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 <cstdio>
#include <cmath>
#include <vector>
#include <algorithm>


const double PI = 3.1415926585;

using namespace std;

class UFO{
public:
	double t;
	int l;
	int r;
	int v;
	
	bool live;
	
	UFO(){
		live = true;
	}
	
	int Getl(int time){
		return l - v * time;
	}
	bool Hit(int time,double d){
		double f = asin((double)r/Getl(time));
		double upper = t + abs(f);
		double lower = t - abs(f);
		//printf("l = %d : t = %f : d = %f : f = %f : ",Getl(time),t,d,f);
		if( isnan(f) != 0){
			//printf("%f - %f :HIT\n",lower,upper);
			return true;
		}
		
		if(lower < 0){ lower = PI * 2 - lower; }
		if(upper > PI * 2){ upper = upper - PI * 2; }
		
		
		
		if(lower < upper){
			//printf("%f - %f",lower,upper);
			if(lower <= d && d <= upper){
				//printf(" : HIT \n");
				return true;
			}else{
				//printf("\n");
				return false;
			}
		}else{
			//printf(": 0 - %f || %f - 2pi",upper,lower);
			if(upper <= d || lower >= d){
				//printf(" : HIT \n");
				return true;
			}else{
				//printf("\n");
				return false;
			}
		}
	}
	bool operator==(const UFO& u){
		if(t == u.t && l == u.l && r == u.r && v == u.v){
			return true;
		}else{
			return false;
		}
	}
};

int lr;
int n;
int time;
vector<UFO> ufo;
vector<int> rems;

void remufo(){
	vector<int>::iterator rit;
	vector<UFO>::iterator it;
	UFO u;
	//printf("REM\n");
	int n = 0;
	for(rit = rems.begin();rit != rems.end();rit++){
		ufo[*rit].live = false;
		
		//u = ufo[*rit - n];
		//it = remove(ufo.begin(),ufo.end(),u);
		//ufo.erase(it,ufo.end());
		//n++;
		//printf("%d\n",*rit);
	}
	rems.clear();
}

int main(){
	int x,y;
	while(1){
		ufo.clear();
		scanf("%d %d",&lr,&n);
		if(!lr && !n){
			break;
		}
		
		
	
		for(int i=0;i<n;i++){
			UFO u;
			scanf("%d %d %d %d",&x,&y,&u.r,&u.v);
			u.t = atan2(y,x);
			if(u.t < 0){
				u.t = 2 * PI + u.t;
			}
			u.l = sqrt(x*x + y*y);
			ufo.push_back(u);
			//printf("(%d,%d) : %d : %f\n",x,y,u.l,u.t);
		}
		
		time = 1;
		vector<UFO>::iterator it;
		int ans = 0;
		int j;
		UFO min;
		while(ufo.size() != 0){
			bool ff = true;
			for(it = ufo.begin();it != ufo.end();it++){
				if(!(*it).live){ continue; }
				ff = false;
				j++;
			}
			if(ff){ break; }
			j=0;
			min = (*ufo.begin());
			min.live = false;
			for(it = ufo.begin();it != ufo.end();it++){
				if(!(*it).live){ continue; }
				
				if((*it).Getl(time) <= lr){
					//printf("%d < %d\n",(*it).Getl(time),lr);
					(*it).live = false;
					ans+=1;
				}else{
					//printf("%d > %d\n",(*it).Getl(time),lr);
					if(min.live != false || (*it).Getl(time) < min.Getl(time)){
						//printf("%d < %d : %f\n",(*it).Getl(time) , min.Getl(time) , (*it).t);
						min = *it;
					}
				}
				j++;
			}
			float f = min.t;
			j = 0;
			//printf("-->%f\n",f);
			for(it = ufo.begin();it != ufo.end();it++){
				if(!(*it).live){ continue; }
				if((*it).Hit(time,f)){
					(*it).live = false;
				}
				j++;
			}
			time++;
		}
		printf("%d\n",ans);
	}
	return 0;
}