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 <map>
#include <vector>
#include <algorithm>
#include <cmath>
#include <complex>

using namespace std;

const double INF = 10000.0;
const double EPS = 1e-8;

typedef complex<double> Point;

struct Segment{
  Point p1, p2;
};

typedef Segment Line;



Point point[100];
int R, N, r[100], v[100], rem;
bool lost[100];

double kabs(const double a){
  return a>=0 ? a : -a;
}

int getCrossPoint(Point& p1, Point& p2, const Line& li, double r, Point o = Point(0, 0)){
  double a = (li.p2.imag()-li.p1.imag())/(li.p2.real()-li.p1.real());
  double b = -1.0;
  double c = -a*li.p1.real()+li.p1.imag();
   
  c = a*o.real() + b*o.imag() + c;
 
  const double aabb = a*a + b*b;
  const double ac = a*c;
  const double bc = b*c;
  const double D1 = ac*ac - aabb * (c*c - b*b*r*r);
  const double D2 = bc*bc - aabb * (c*c - a*a*r*r);
 
  if(D1 < 0 || D2 < 0) return 0;
 
  int ret;
 
  if(D1 == 0 && D2 == 0) ret = 1;
  else ret = 2;
   
  if(kabs(b) >= kabs(a)){      
    p1.real() = (-ac + sqrt(D1)) / aabb;
    p1.imag() = -(a*p1.real() + c) / b;
    p2.real() = (-ac - sqrt(D1)) / aabb;
    p2.imag() = -(a*p2.real() + c) / b;
  }else{
    p1.imag() = (-bc + sqrt(D2)) / aabb;
    p1.real() = -(b*p1.imag() + c) / a;
    p2.imag() = (-bc - sqrt(D2)) / aabb;
    p2.real() = -(b*p2.imag() + c) / a;
  }
   
  p1.real() += o.real();  p1.imag() += o.imag();
  p2.real() += o.real();  p2.imag() += o.imag();
   
  return ret;
}


double dist(Point a, Point b = Point(0, 0)){
  return abs(a-b);
}

double dist(int time, int n){
  return dist(point[n])-v[n]*time;
}

void shoot(int n){
  Point p1, p2;
  Line li = {Point(0, 0), point[n]};
  for(int i=0;i<N;i++){
    if(lost[i]) continue;
    int num = getCrossPoint(p1, p2, li, R);
    if(num >= 1){
      if(abs(p1-Point(0, 0)) > EPS+R){
        lost[i] = true;
        --rem;
        continue;
      }
      if(num == 2){
        if(abs(p2-Point(0, 0)) > EPS+R){
          lost[i] = true;
          --rem;
        }
      }
    }
  }
}

int solve(){
  int res = 0;
  rem = N;
  fill(lost, lost+N, false);
  for(int t=0;rem>0;t++){
    double valm = INF;
    int idx;
    for(int i=0;i<N;i++){
      if(lost[i]) continue;
      double tmp = dist(t, i);
      if(tmp < R+EPS){
        lost[i] = true;
        ++res;
        --rem;
        continue;
      }
      if(valm > tmp){
        idx = i;
        valm = tmp;
      }
    }
    shoot(idx);
    lost[idx] = true;
    --rem;
  }
  return res;
}

main(){
  while(cin >> R >> N && (R|N)){
    for(int i=0;i<N;++i){
      cin >> point[i].real() >> point[i].imag() >> r[i] >> v[i];
    }
    cout << solve() << endl;
  }
  return 0;
}