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<complex>
#include<vector>
#include<cmath>
#define EPS 1e-6
using namespace std;

typedef complex<double> P;

class ufo{
public:
  P u;
  double r,v;
  ufo(void){}
  ufo(double x,double y, double z,double w){u.real()=x;u.imag()=y;r=z;v=w;}
};

double dot(P a,P b){return a.real()*b.real()+a.imag()*b.imag();}

double cross(P a,P b){return a.real()*b.imag()-a.imag()*b.real();}

bool on_line(P a,P b,P c){return (abs(a-c)+abs(c-b)<abs(a-b)+EPS);}

bool cross_l_c(P a,P b,ufo c){
  double dis = abs(cross(b-a,c.u-a))/abs(b-a);
  if(dis>c.r+EPS)return false;
  //cout << "{" << c.u.real() << " " << c.u.imag() << "}" << endl; 
  P n = b*P(0,1) + c.u;
  P u = b/abs(b);
  P cp = a + (b-a)*cross(n-c.u,c.u-a) / cross(n-c.u,b-a);
  //cout << "[" << cp.real() << " " << cp.imag() << "]" << endl;
  double len = sqrt(c.r*c.r-dis*dis);
  P p1 = cp+len*u,p2 = cp-len*u;
  /*
  cout << "[" << p1.real() << " " << p1.imag() << "]" << endl;
  cout << "[" << p2.real() << " " << p2.imag() << "]" << endl;
  cout << on_line(a,b,p1) << on_line(a,b,p2) << endl;
  */
  return (on_line(a,b,p1) || on_line(a,b,p2));
}

int main(){
  int n,R;
  double x,y,r,v;

  for(;;){
    cin >> R >> n;
    if(!R && !n)break;

    vector<ufo> ob;
    for(int i=0;i<n;i++){
      cin >> x >> y >> r >>v;
      ob.push_back(ufo(x,y,r,v));
    }

    int ans = 0;
    while(ob.size()){
      P m(10000,10000);
      for(int i=0;i<(int)ob.size();i++){
	P tmp = ob[i].u;
	ob[i].u.real() -= ob[i].v*dot(P(1,0),tmp)/abs(tmp);
	ob[i].u.imag() -= ob[i].v*cross(P(1,0),tmp)/abs(tmp);
      }
      //for(int i=0;i<(int)ob.size();i++)cout << ob[i].u.real() << " " << ob[i].u.imag() << endl;
      for(int i=0;i<(int)ob.size();i++){
	if(abs(ob[i].u) < R+EPS){
	  ans++;
	  ob.erase(ob.begin()+i--);
	}else if(abs(ob[i].u)<abs(m)+EPS)m = ob[i].u;
      }
      //cout << ob.size() << " " << m.real() << " " << m.imag() << endl;
      //cout << ob.size() << endl;
      m.real()*=1000;
      m.imag()*=1000;
      for(int i=0;i<(int)ob.size();i++){
	if(cross_l_c(P(0,0),m,ob[i]))ob.erase(ob.begin()+i--);
      }
      //cout << ob.size() << endl;
    }
    cout << ans << endl;
  }
}

C++: #include <iostream>
#include <sstream>
#include <string>
#include <algorithm>
#include <vector>
#include <iomanip>
#include <queue>
#include <cmath>
#include <set>
#include <map>
#include <cstdlib>
#include <cstdio>
using namespace std;

const double EPS = 1e-9;
const double M_PI = 3.1415926535897932384626433832795;

class UFO{
public:
	double x;
	double y;
	int r;
	double vx;
	double vy;
	bool dead;
	bool invalid;
};

double dist_sq(UFO u){
	return (u.x*u.x+u.y*u.y);
}

double Cross(UFO a, UFO b){
	return a.x*b.y-b.x*a.y;
}

int main(){
	int R, N;
	while(cin >> R >> N, N){
		vector<UFO> ufo(N);

		for(int i = 0; i < N; i++){
			int v;
			cin >> ufo[i].x >> ufo[i].y >> ufo[i].r >> v;
			double theta = atan2(ufo[i].y, ufo[i].x)-M_PI;
			ufo[i].vx = v*cos(theta);
			ufo[i].vy = v*sin(theta);
		}

		while(true){
			double min = R*R;
			int target = -1;
			for(int i = 0; i < N; i++){
				if(!ufo[i].dead && !ufo[i].invalid){
					// 位置更新
					double p = ufo[i].x;
					ufo[i].x += ufo[i].vx;
					ufo[i].y += ufo[i].vy;
					if(p*ufo[i].x < 0 || min >= dist_sq(ufo[i])){
						ufo[i].invalid = true;
					}else{
						// ターゲット選定
						if(target == -1){
							target = i;
						}
						else if(dist_sq(ufo[i]) < dist_sq(ufo[target])){
							target = i;
						}
					}
				}
			}

			// 続行判定
			if(target == -1){
				break;
			}

			// レーザー判定
			ufo[target].dead = true;
			for(int i = 0; i < N; i++){
				if(!ufo[i].dead && !ufo[i].invalid){
					double cr = Cross(ufo[target], ufo[i]);
					if(cr*cr/dist_sq(ufo[target]) <= ufo[i].r*ufo[i].r){
						ufo[i].dead = true;
					}
				}
			}
			
		}

		int count = 0;
		for(int i = 0; i < N; i++){
			if(ufo[i].invalid){
				count++;
			}
		}
		cout << count << endl;
	}
	return 0;
}