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++: /*
 * src.cpp
 *
 *  Created on: 2016/08/01
 *      Author: joi
 */

#include <bits/stdc++.h>

using namespace std;

#define FOR(i,a,b) for(int i=(a);i<(b);i++)
#define REP(i,a) FOR(i,0,a)

const int MAX_N=1e2;
const double EPS=1e-10;

#define EQ(a,b) fabs(a-b)<EPS

int R,N;

struct Point{
	double x,y;
	Point(double x=0.0,double y=0.0):x(x),y(y){}
	Point operator +(const Point &p){
		return Point(x+p.x,y+p.y);
	}
	Point operator -(const Point &p){
		return Point(x-p.x,y-p.y);
	}
	Point operator *(double k){
		return Point(x*k,y*k);
	}
	Point operator /(double k){
		return Point(x/k,y/k);
	}
	double norm(){
		return x*x+y*y;
	}
	double abs(){
		return sqrt(norm());
	}
};

typedef pair<Point,Point> P;

typedef Point Vector;

double dot(const Vector &a,const Vector &b){
	return a.x*b.x+a.y*b.y;
}

double cross(const Vector &a,const Vector &b){
	return a.x*b.y-a.y*b.x;
}

struct Segment{
	Point p1,p2;
	Segment(Point p1=Point(),Point p2=Point()):p1(p1),p2(p2){}
};

typedef Segment line;

Point project(Segment s,Point p){
	Vector base=s.p2-s.p1;
	double r=dot(base,p-s.p1)/base.norm();
	return s.p1+base*r;
}

struct Circle{
	Point c;
	double r;
	Circle(Point c=Point(),double r=0.0):c(c),r(r){}
};

struct UFO{
	Circle cir;
	Vector v;
	bool flg;
};

UFO u[MAX_N];

P getCrossPoints(Circle c,line l){
	Point pr=project(l,c.c);
	Vector e=(l.p2-l.p1)/(l.p2-l.p1).abs();
	double base=sqrt(c.r*c.r-(c.c-pr).norm());
	return make_pair(pr+e*base,pr-e*base);
}

int main(){
	do{
		scanf("%d %d",&R,&N);
		if (R || N){
			REP(i,N){
				int x,y,r,v;
				scanf("%d %d %d %d",&x,&y,&r,&v);
				Vector p=Point((double)x,(double)y);
				u[i].cir=Circle(p,(double)r);
				u[i].flg=true;
				if (EQ(p.abs(),0)){
					u[i].v=Point(0.0,0.0);
				}else{
					u[i].v=p*(-1)/p.abs()*(double)v;
				}
			}
			while (1){
				REP(i,N){
					if (u[i].flg){
						if (u[i].cir.c.norm()<u[i].v.norm()){
							u[i].cir.c=Point(0.0,0.0);
						}else{
							u[i].cir.c=u[i].cir.c+u[i].v;
						}
					}
				}
				int a=-1;
				REP(i,N){
					if (u[i].flg){
						if (u[i].cir.c.norm()>R*R){
							if (a==-1 || u[i].cir.c.norm()<u[a].cir.c.norm()){
								a=i;
							}
						}
					}
				}
				if (a==-1){
					break;
				}
				line laser=Segment(Point(),u[a].cir.c);
				Vector e=u[a].cir.c/u[a].cir.c.abs();
				REP(i,N){
					if (u[i].flg){
						if (u[i].cir.c.norm()>R*R){
							Vector pr=project(laser,u[i].cir.c);
							if ((u[i].cir.c-pr).norm()<u[i].cir.r*u[i].cir.r){
								P pa=getCrossPoints(u[i].cir,laser);
								if (dot(e,pa.first)>=0 || dot(e,pa.second)>=0){
									u[i].flg=false;
								}
							}
						}
					}
				}
			}
			int ans=0;
			REP(i,N){
				if (u[i].flg){
					ans++;
				}
			}
			printf("%d\n",ans);
		}
	}while (R || N);
	return 0;
}

C++: #include <iostream>
#include <complex>
#include <vector>
#include <algorithm>
#include <utility>
#include <cmath>
using namespace std;
typedef complex<double> P;
typedef pair<P, P> L;
typedef pair<P, double> C;
#define X real()
#define Y imag()
const double INF = 1e9;
const double EPS = 1e-10;

double dot(P a, P b){return a.X*b.X + a.Y*b.Y;}

double cross(P a, P b){return a.X*b.Y - a.Y*b.X;}

int ccw(P a, P b, P c){
  b -= a;
  c -= a;
  if(cross(b, c) > EPS) return 1;
  if(cross(b, c) < -EPS) return -1;
  if(dot(b, c) < -EPS) return -2;
  if(norm(c) > norm(b) + EPS) return 2;
  return 0;
}

double ufo_to_lazer_dist(P p, P d){
  if(dot(p, d) < -EPS) return abs(p);
  return abs(cross(p, d));
}

int main(){
  int R, N;
  while(cin >> R >> N){
    if(R == 0 && N == 0) break;
    vector<C> UFO(N);
    vector<int> V(N);
    for(int i = 0; i < N; ++i){
      double x, y, r;
      cin >> x >> y >> r >> V[i];
      UFO[i] = C(P(x, y), r);
    }
    int c = 0, ans = 0, t = 0;
    vector<bool> U(N, false);
    while(c < N){
      double closest = INF;
      int id = -1;
      for(int i = 0; i < N; ++i){
        if(U[i]) continue;
        if(abs(UFO[i].first) - t*V[i] < closest){
          if(abs(UFO[i].first) - t*V[i] < R + EPS){
            ++c;
            ++ans;
            U[i] = true;
          }else{
            closest = abs(UFO[i].first) - t*V[i];
            id = i;
          }
        }
      }
      if(id < 0) continue;
      P d = UFO[id].first;
      U[id] = true;
      ++c;
      for(int i = 0; i < N; ++i){
        if(U[i]) continue;
        if(ufo_to_lazer_dist(UFO[i].first, d) < UFO[i].second + EPS){
          U[i] = true;
          ++c;
        }
      }
      ++t;
    }
    cout << ans << endl;
  }
  return 0;
}