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 <vector>
#include <algorithm>
#include <complex>
using namespace std;
typedef complex<double> P;

struct ufo
{
  P p;
  int r;
  int v;

  bool operator<(const ufo& that) const
  {
    return abs(p) < abs(that.p);
  }
};

struct invaded
{
  int R;
  invaded(int r) : R(r) {}
  bool operator()(const ufo& u) const
  {
    return abs(u.p) <= R;
  }
};

struct move
{
  ufo operator()(const ufo& u) const
  {
    ufo v;
    v.r = u.r;
    v.v = u.v;
    const P e = u.p / abs(u.p);
    v.p = u.p - double(u.v)*e;
    return v;
  }
};

double cross(const P& p, const P& q)
{
  return p.real()*q.imag() - p.imag()*q.real();
}

double distance_point_line(const P& p, const pair<P,P>& line)
{
  const P a = p - line.first;
  const P b = line.second - line.first;
  return abs(cross(a, b)) / abs(b);
}

double dot(const P& p, const P& q)
{
  return p.real()*q.real() + p.imag()*q.imag();
}

struct hit
{
  P p;
  hit(const P& a) : p(a) {}
  bool operator()(const ufo& u) const
  {
    static const P orig(0.0, 0.0);
    const double d = distance_point_line(u.p, make_pair(orig, p));
    return d <= u.r;
  }
};

int main()
{
  int R, N;
  while (cin >> R >> N && R != 0) {
    vector<ufo> us;
    for (int i = 0; i < N; i++) {
      ufo u;
      cin >> u.p.real() >> u.p.imag() >> u.r >> u.v;
      us.push_back(u);
    }

    int ans = 0;
    for (int t = 1; t <= 100 && !us.empty(); t++) {
      vector<ufo> vs;
      transform(us.begin(), us.end(), back_inserter(vs), move());
      for (vector<ufo>::iterator it = us.begin(), jt = vs.begin(); jt != vs.end(); ++it) {
        if (dot(it->p, jt->p) < 0) {
          jt = vs.erase(jt);
          ++ans;
        } else {
          ++jt;
        }
      }
      if (vs.empty()) {
        break;
      }
      us = vs;

      vector<ufo>::iterator it = remove_if(us.begin(), us.end(), invaded(R));
      ans += distance(it, us.end());
      us.erase(it, us.end());

      it = min_element(us.begin(), us.end());
      const P p = it->p;
      us.erase(it);
      us.erase(remove_if(us.begin(), us.end(), hit(p)), us.end());
    }
    cout << ans << endl;
  }
  return 0;
}

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

typedef complex<double> P;

#define INF 999999999
#define EPS (1e-10)

//OÏ
double cross(P a,P b){
	return (a.real() * b.imag() - a.imag() * b.real());
}

//¼üabÆ_cÆÌ£
double distance_l_p(P a,P b,P c){
	return abs(cross(b-a, c-a)) / abs(b-a);
}

//üªabãÉ_cª é©
int is_point_on_line(P a,P b,P c){
	return (abs(a-c) + abs(c-b) < abs(a-b) + EPS);
}

//pÌÚ®ãÌÊuðßé
P move(P p,double v){
	P b = -p / abs(-p); //-p ÌPÊxNg
	return p + b * v;
}

int main(void){
	int n;
	double R;

	while(cin>>R>>n && (R||n)){
		int ans = 0;
		vector<P> p(n);
		vector<double> r(n),v(n);

		for(int i=0;i<n;i++){
			cin>>p[i].real()>>p[i].imag()>>r[i]>>v[i];
		}

		while(p.size() != 0){
			int minIdx = -1;
			double minDist = INF;

			for(int i=0;i<p.size();i++){
				//r[ª ½çÈ¢êÈçJEg
				if(abs(p[i]) < R + EPS){
					ans++;
					p.erase(p.begin()+i);
					r.erase(r.begin()+i);
					v.erase(v.begin()+i);
					i--;
					continue;
				}

				P aft = move(p[i],v[i]);
				double dist = abs(aft);

				//(0,0)ðÊßµÄµÜ¤©,¼aRÌÍÍàÈçJEg
				if(is_point_on_line(p[i],aft,P(0,0)) || dist < R + EPS){
					ans++;
					p.erase(p.begin()+i);
					r.erase(r.begin()+i);
					v.erase(v.begin()+i);
					i--;
					continue;
				}

				p[i] = aft;
				if(minDist > dist){
					minIdx = i;
					minDist = dist;
				}
			}

			if(minIdx == -1) break;

			P pp = p[minIdx];
			for(int i=0;i<p.size();i++){
				//´_©çppÖLÑé¼üÆ p[i] Ì£ª r[i] æè¬³¯êÎ ½é
				if(distance_l_p(P(0,0),pp,p[i]) < r[i] + EPS){
					//½¾µ¯¶ÛÉ¢éKvª é
					bool flgppX = pp.real() > 0;
					bool flgppY = pp.imag() > 0;
					bool flgpX = p[i].real() > 0;
					bool flgpY = p[i].imag() > 0;
					if(flgppX != flgpX || flgppY != flgpY) continue;

					p.erase(p.begin()+i);
					r.erase(r.begin()+i);
					v.erase(v.begin()+i);
					i--;
				}
			}
		}

		cout<<ans<<endl;
	}

	return 0;
}