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<cfloat>
#include<cmath>
#include<vector>
using namespace std;
#define EPS (1e-8)
#define equals(a, b) (fabs((a) - (b)) < EPS )
#define dle(a, b) (equals(a, b) || a < b )
static const double PI = acos(-1);
class Point{
public:
double x, y;
Point ( double x = 0, double y = 0): x(x), y(y){}
Point operator + ( Point p ){ return Point(x + p.x, y + p.y); }
Point operator - ( Point p ){ return Point(x - p.x, y - p.y); }
Point operator * ( double a ){ return Point(x*a, y*a); }
double abs() { return sqrt(norm());}
double norm() { return x*x + y*y; }
bool operator < ( const Point &p ) const {
return x != p.x ? x < p.x : y < p.y;
}
bool operator == ( const Point &p ) const {
return fabs(x-p.x) < EPS && fabs(y-p.y) < EPS;
}
};
typedef Point Vector;
class Segment{
public:
Point p1, p2;
Segment(Point s = Point(), Point t = Point()): p1(s), p2(t){}
};
typedef Segment Line;
class Circle{
public:
Point c;
double r;
Circle(Point c = Point(), double r = 0.0): c(c), r(r){}
};
typedef vector<Point> Polygon;
double norm( Vector a ){ return a.x*a.x + a.y*a.y; }
double abs( Vector a ){ return sqrt(norm(a)); }
Point polar( double a, double r ){ return Point(cos(r)*a, sin(r)*a);}
double getDistance( Vector a, Vector b ){ return abs(a - b); }
double dot( Vector a, Vector b ){ return a.x*b.x + a.y*b.y; }
double cross( Vector a, Vector b ){ return a.x*b.y - a.y*b.x; }
static const int COUNTER_CLOCKWISE = 1;
static const int CLOCKWISE = -1;
static const int ONLINE_BACK = 2;
static const int ONLINE_FRONT = -2;
static const int ON_SEGMENT = 0;
int ccw( Point p0, Point p1, Point p2 ){
Vector a = p1 - p0;
Vector b = p2 - p0;
if ( cross(a, b) > EPS ) return COUNTER_CLOCKWISE;
if ( cross(a, b) < -EPS ) return CLOCKWISE;
if ( dot(a, b) < -EPS ) return ONLINE_BACK;
if ( norm(a) < norm(b) ) return ONLINE_FRONT;
return ON_SEGMENT;
}
double arg(Vector p){
return atan2(p.y, p.x);
}
double getDistanceLP(Line s, Point p){
return abs(cross(s.p2 - s.p1, p - s.p1)/abs(s.p2 - s.p1));
}
bool isIntersect( Circle c1, Line l ){
double d = getDistanceLP(l, c1.c);
return ( equals(d, c1.r) || d < c1.r );
}
pair<Point, Point> getCrossPoints(Circle c1, Line l ){
double d = getDistanceLP(l, c1.c);
Point v = l.p2 - l.p1;
if ( ccw(l.p1, l.p2, c1.c) == COUNTER_CLOCKWISE ){
v = polar(abs(v), arg(v)-acos(-1)/2);
} else {
v = polar(abs(v), arg(v)+acos(-1)/2);
}
double th = acos(d/c1.r);
Point v1 = polar(c1.r, arg(v) + th );
Point v2 = polar(c1.r, arg(v) - th );
return make_pair(c1.c+v1, c1.c+v2);
}
#define NON 0
#define IN 1
#define OUT 2
double R;
class UFO{
public:
Circle body;
double v, dx, dy;
int state;
UFO( Circle c = Circle(Point(0,0),0), double v=0):body(c), v(v){
Point ct = Point(0, 0);
Vector a = ct - body.c;
dx = v*cos(arg(a));
dy = v*sin(arg(a));
state = NON;
}
void move(){
if ( state != NON ) return;
double pred = getDistance(Point(0, 0), body.c);
//if ( v > pred || equals(v, pred)){ state = IN; return; }
body.c.x += dx;
body.c.y += dy;
double d = getDistance(Point(0, 0), body.c);
if ( R > d || equals(R, d) ) state = IN;
}
};
#define MAX 100
UFO U[MAX];
int n;
void attack( Point p1, Point p2){
Line l = Line(p1, p2);
for ( int i = 0; i < n; i++ ){
if ( U[i].state != NON ) continue;
if ( !isIntersect(U[i].body, l) ) continue;
pair<Point, Point> pp = getCrossPoints(U[i].body, l);
 if ( ccw(p1,p2,pp.first)==ONLINE_FRONT || ccw(p1,p2,pp.first)==ON_SEGMENT) {
U[i].state = OUT;
}
if ( ccw(p1,p2,pp.second)==ONLINE_FRONT || ccw(p1,p2,pp.second)==ON_SEGMENT) {
U[i].state = OUT;
}
}
}
int simulate(){
while(1){
int life = 0;
for ( int i = 0; i < n; i++ ) {
U[i].move();
if ( U[i].state == NON ) life++;
}
if ( life == 0 ) break;
int target = -1;
double md = 1000000;
for ( int i = 0; i < n; i++ ){
if ( U[i].state != NON ) continue;
double d = getDistance(Point(0, 0), U[i].body.c);
if ( d < md ){
md = d;
target = i;
}
}
 attack(U[target].body.c*(R/abs(U[target].body.c)), U[target].body.c);
}
int cnt = 0;
for ( int i = 0; i < n; i++ ) if ( U[i].state == IN ) cnt++;
return cnt;
}
main(){
double x, y, r, v;
while( cin >> R && R ){
cin >> n;
for ( int i = 0; i < n; i++ ){
cin >> x >> y >> r >> v;
U[i] = UFO(Circle(Point(x, y), r), v);
}
cout << simulate() << endl;
}
}