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 <math.h>

class UFO
{
  private:
	double	dist; 	/* ??????????????????????????§????????¢ */
	int		speed;	/* ??\????????? */
	double	rad; 	/* ?????\?§???? */
	int		r;		/* UFO????????? */
	bool	alive;
  public:
	UFO(int x, int y, int r,int v);
	bool	IsAlive();
	double	EchoDist();
	double	EchoRad();
	int		EchoSize();
	void	PastTime();
	void	Hit();
};
int UFOShootingDownOperation();

int main()
{
	while (0 == UFOShootingDownOperation());
	return 0;
}

UFO::UFO(int x, int y, int r,int v) : r(r), speed(v), alive(true)
{
	dist = sqrt(pow(x,2) + pow(y,2));
	rad = acos(x / dist);
	rad *= 180.0 / M_PI;
	if (y < 0) {
		rad = 360 - rad;
	}
}

bool UFO::IsAlive()
{
	return alive;
}

double	UFO::EchoDist()
{
	return dist;
}

double	UFO::EchoRad()
{
	return rad;
}

int	UFO::EchoSize()
{
	return r;
}

void UFO::PastTime()
{
	dist -= speed;
}

void UFO::Hit()
{
	alive = false;
}

int UFOShootingDownOperation()
{
	using namespace std;
	int		R;				/*??¬?????¶???????¨??????????????????????*/
	int		N;				/*UFO?????°*/
	int 	x0;				/* UFO?????????????????????????????? */
	int		y0;				/* UFO?????????????????????????????? */
	int		r;				/* UFO???????????????????????? */
	int		v;				/* UFO???????????????????????? */
	bool	existsTarget; 	/* ?????????UFO????????£????????????????????? */
	int		aliveUFO;		/* ???????????£???UFO??????????????? */
	double	difRad;			/* UFO?????????????§???¨??¬?????¶?????¨????§?????????????????´?(<=180) */
	vector<UFO>	aliens; 	/* UFO????????± */
	vector<UFO>::iterator itr;
	vector<UFO>::iterator target;
	
	cin >> R >> N;
	
	if (0 == R && 0 == N) {/* ???????????? */
		return -1;
	}
	
	/* ??\??? */
	for (int i = 0; N > i; ++i) {
		cin >> x0 >> y0 >> r >> v;
		aliens.push_back(UFO(x0, y0, r, v));
	}
	/* ????????????1????????????????????? */
	for (itr = aliens.begin(); aliens.end() != itr; ++itr) {
		itr->PastTime();
	}
	/* ???????????????????±?????????¬?????¶??????????°??????????????????? */
	existsTarget = true;
	while (existsTarget) {
		existsTarget = false;
		target = aliens.end();
		for (itr = aliens.begin(); aliens.end() != itr; ++itr) {
			if (false == itr->IsAlive()) {/* ??¬?????¶??????????????????UFO??????????????? */
				continue;
			}
			
			if (itr->EchoDist() > R) {
				if (aliens.end() == target) {
					target = itr;
				}
				else if (target->EchoDist() > itr->EchoDist()){
					target = itr;
				}
				existsTarget = true;
			}
		}
		/* ???????????? */
		for (itr = aliens.begin(); aliens.end() != itr; ++itr) {
			if (false == itr->IsAlive()) {/* ??¬?????¶??????????????????UFO??????????????? */
				continue;
			}
			
			difRad = fabs(target->EchoRad() - itr->EchoRad());
			if (difRad >180) {
				difRad = 360 - difRad;
			}
			if (difRad < 90) {
				if (itr->EchoDist() * sin(difRad * M_PI / 180.0) < itr->EchoSize()) {
					if (itr->EchoDist() > R) {
						itr->Hit();
					}
				}
			}
			else {
				if (itr->EchoDist() < itr->EchoSize()) {
					if (itr->EchoDist() > R) {
						itr->Hit();
					}
				}
			}
			
			/*???????????????*/
			itr->PastTime();
		}
	}
	
	aliveUFO = 0;
	for (itr = aliens.begin(); aliens.end() != itr; ++itr) {
		if (true == itr->IsAlive()) {
			++aliveUFO;
		}
	}
	cout << aliveUFO << endl;
	return 0;
}