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 <cstdio>
#include <complex>
#include <vector>
#include <list>
#include <algorithm>
#include <cmath>
using namespace std;

#define EPS 1e-6
typedef complex<double> P;

struct L : public vector<P> {
  L(const P &a, const P &b) {
    push_back(a); push_back(b);
  }
};

struct C {
  P p; double r;
  C(const P &p, double r) : p(p), r(r) { }
};

double cross(const P& a, const P& b) {
  return imag(conj(a)*b);
}

double dot(const P& a, const P& b) {
  return real(conj(a)*b);
}

double dist(const P& a, const P& b)
{
	return sqrt((a.real()-b.real())*(a.real()-b.real())+(a.imag()-b.imag())*(a.imag()-b.imag()));
}

bool isIntoC(const P& p, const C& c)
{
	return dist(p, c.p) < c.r+EPS;
}

bool isIntoC(const L& l, const C& c)
{
	return dist(l[0], c.p) < c.r+EPS && dist(l[1], c.p) < c.r+EPS;
}

int CrossPtNum(const C& c, const L& l)
{
	P LV=l[0]-l[1];
	double A=(LV.real()*LV.real())+(LV.imag()*LV.imag());
	double B=(LV.real()*l[0].real())-(LV.real()*c.p.real())+(LV.imag()*l[0].imag())-(LV.imag()*c.p.imag());
	double C=(l[0].real()-c.p.real())*(l[0].real()-c.p.real())+(l[0].imag()-c.p.imag())*(l[0].imag()-c.p.imag())-(c.r*c.r);

	if(fabs(B*B-A*C) < EPS) return 1;
	if(B*B-A*C  > 0) return 2;
	
	return 0;
}

bool intersectSC(const L& l, const C& c)
{	
	double vc=dot(l[1]-l[0], c.p-l[0]);
	if(vc<0)
	{
		double dif=c.r-dist(l[0], c.p);
		return dif+EPS > 0;
	}
	
	double vv=dot(l[1]-l[0], l[1]-l[0]);
	
	if(vc > vv)
	{
		double d=dist(l[1], c.p);
		double dif=c.r*c.r-d*d;
		
		return dif+EPS > 0;
	}
	
	double cc=dot(c.p-l[0], c.p-l[0]);
	double dif=c.r*c.r-(cc-(vc/vv)*vc);
	
	return dif+EPS > 0;
}

int tmr;	

class UFO
{
	public:

		double x,y,r,v,d,x0,y0;

		UFO(int X, int Y, int R, int V)
		{
			x0=X;
			y0=Y;
			r=R;
			v=V;
			d=sqrt(x0*x0+y0*y0);
		}

		int move()
		{
			x=x0-tmr*v*x0/sqrt(x0*x0+y0*y0);
			y=y0-tmr*v*y0/sqrt(x0*x0+y0*y0);
			d-=v;
			return d;
		}
};

int main()
{
	int R,N,x,y,r,v;
	while(cin >> R >> N, (R||N))
	{
		list<UFO> ls;
		while(N--)
		{
			cin >> x >> y >> r >> v;
			ls.push_back(UFO(x,y,r,v));
		}

		int cnt = 0;
		tmr = 0;
		while(true)
		{
			tmr++;
			double md = 1e20;
			double mx,my;
			for(list<UFO>::iterator it=ls.begin(); it!=ls.end();)
			{
				it->move();
				if(it->d <= R)
				{
					it = ls.erase(it);
					cnt++;
				}
				else
				{
					if(md>it->d)
					{
						mx=it->x;
						my=it->y;
						md=it->d;
					}
					it++;
				}
			}
			if(ls.empty()) { cout << cnt << endl; break; }

			L laser(P(R*mx/sqrt(mx*mx+my*my)+EPS,R*my/sqrt(mx*mx+my*my))+EPS,P(mx*3000,my*3000));
			for(list<UFO>::iterator it=ls.begin(); it!=ls.end();)
			{
				C ufo(P(it->x,it->y),it->r);
				if(intersectSC(laser,ufo))
				{
					it = ls.erase(it);
				}
				else
				{
					it++;
				}
			}
		}


	}

	return 0;
}

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);
	});
      rem.erase(remove_if(begin(rem),end(rem),[&](int x){
	    complex<double> rp=polar(d(x),atan2(y0[x],x0[x])-atan2(y0[*cl],x0[*cl]));
	    return rp.real()+r[x]>=0&&(rp.imag()+r[x])*(rp.imag()-r[x])<=eps;
	  }),end(rem));
    }
    cout<<ans<<endl;
  }
}