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<complex>
#include<vector>
#include<algorithm>
#include<cmath>

using namespace std;

template<class T> T sqr(T x){
  return x*x;
}

const double eps=1e-9;

int main(){
  for(int R,N;cin>>R>>N,R;){
    int x0[100],y0[100],r[100],v[100];
    vector<int> rem(N);
    for(int i=0;i<N;i++){
      cin>>x0[i]>>y0[i]>>r[i]>>v[i];
      rem[i]=i;
    }
    int ans=0;
    for(int i=1;;i++){
      auto d=[&](int x){
	return sqrt(sqr(x0[x])+sqr(y0[x]))-i*v[x];
      };
      auto it=remove_if(begin(rem),end(rem),[&](int x){
	  return d(x)<=R+eps;
	});
      ans+=end(rem)-it;
      rem.erase(it,end(rem));
      if(rem.empty())break;
      auto cl=min_element(begin(rem),end(rem),[&](int a,int b){
	  return d(a)<d(b);
	});
      double arg=atan2(y0[*cl],x0[*cl]);
      double xc=d(*cl);
      rem.erase(remove_if(begin(rem),end(rem),[&](int x){
	    complex<double> rp=polar(d(x),atan2(y0[x],x0[x])-arg);
	    return r[x]>=fabs(rp.imag())&&sqrt(sqr(r[x])-sqr(rp.imag()))+rp.real()>R;
	  }),end(rem));
    }
    cout<<ans<<endl;
  }
}

C++: #include <cstdio>
#include <cstdlib>
#include <cstring>
#include <climits>
#include <cassert>
#include <iostream>
#include <iomanip>
#include <sstream>
#include <algorithm>
#include <numeric>
#include <complex>
#include <stack>
#include <queue>
#include <list>
#include <set>
#include <map>
#include <bitset>
#include <functional>
#include <iterator>

using namespace std;

#define dump(n) cout<<"# "<<#n<<"="<<(n)<<endl
#define repi(i,a,b) for(int i=int(a);i<int(b);i++)
#define peri(i,a,b) for(int i=int(b);i-->int(a);)
#define rep(i,n) repi(i,0,n)
#define per(i,n) peri(i,0,n)
#define iter(c) __typeof__((c).begin())
#define foreach(i,c) for(iter(c) i=(c).begin();i!=(c).end();++i)
#define all(c) (c).begin(),(c).end()
#define mp make_pair

typedef unsigned int uint;
typedef long long ll;
typedef unsigned long long ull;
typedef vector<int> vi;
typedef vector<vi> vvi;
typedef vector<double> vd;
typedef vector<vd> vvd;
typedef vector<string> vs;
typedef pair<int,int> pii;

const int INFTY=1<<29;
const double EPS=1e-9;

template<typename T1,typename T2>
ostream& operator<<(ostream& os,const pair<T1,T2>& p){
	return os<<'('<<p.first<<','<<p.second<<')';
}
template<typename T>
ostream& operator<<(ostream& os,const vector<T>& a){
	os<<'[';
	rep(i,a.size()) os<<(i?" ":"")<<a[i];
	return os<<']';
}

typedef complex<double> Point;

struct Line{
	Point pos,dir;
	Line(){}
	Line(Point p,Point d):pos(p),dir(d){}
};
typedef Line Segment;

int Signum(double x)
{
	return abs(x)<EPS?0:x<0?-1:1;
}

double Dot(Point a,Point b)
{
	return real(conj(a)*b);
}

double Cross(Point a,Point b)
{
	return imag(conj(a)*b);
}

Point Proj(Line l,Point p)
{
	Point a=p-l.pos,b=l.dir;
	return Dot(a,b)/norm(b)*b+l.pos;
}

int CCW(Point a,Point b,Point c)
{
	Point d1=b-a,d2=c-a;
	if(int sign=Signum(Cross(d1,d2)))
		return sign;	// 1:ccw,-1:cw
	if(Dot(d1,d2)<-EPS)
		return -2;		// c-a-b
	if(norm(d1)<norm(d2)-EPS)
		return 2;		// a-b-c
	return 0;			// a-c-b
}

double DistLP(Line l,Point p)
{
	return abs(Proj(l,p)-p);
}

double DistSP(Segment s,Point p)
{
	int ccw=CCW(s.pos,s.pos+s.dir,Proj(s,p));
	if(ccw==-2)
		return abs(p-s.pos);
	if(ccw==2)
		return abs(p-(s.pos+s.dir));
	return DistLP(s,p);
}

int main()
{
	for(int r,n;cin>>r>>n,r|n;){
		vector<Point> ps(n);
		vi rs(n),vs(n);
		rep(i,n) cin>>real(ps[i])>>imag(ps[i])>>rs[i]>>vs[i];
		
		vi in(n),down(n);
		rep(i,n)
			if(norm(ps[i])<r*r+EPS)
				in[i]=1;
		
		for(int t=1;;t++){
			rep(i,n) if(!in[i] && !down[i]){
				Point d=ps[i]/abs(ps[i]);
				Point p=ps[i]-1.*vs[i]*t*d;
				if(Signum(real(p))!=Signum(real(ps[i])) || abs(p)<r+EPS)
					in[i]=1;
			}
			
			int target=-1;
			rep(i,n) if(!in[i] && !down[i])
				if(target==-1 || abs(ps[i])<abs(ps[target])-EPS)
					target=i;
			if(target==-1)
				break;
			
			Point pt=ps[target]/abs(ps[target]);
			Segment laser(1.*r*pt,1000.*pt);
			rep(i,n) if(!in[i] && !down[i])
				if(DistSP(laser,ps[i])<rs[i]+EPS)
					down[i]=1;
		}
		
		cout<<count(all(in),1)<<endl;
	}
	
	return 0;
}