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 <stdio.h>
#include <math.h>

#define PI 3.1415926

struct ufo_t
{
	float x,y,r,v;
	int life;
};

inline float ufo_dist(ufo_t *ufo)
{
	return sqrt(ufo->x * ufo->x + ufo->y * ufo->y);
}

bool is_ufo_left(ufo_t *ufo,int n,float r)
{
	for(int i=0; i<n; i++)
	{
		if(ufo[i].life && ufo_dist(&ufo[i]) >= r) return true;
	}
	return false;
}

void ufo_move(ufo_t *ufo,int n,float r)
{
	for(int i=0; i<n; i++)
	{
		float dist = ufo_dist(&ufo[i]);
		if(dist <= r) continue;
		
		if(dist < ufo[i].v)
		{
			ufo[i].x = 0.0;
			ufo[i].y = 0.0;
		}
		else
		{
			ufo[i].x -= ufo[i].v * ufo[i].x / dist;
			ufo[i].y -= ufo[i].v * ufo[i].y / dist;
		}
	}
}

ufo_t * get_nearest_ufo(ufo_t *ufo,int n,float r)
{
	ufo_t *min = NULL;
	for(int j=0; j<n; j++)
	{
		if(ufo_dist(&ufo[j]) >= r && ufo[j].life)
		{
			min = &ufo[j];
			for(int i=j+1; i<n; i++)
			{
				if(ufo[i].life && ufo_dist(min) > ufo_dist(&ufo[i]) && ufo_dist(&ufo[i]) >= r) min = &ufo[i];
			}
			break;
		}
	}
	return min;
}

int count_intruders(ufo_t *ufo,int n,float r)
{
	int count = 0;
	for(int i=0; i<n; i++)
	{
		if(ufo_dist(&ufo[i]) < r) count++;
	}
	return count;
}

float ang_diff(float a,float b)
{
	float d = fmod(fabs(a-b),PI * 2.0);
	if(d > PI) d = PI * 2.0 - d;
	return d;
}

int main(void)
{
	while(1)
	{
		float critical_range;
		int ufo_num;
		
		scanf("%d %d",&critical_range,&ufo_num);
		
		if(ufo_num <= 0) break;
		
		ufo_t *ufo = new ufo_t[ufo_num];
		
		for(int i=0; i<ufo_num; i++)
		{
			scanf("%f %f %f %f",&(ufo[i].x),&(ufo[i].y),&(ufo[i].r),&(ufo[i].v));
			ufo[i].life = 1;
		}
		
		while(is_ufo_left(ufo,ufo_num,critical_range))
		{
			ufo_move(ufo,ufo_num,critical_range);
			
			ufo_t *target = get_nearest_ufo(ufo,ufo_num,critical_range);
			
			if(target == NULL) break;
			
			float target_angle = atan2(target->y,target->x);
			
			printf("----------------\n");
			
			for(int i=0; i<ufo_num; i++)
			{
				if(ufo[i].life) printf("%d %f %f %f %f\n",i,ufo[i].x,ufo[i].y);
				
				float angle = atan2(ufo[i].y,ufo[i].x);
				
				if(ufo[i].r > ufo_dist(&ufo[i]))
				{
					ufo[i].v = 0.0;
					ufo[i].life = 0;
				}
				else
				{
					float ufo_s = asin(ufo[i].r / ufo_dist(&ufo[i]));
					if(ang_diff(target_angle,angle) <= ufo_s)
					{
						ufo[i].v = 0.0;
						ufo[i].life = 0;
					}
				}
				//if(ang_diff(target_angle,angle) > 1.0) continue;
				
				//float laser_dist = fabs(a * ufo[i].x + b * ufo[i].y) / sqrt(a * a + b * b);
				
				/*if(laser_dist <= ufo[i].r)
				{
					ufo[i].life = 0;
					ufo[i].v = 0.0;
				}*/
			}
		}
		
		printf("%d\n",count_intruders(ufo,ufo_num,critical_range));
		
		delete[] ufo;
	}
	
	return 0;
}