
}

func getDistance(a, b *Point) float64 {
	return abs(a.minus(b))
}

func dot(a, b *Point) float64 {
	return a.x*b.x + a.y*b.y
}

func cross(a, b *Point) float64 {
	return a.x*b.y - a.y*b.x
}

func getDistanceLP(s Segment, p *Point) float64 {
	return cross(s.p2.minus(s.p1), p.minus(s.p1))/ abs(s.p2.minus(s.p1))
}

func getDistanceSP(s Segment, p *Point) float64 {
	if dot(s.p2.minus(s.p1), p.minus(s.p1)) < 0 {
		return abs(p.minus(s.p1))
	}
	if dot(s.p1.minus(s.p2), p.minus(s.p2)) < 0 {
		return abs(p.minus(s.p2))
	}
	return getDistanceLP(s, p)
}

func main() {
	for scanner.Scan() {
		buf := strings.Split(scanner.Text(), " ")
		R, _ := strconv.Atoi(buf[0])
		N, _ := strconv.Atoi(buf[1])
		if R == 0 && N == 0 {
			break
		}
		p := make([]*Point, N)
		r := make([]float64, N)
		v := make([]float64, N)
		d := make([]float64, N)
		nd := make([]float64, N)
		die := make([]bool, N)
		for i := 0; i < N; i++ {
			scanner.Scan()
			buf_ := strings.Split(scanner.Text(), " ")
			_x, _ := strconv.ParseFloat(buf_[0], 64)
			_y, _ := strconv.ParseFloat(buf_[1], 64)
			_r, _ := strconv.ParseFloat(buf_[2], 64)
			_v, _ := strconv.ParseFloat(buf_[3], 64)
			tmp := &Point{_x, _y}
			p[i] = tmp
			r[i] = _r
			v[i] = _v
			nd[i] = getDistance(p[i], &Point{0, 0})
			d[i] = getDistance(p[i], &Point{0, 0})
			die[i] = false
		}
		for {
			for i := 0; i < N; i++ {
				nd[i] = math.Max(float64(R), nd[i]-v[i])
			}
			mini := float64(INF)
			id := -1
			for i := 0; i < N; i++ {
				if die[i] {
					continue
				}
				if nd[i] < EPS+float64(R) {
					continue
				}
				if nd[i] > mini {
					continue
				}
				mini = nd[i]
				id = i
			}
			if id == -1 {
				break
			}
			s := Segment{p[id], p[id]}
			s.p1 = s.p1.div(d[id])
			s.p1 = s.p1.multi(float64(R))
			s.p2 = s.p2.div(d[id])
			s.p2 = s.p2.multi(10000000.0)
			for i := 0; i < N; i++ {
				if nd[i] < EPS + float64(R) {
					continue
				}
				a := p[i]
				a = a.div(d[i])
				a = a.multi(nd[i])
				if getDistanceSP(s, a) < EPS + r[i] {
					die[i] = true
				}
			}
		}
		ans := 0
		for i := 0; i < N; i++ {
			if !die[i] {
				ans++
			}
		}
		fmt.Println(ans)
	}
}

C++: #include <iostream>
#include <math.h>
using namespace std;

struct ufo {
	double x,y,sx,sy,sl,r,v;
};
ufo uf[100];
int cnt,n,m,r,mn,f[100];
double s,hx1,hy1,hx2,hy2;

void move() {
	int i;
	double x,y,g;
	g=999999;
	for (i=0;i<n;i++) {
		if (f[i]==1) continue;
		x=uf[i].sx-uf[i].sx*uf[i].v*s/uf[i].sl;
		y=uf[i].sy-uf[i].sy*uf[i].v*s/uf[i].sl;
		if (x*x+y*y<=r*r || x*uf[i].sx<0 || y*uf[i].sy<0) { f[i]=1; cnt++; m--;}
		if (f[i]==0) { uf[i].x=x; uf[i].y=y;
		     if (x*x+y*y<g) { g=x*x+y*y; mn=i;}
		     } 
	    }
	  };

void hit(double x,double y,double r,double a) {
	int f=0;
	double c,z;
	if (a==9999) { a=0; z=x; x=y; y=z; f=1;}
	c=(2*x+2*a*y)*(2*x+2*a*y)-4*(1+a*a)*(y*y+x*x-r*r);
	if (c<0) { hx1=9999; return;}
	hx1=(2*x+2*a*y+sqrt(c))/(2*(1+a*a));
	hx2=(2*x+2*a*y-sqrt(c))/(2*(1+a*a));
	hy1=a*hx1; hy2=a*hx2;
	if (f==1) { hy1=hx1; hy2=hx2; hx1=hx2=0;}
} 

void attck() {
	int i;
	double a=0;
	if (uf[mn].x!=0) { a=uf[mn].y/uf[mn].x;} else a=9999;
	for (i=0;i<n;i++) {
		if (f[i]==1) continue;
		hit(uf[i].x,uf[i].y,uf[i].r,a);
		if (hx1==9999) continue;
		if (hx1*uf[mn].x>=0 && hy1*uf[mn].y>=0 && hx1*hx1+hy1*hy1>r*r) { f[i]=1; m--;}
		else if (hx2*uf[mn].x>=0 && hy2*uf[mn].y>=0 && hx2*hx2+hy2*hy2>r*r) { f[i]=1; m--;}
	}
	};

int main() {
    int i;
    while(cin >> r >> n) {
		if (n==0) break;
		m=n; s=0; cnt=0;
		for (i=0;i<n;i++) {
			f[i]=0;
		    cin >> uf[i].sx >> uf[i].sy >> uf[i].r >> uf[i].v;
		    uf[i].sl=sqrt(uf[i].sx*uf[i].sx+uf[i].sy*uf[i].sy);
		    uf[i].x=uf[i].sx; uf[i].y=uf[i].sy;
		}
		while(m>0) {
			s+=1;
			move();
			attck();
			}
		cout << cnt << endl;
	} 
	return 0;
}

C++: #include <iostream>
#include <complex>
#include <vector>
#include <algorithm>
#include <cmath>
#include <queue>
using namespace std;

#define EPS 1e-6
typedef complex<double> P;

struct L : public vector<P> {
  L(const P &a, const P &b) {
    push_back(a); push_back(b);
  }
};

struct C {
  P p; double r;
  C(const P &p, double r) : p(p), r(r) { }
};

double cross(const P& a, const P& b) {
  return imag(conj(a)*b);
}

double dot(const P& a, const P& b) {
  return real(conj(a)*b);
}

double dist(const P& a, const P& b)
{
	return sqrt((a.real()-b.real())*(a.real()-b.real())+(a.imag()-b.imag())*(a.imag()-b.imag()));
}

bool intersectSC(const L& l, const C& c)
{
	double vc=dot(l[1]-l[0], c.p-l[0]);
	if(vc<0)
	{
		double dif=c.r-dist(l[0], c.p);
		return dif+EPS > 0;
	}
	
	double vv=dot(l[1]-l[0], l[1]-l[0]);
	
	if(vc > vv)
	{
		double d=dist(l[1], c.p);
		double dif=c.r*c.r-d*d;
		
		return dif+EPS > 0;
	}
	
	double cc=dot(c.p-l[0], c.p-l[0]);
	double dif=c.r*c.r-(cc-(vc/vv)*vc);
	
	return dif+EPS > 0;
}

class UFO
{
public:
	C c;
	int v;
	double d;
	UFO(C c, int v, double d)
	:c(c),v(v),d(d)
	{}
	
	bool operator<(const UFO& u) const
	{
		return d>u.d;
	}
};

int main()
{
	int R,N;
	while(cin >> R >> N,(R||N))
	{
		priority_queue<UFO> q;
		while(N--)
		{
			int x,y,r,v;
			cin >> x >> y >> r >> v;
			q.push(UFO(C(P(x,y),r),v, dist(P(0,0), P(x,y))));
		}
		
		int cnt=0;
		while(!q.empty())
		{
			UFO u=q.top(); q.pop();
			if(u.d < R+EPS)
			{
				cnt++;
				continue;
			}
			
			priority_queue<UFO> tq;
			L s(P(0,0),P(u.c.p.real()*1000, u.c.p.imag()*1000));
			while(!q.empty())
			{
				UFO uf=q.top(); q.pop();
				if(intersectSC(s, uf.c)) continue;
				tq.push(UFO(uf.c, uf.v, uf.d-uf.v));
			}
			
			while(!tq.empty())
			{
				q.push(tq.top()); tq.pop();
			}
		}
		
		cout << cnt << endl;
	}
}