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 <bits/stdc++.h>

using namespace std;

#define EPS 1e-10
#define equal(a,b) (fabs(a-b) < EPS)
#define lt(a,b) (a-b < -EPS)
#define le(a,b) (lt(a,b) || equal(a,b))
#define MAX_N 110
#define INF 1e9
#define PI acos(-1)

struct Point{
  double x,y;

  Point(){}
  Point(double x,double y) : x(x),y(y) {}

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

double dot(const Point &a,const Point &b){ return a.x*b.x+a.y*b.y; }
double cross(const Point &a,const Point &b){ return a.x*b.y - b.x*a.y; }
double norm(const Point &p){ return dot(p,p); }
double abs(const Point &p){ return sqrt(norm(p)); }
double dist(const Point &a,const Point &b){
  return sqrt(pow(a.x-b.x,2) + pow(a.y-b.y,2));
}

typedef Point Vector;

struct Line{
  Point s,t;
  Line(){}
  Line(Point s,Point t) : s(s),t(t) {}
};

Point projection(const Line &l,const Point &p){
  Vector b = l.t-l.s;
  double t = dot(p-l.s,b)/norm(b);
  return l.s+b*t;
}

struct Circle{
  Point p;
  double r;
  Circle(){}
  Circle(Point p,double r) : p(p),r(r) {}
};

double distanceLP(const Line &l,const Point &p){
  return abs(p-projection(l,p));
}

bool isIntersectCL(const Circle &c,const Line &l){
  double d = distanceLP(l,c.p);
  if(lt(c.r,d)){ return false; }
  return true;
}

istream &operator >> (istream &is,Circle &c){
  return is >> c.p.x >> c.p.y >> c.r;
}

struct Data{
  Circle c;
  double v;
  Data(){}
  Data(Circle c,double v) : c(c), v(v) {}
};

int main(){
  double R;
  int N;
  while(true){
    cin >> R >> N;
    if(R == 0 && N == 0){ break; }
    vector<Data> UFO(N);
    double d[MAX_N];
    for(int i = 0 ; i < N ; i++){
      cin >> UFO[i].c >> UFO[i].v;
      d[i] = dist(Point(0,0),UFO[i].c.p);
    }
    int r = N;
    bool can[MAX_N];
    fill(can,can+N,true);
    for(int i = 0 ; i < N ; i++){
      int idx = -1;
      double mind = INF;
      for(int j = 0 ; j < N ; j++){
        d[j] -= UFO[j].v;
        Vector v = UFO[j].c.p/abs(UFO[j].c.p);
        v = v*UFO[j].v;
        UFO[j].c.p = UFO[j].c.p-v;
        if(le(d[j],R)){
          can[j] = false;
        }
      }
      for(int j = 0 ; j < N ; j++){
        if(!can[j]){ continue; }
        if(lt(d[j],mind)){
          mind = d[j];
          idx = j;
        }
      }
      if(mind == INF){ break; }
      Line l(Point(0,0),UFO[idx].c.p);
      for(int j = 0 ; j < N ; j++){
        Circle c = UFO[j].c;
        if(can[j] && isIntersectCL(c,l)){
          can[j] = false;
          r--;
        }
      }
    }
    cout << r << endl;
  }
  return 0;
}