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 <cmath>
#include <algorithm>
#include <vector>
using namespace std;

#define EPS 1e-9

struct ufo {
	double x, y;
	double r, v;

	ufo() {}
	ufo(double x_, double y_, double r_, double v_) {
		x = x_; y = y_; r = r_; v = v_;
	}

	bool operator<(const ufo & obj) const {
		return x*x + y*y < obj.x*obj.x + obj.y*obj.y;
	}

	bool operator==(const ufo & obj) const {
		return x==obj.x && y==obj.y && r==obj.r && v==obj.v;
	}
};

int main() {
	int N, R;

	while(cin >> R >> N, R || N) {
		vector<ufo> u;
		for(int i = 0; i < N; i++) {
			double x, y, r, v;
			cin >> x >> y >> r >> v;
			u.push_back(ufo(x,y,r,v));
		}

		int ret = 0;
		int count = 0;
		while(!u.empty()) {
			for(int i = 0; i < u.size(); i++) {
				double x, y;
				x = u[i].x; y = u[i].y;
				x -= u[i].v * cos(atan2(u[i].y, u[i].x));
				y -= u[i].v * sin(atan2(u[i].y, u[i].x));
				u[i].x = x; u[i].y = y;
			}

			sort(u.begin(), u.end());
			ufo aim(0,0,0,0);
			for(int i = 0; i < u.size(); i++) {
				if(u[i].x*u[i].x + u[i].y*u[i].y < R*R + EPS) {
					u.erase(u.begin() + i);
					i--;
					ret++;
				}
				else {
					if(aim == ufo(0,0,0,0)) {
						aim = u[i];
						u.erase(u.begin() + i);
						i--;
					}
					else {
						double theta = (atan2(aim.y, aim.x)- atan2(u[i].y, u[i].x));
						double d0, d1, d2;
						theta = abs(theta);
						d0 = sqrt(u[i].x*u[i].x + u[i].y*u[i].y);
						d1 = d0 * cos(theta);
						d2 = d0 * sin(theta);

						if(d2 < u[i].r + EPS && d1 > 0) {
							double d3;
							d3 = sqrt(u[i].r*u[i].r - d2*d2);

							//if(d1 + d3 > R) {
								u.erase(u.begin() + i);
								i--;
							//}
						}
					}
				}
			}
		}

		cout << ret << endl;
	}
}

C++: #include <iostream>
#include <complex>
#include <vector>
#include <algorithm>
#include <utility>
#include <cmath>
using namespace std;
typedef complex<double> P;
typedef pair<P, P> L;
typedef pair<P, double> C;
#define X real()
#define Y imag()
const double INF = 1e9;
const double EPS = 1e-10;

double dot(P a, P b){return a.X*b.X + a.Y*b.Y;}

double cross(P a, P b){return a.X*b.Y - a.Y*b.X;}

int ccw(P a, P b, P c){
  b -= a;
  c -= a;
  if(cross(b, c) > EPS) return 1;
  if(cross(b, c) < -EPS) return -1;
  if(dot(b, c) < -EPS) return -2;
  if(norm(c) > norm(b) + EPS) return 2;
  return 0;
}

P projection(P a, P b){
  return dot(a, b)/norm(b)*b;
}

bool is_attacked(C ufo, P d, int R){
  //return (abs(ufo.first - d*(double)R) < ufo.second + EPS) || (dot(ufo.first, d) > EPS && abs(projection(ufo.first, d)) > R - EPS && abs(cross(ufo.first, d)) < ufo.second + EPS);
  P D = d*(double)R, p = ufo.first - D;
  double dist;
  if(dot(p, D) > EPS) dist = abs(cross(ufo.first, d));
  else dist = abs(p);
  return dist < ufo.second + EPS;
}

int main(){
  int R, N;
  while(cin >> R >> N){
    if(R == 0 && N == 0) break;
    vector<C> UFO(N);
    vector<int> V(N);
    for(int i = 0; i < N; ++i){
      double x, y, r;
      cin >> x >> y >> r >> V[i];
      UFO[i] = C(P(x, y), r);
    }
    int c = 0, ans = 0, t = 0;
    vector<bool> U(N, false);
    while(c < N){
      ++t;
      double closest = INF;
      int id = -1;
      for(int i = 0; i < N; ++i){
        if(U[i]) continue;
        if(abs(UFO[i].first) - t*V[i] < closest){
          if(abs(UFO[i].first) - t*V[i] <= R + EPS){
            ++c;
            ++ans;
            U[i] = true;
          }else{
            closest = abs(UFO[i].first) - t*V[i];
            id = i;
          }
        }
      }
      if(id < 0) continue;
      P d = UFO[id].first;
      d /= abs(d);
      U[id] = true;
      ++c;
      for(int i = 0; i < N; ++i){
        if(U[i]) continue;
        C ufo;
        P p = UFO[i].first;
        ufo.first = (abs(p) - t*V[i])/abs(p)*p;
        ufo.second = UFO[i].second;
        if(is_attacked(UFO[i], d, R)){
          U[i] = true;
          ++c;
        }
      }
    }
    cout << ans << endl;
  }
  return 0;
}