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

struct P{
	double x, y;
};

typedef P Vector;

struct UFO{
	P p;
	double r, v;
};

const P ORIGIN_P = {0, 0};
const double EPS = 1e-10;

double distance(P p1, P p2){
	double x_diff = p1.x - p2.x,
		y_diff = p1.y - p2.y;
	return sqrt(x_diff*x_diff + y_diff*y_diff);
}

double crossProduct(Vector v1, Vector v2){
	return v1.x*v2.y - v1.y*v2.x;
}

Vector createUnitVector(Vector v){
	double dist = distance(v, ORIGIN_P);
	return {v.x / dist, v.y / dist};
}

Vector createNormalVector(Vector v){
	return {-v.y, v.x};
}

Vector operator*(const double k, const Vector v){
	return {k * v.x, k * v.y};
}

Vector operator+(const Vector v1, const Vector v2){
	return {v1.x+v2.x, v1.y+v2.y};
}

double abs(double d){
	return (d>0)?d:-d;
}

bool comp(const UFO& l_ufo, const UFO& r_ufo){
	return distance(l_ufo.p, ORIGIN_P) < distance(r_ufo.p, ORIGIN_P);
}

int R, n;

void moveUFO(std::vector<UFO> &uv){//UFOの移動
	int uv_size = uv.size();
	for(int i=0;i<uv_size;i++){
		UFO &u = uv[i];
		Vector v = -u.v * createUnitVector(u.p);
		u.p = u.p + v;
	}
}

int countUFO(std::vector<UFO> &uv){//生存確定したUFOの数を返す
	int res = 0,
		uv_size = uv.size();
	std::vector<UFO> temp_uv;
	for(int i=0;i<uv_size;i++){
		if(distance(uv[i].p, ORIGIN_P) - R < EPS){
			res++;
		}else{
			temp_uv.push_back(uv[i]);
		}
	}
	uv = temp_uv;
	return res;
}

void shoot(std::vector<UFO> &uv){
	int uv_size = uv.size();
	std::vector<UFO> temp_uv;
	UFO attacked_u = uv[0];

	std::sort(uv.begin(), uv.end(), comp);
	for(int i=1;i<uv_size;i++){
		UFO u = uv[i];
		double A = distance(attacked_u.p, ORIGIN_P),
			c_product = crossProduct(attacked_u.p, u.p),
			dist = abs(c_product / A);
		if(dist - u.r < EPS){//破壊
				
		}else{//生き残る
			temp_uv.push_back(u);
		}
	}

	uv = temp_uv;
}

int main(){
	while(std::cin >> R >> n, R){
		std::vector<UFO> uv;
		for(int i=0;i<n;i++){
			UFO u;
			std::cin >> u.p.x >> u.p.y >> u.r >> u.v;
			uv.push_back(u);
		}

		std::sort(uv.begin(), uv.end(), comp);

		int res = 0;//生き残ったUFO
		while(!uv.empty()){
			res += countUFO(uv);
			moveUFO(uv);
			res += countUFO(uv);
			shoot(uv);
		}

		std::cout << res << std::endl;
	}
}

C++: //45
#include<iostream>
#include<deque>
#include<cmath>
#include<complex>

using namespace std;

typedef complex<double> P;

int main(){
  for(int lr,n;cin>>lr>>n,lr|n;){
    int x[100],y[100],r[100],v[100];
    P p[100];
    for(int i=0;i<n;i++){
      cin>>x[i]>>y[i]>>r[i]>>v[i];
      p[i]=P(x[i],y[i]);
    }
    int nf=0;
    bool u[100]={};
    for(;;){
      int idx;
      double d=1<<30;
      for(int i=0;i<n;i++){
	if(!u[i]){
	  double ds=abs(p[i])-v[i];
	  p[i]=polar(ds,arg(p[i]));
	  if(ds<=lr){
	    nf++;
	    u[i]=true;
	  }else if(ds<d){
	    d=ds;
	    idx=i;
	  }
	}
      }
      if(d==1<<30)break;
      for(int i=0;i<n;i++){
	double ad=arg(p[i])-arg(p[idx]);
	u[i]|=cos(ad)>=0&&abs(p[i])*sin(fabs(ad))<=r[i]+1e-9;
      }
    }
    cout<<nf<<endl;
  }
  return 0;
}