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++: /**************** Geometrical Library ****************/

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

#define	EPS	1e-9

enum {CCW=1,CW=-1,ON=0};

#define	pb	push_back

using namespace std;

class Point{
public:
	double x,y;
	Point(){}
	Point(double xx,double yy):x(xx),y(yy){}
};

class Line:public vector<Point>{
public:
	Line(){}
	Line(const Point &a,const Point &b){
		pb(a),pb(b);
	}
};

class Segment:public Line{
public:
	Segment(){}
	Segment(const Point &a,const Point &b):Line(a,b){}
};

class Circle{
public:
	Point c;
	double r;
	Circle(){}
	Circle(const Point &cc,double rr):c(cc),r(rr){}
};

Point &operator +=(Point &a,const Point &b){
	a.x+=b.x,a.y+=b.y;
	return a;
}

Point &operator -=(Point &a,const Point &b){
	a.x-=b.x,a.y-=b.y;
	return a;
}

Point &operator *=(Point &a,double c){
	a.x*=c,a.y*=c;
	return a;
}

Point &operator /=(Point &a,double c){
	a.x/=c,a.y/=c;
	return a;
}

Point operator +(const Point &a,const Point &b){
	Point c=a;
	return c+=b;
}

Point operator -(const Point &a,const Point &b){
	Point c=a;
	return c-=b;
}

Point operator *(double c,const Point &a){
	Point b=a;
	return b*=c;
}

Point operator /(const Point &a,double c){
	Point b=a;
	return b/=c;
}

bool operator <(const Point &a,const Point &b){
	return (a.x==b.x)?(a.y<b.y):(a.x<b.x);
}

bool operator >(const Point &a,const Point &b){
	return b<a;
}

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

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

double norm2(const Point &a){
	return dot(a,a);
}

int ccw(const Point &a,Point b,Point c){
	b-=a,c-=a;
	double rotdir=cross(b,c);
	if(rotdir>EPS)		return CCW;
	if(rotdir<-EPS)		return CW;
	return ON;
}

inline void calc_abc(const Line &l,double &a,double &b,double &c){	// l : ax+by+c=0
	a=l[0].y-l[1].y;
	b=l[1].x-l[0].x;
	c=l[0].x*l[1].y-l[1].x*l[0].y;
}

Point perp_foot(const Point &p,const Line &l){
	double a,b,c;
	calc_abc(l,a,b,c);
	return p-(a*p.x+b*p.y+c)/(a*a+b*b)*Point(a,b);
}

int intersect(const Circle &c,const Line &l,Point *p=NULL,Point *q=NULL){
	Point m=perp_foot(c.c,l);
	double d2=norm2(c.c-m);
	if(c.r*c.r+EPS<d2)	return 0;
	else if(abs(c.r*c.r-d2)<EPS){
		if(p&&q)	*p=*q=m;
		return 1;
	}
	else{
		if(p&&q){
			Point v;
			double n0=norm2(l[0]-m),n1=norm2(l[1]-m);
			if(n0<n1)	v=l[1]-m,n0=n1;
			else		v=l[0]-m;
			v*=sqrt((c.r*c.r-d2)/n0);
			*p=m+v,*q=m-v;
		}
		return 2;
	}
}

int intersect(const Circle &c,const Segment &s,Point *p=NULL,Point *q=NULL){
	Point pp,qq;
	int n=intersect(c,Line(s[0],s[1]),&pp,&qq);
	if(n==0)	return 0;
	else if(n==1){
		if(dot(pp-s[0],pp-s[1])<EPS){
			if(p&&q)	*p=*q=pp;
			return 1;
		}
		return 0;
	}
	else{
		bool bp=(dot(pp-s[0],pp-s[1])<EPS);
		bool bq=(dot(qq-s[0],qq-s[1])<EPS);
		if(bp&&bq){
			if(p&&q)	*p=pp,*q=qq;
			return 2;
		}
		if(bp||bq){
			if(p&&q)	*p=(bp?pp:qq);
			return 1;
		}
		return 0;
	}
}

/**************** Library END ****************/

#include<cstdio>

using namespace std;

int main(){
	for(int R,n;scanf("%d%d",&R,&n),R;){
		static int v[500];
		static Circle ufo[500];
		static bool checked[500];
		for(int i=0;i<n;i++){
			scanf("%lf%lf%lf%d",&ufo[i].c.x,&ufo[i].c.y,&ufo[i].r,v+i);
			checked[i]=false;
		}

		int cnt=0,cnt_chk=0;
		for(int t=1;cnt_chk<n;t++){
			int target=-1;
			double dmin=1e30;
			// lock on & neighborhood test
			for(int i=0;i<n;i++){
				if(checked[i])	continue;
				double d=sqrt(norm2(ufo[i].c))-v[i]*t;
				if(d<R+EPS){	// ufo is in the neighborhood
					checked[i]=true;
					cnt_chk++;
					cnt++;
				}
				else{
					if(d<dmin){
						target=i;
						dmin=d;
					}
				}
			}

			// laser
			if(~target){
				Point unit=ufo[target].c/sqrt(norm2(ufo[target].c));
				Point ufopos=ufo[target].c-v[target]*t*unit;
				Segment laser(R*unit,1e9*ufopos);	// harf line
				for(int i=0;i<n;i++){
					if(checked[i])	continue;
					ufopos=ufo[i].c;
					ufopos-=v[i]*t*ufopos/sqrt(norm2(ufopos));
					Circle moved(ufopos,ufo[i].r);
					if(intersect(moved,laser)){
						checked[i]=true;
						cnt_chk++;
					}
				}
			}
		}

		printf("%d\n",cnt);
	}

	return 0;
}