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<cstdio>
#include<cstring>
#include<cmath>
#include<complex>

using namespace std;
typedef complex<double> P;
const double PI = acos(-1.0);
const double EPS = 1e-10;

inline double dot(P a, P b) {return real( conj(a)*b);}
inline double cross(P a, P b) {return imag( conj(a)*b);}
inline double sq(double x) {return x * x;}

#define REP(i,n) for(int i=0;i<(int)(n);++i)

struct C : public P {
  double r;
  C() {}
  C(const P &p,double r):P(p),r(r){}
};

struct UFO {
  C c;
  int v;
  bool alive;

  void move() {
    P dif = c / abs(c) * (double)v;
    if (norm(dif) > norm(c)) dif = c;
    c -= dif;
  }
};

double DistanceSP(P a, P b, P c) {
  if ( dot(b-a, c-a) < EPS ) return abs(c-a); // c a--b
  if ( dot(a-b, c-b) < EPS ) return abs(c-b); // a--b c
  return abs(cross(b-a, c-a)) / abs(b-a);
}

int main() {
  for (int N, R; scanf("%d%d", &R, &N), (N || R); ) {
      vector<UFO> ufo;
      REP(i, N) {
          int x, y, r, v; scanf("%d%d%d%d",&x, &y, &r, &v);
          ufo.push_back( (UFO){ C(P(x, y), r), v, 1} );
      }

      for (;;) {
          REP(i, N) if (ufo[i].alive && norm(ufo[i].c) > R * R + EPS) ufo[i].move();
          int tget = -1;
          double best = 0;
          REP(i, N) {
              if (ufo[i].alive && norm(ufo[i].c) > R * R + EPS) {
                  if (tget == -1 || best > norm(ufo[i].c)) {
                      tget = i;
                      best = norm(ufo[i].c);
                  }

              }
          }
          if (tget == -1) break;

          P o(0, 0);
          P t = ufo[tget].c;
          t *= 1000000;

          REP(i, N) {
              if (ufo[i].alive && norm(ufo[i].c) > R * R + EPS) {
                  if (DistanceSP(o, t, ufo[i].c) <= ufo[i].c.r + EPS) {
                      ufo[i].alive = false;
                  }
              }
          }
      }
      int ans = 0;
      REP(i, N) if (ufo[i].alive) ++ans;
      cout << ans << endl;
  }
  return 0;
}

C++: //45
#include<iostream>
#include<deque>
#include<cmath>
#include<complex>

using namespace std;

typedef complex<double> P;

int main(){
  for(int lr,n;cin>>lr>>n,lr|n;){
    int x[100],y[100],r[100],v[100];
    P p[100];
    for(int i=0;i<n;i++){
      cin>>x[i]>>y[i]>>r[i]>>v[i];
      p[i]=P(x[i],y[i]);
    }
    int nf=0;
    bool u[100]={};
    for(;;){
      int idx;
      double d=1<<30;
      for(int i=0;i<n;i++){
	if(!u[i]){
	  double dp=abs(p[i])-v[i];
	  p[i]=polar(dp,arg(p[i]));
	  double ds=abs(p[i]);
	  if(dp<0||ds<=lr){
	    nf++;
	    u[i]=true;
	  }else if(ds<d){
	    d=ds;
	    idx=i;
	  }
	}
      }
      if(d==1<<30)break;
      for(int i=0;i<n;i++){
	u[i]|=abs(p[i])*sin(fabs(arg(p[i])-arg(p[idx])))<=r[i];
      }
    }
    cout<<nf<<endl;
  }
  return 0;
}