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<algorithm>
#include<cassert>
#include<map>
#include<vector>
#include<cmath>
#include<complex>
using namespace std;

#define REP(i,b,n) for(int i=b;i<n;i++)
#define rep(i,n)   REP(i,0,n)
#define N 100
#define DEAD false
#define ARRIVE true
#define eps 1e-10

typedef complex<double> P;

double dot(P a,P b){
  return a.real()*b.real()+a.imag()*b.imag();
}

double cross(P a,P b){
  return a.real()*b.imag()-a.imag()*b.real();
}

double distance_ls_p(P a,P b,P c,double r){
  if ( dot(b-a,c-a)<0)return r*2;
  else if ( dot(a-b,c-b)<0)return r*2;
  return abs(cross(b-a,c-a))/abs(b-a);
}


bool is_intersect_cl(P a,P b,P circle,double radius){
  bool flag1 = abs(a-circle)<=radius?1:0;
  bool flag2 = abs(b-circle)<=radius?1:0;
  
  if ( flag1 == true)return true;
  else if ( flag2 == true)return true;
  if (  distance_ls_p(a,b,circle,radius)<radius+eps)return true;
  return false;
}

class UFO{

public:
  P now;
  double r,v,theta,time;
  double vx,vy;
  bool flag;
  UFO(){};
  UFO(double tx,double ty,double tr,double tv,double R){
    flag = ARRIVE;
    now.real()=tx;
    now.imag()=ty;
    v=tv;
    r=tr;
    theta = arg(now);
    time = sqrt(tx*tx+ty*ty)-R;
    if (time < 0)flag=DEAD;
    else time/=v;
    vx=-cos(theta)*v;
    vy=-sin(theta)*v;    
  }

  void move(double t){    
    if (flag == DEAD){return;}
    now.real()+=vx;
    now.imag()+=vy;
    if ( time < t+eps){flag = DEAD;return ;}
  }

  bool crash_check(P a,P b){
    if ( flag == DEAD)return false;
    if ( is_intersect_cl(a,b,now,r)==true){
      flag = DEAD;
      return true;
    }
    return false;
  }
};


int solve(int n,UFO *data,double R){
  const double INF = 20000;
  int cnt=0;
  double time=1;
  while(true){
    double dist = 1000*1000;
    int minindex = -1;
    rep(i,n){
      data[i].move(time);
      if (data[i].flag == ARRIVE&& abs(data[i].now)<dist){
	dist=abs(data[i].now);
	minindex=i;
      }
    }
    if ( minindex == -1)break;
    
    P a,b,e;
    e = data[minindex].now/abs(data[minindex].now);
    a=e*R;
    b=e*INF;
    rep(i,n){
      if ( data[i].crash_check(a,b) == true)cnt++;
    }


    time+=1;
  }

  return n-cnt;
}

main(){
  double R;
  int n;
  while(cin>>R >> n && n){
    UFO data[n];
    rep(i,n){
      double x,y,r,v;
      cin>>x>>y>>r>>v;
      data[i]=UFO(x,y,r,v,R);
    }
    cout << solve(n,data,R) << endl;
  }

}