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



struct Point {
  double x, y;
  Point(double x=0, double y=0) : x(x), y(y) {}
  Point operator + (Point p) { return Point(x + p.x, y + p.y); }
  Point operator - (Point p) { return Point(x - p.x, y - p.y); }
  Point operator * (double a) { return Point(x * a, y * a); }
  Point operator / (double a) { return Point(x / a, y / a); }
};
typedef Point Vector;
struct Segment {
  Point p1, p2;
};
typedef Segment Line;

double norm(Vector a) { return a.x*a.x + a.y*a.y; }
double abs(Vector a) { return sqrt(norm(a)); }
double dot(Vector a, Vector b) { return a.x*b.x + a.y*b.y; }
double cross(Vector a, Vector b) { return a.x*b.y - a.y*b.x; }
double getDistanceLP(Line s, Point p) {
  return fabs(cross(s.p2 - s.p1, p - s.p1))/abs(s.p2 - s.p1);
}

double getDistanceSP(Segment s, Point p) {
  if(dot(s.p2 - s.p1, p - s.p1) < 0.0) return abs(p - s.p1);
  if(dot(s.p1 - s.p2, p - s.p2) < 0.0) return abs(p - s.p2);
  return getDistanceLP(s, p);
}

const int N_MAX = 101;
struct Ufo {
  Point p;
  int r, v;
  double dist() const { return abs(p); }
  bool operator < (const Ufo &u) const {
    return dist() < u.dist();
  }
};
int R, N;
vector<Ufo> U;

void init() {
  U.clear();
}

int solve() {
  int ans = 0;
  while(!U.empty()) {
    for(vector<Ufo>::iterator it = U.begin(); it != U.end(); ) {
      double D = it->dist();
      it->p.x = it->p.x * (D - it->v)/D;
      it->p.y = it->p.y * (D - it->v)/D;
      if(D <= it->v || it->dist() <= R) {
	ans++;
	it = U.erase(it);
      } else {
	it++;
      }
    }
    sort(U.begin(), U.end());
    Segment s;
    s.p1 = Point(0, 0);
    s.p2 = U[0].p * 100000;
    U.erase(U.begin());
    for(vector<Ufo>::iterator it = U.begin(); it != U.end(); ) {
      if(getDistanceSP(s, it->p) <= it->r) {
	it = U.erase(it);
      } else {
	it++;
      }
    }
  }
  return ans;
}

main() {
  while((cin >> R >> N) && (R || N)) {
    init();
    for(int i = 0; i < N; i++) {
      Ufo u;
      int x, y;
      cin >> u.p.x >> u.p.y >> u.r >> u.v;
      U.push_back(u);
    }
    cout << solve() << endl;
  }
}

C++: #include <iostream>
#include <stdio.h>
#include <sstream>
#include <string>
#include <vector>
#include <map>
#include <queue>
#include <algorithm>
#include <set>
#include <math.h>
#include <utility>
#include <stack>
#include <string.h>
using namespace std;
typedef pair<int,int> P;
const int INF = 1<<29;
const double EPS = 1e-8;

struct ufo{
    int x,y,r,v;
    bool active;
};

double dist(ufo &a, int t){
    return sqrt(a.x*a.x+a.y*a.y) - a.v*t;
}

int main(){
    while(1){
        int R,N;
        scanf("%d %d",&R,&N);
        if(N==0)break;

        vector<ufo> enemys(N);
        for(int i=0;i<N;i++){
            int x,y,r,v;
            scanf("%d %d %d %d",&x,&y,&r,&v);
            enemys[i] = (ufo){x,y,r,v,true};
        }

        int count = 0, t = 1, ans = 0;
        while(count!=N){
            double min_d = 1500;
            int min_i = -1;
            for(int i=0;i<N;i++){
                if(!enemys[i].active) continue;
                double d = dist(enemys[i], t);
                if(d <= R+EPS){
                    //printf("goal %d at %d\n",i,t);
                    enemys[i].active = false;
                    ans++;
                    count++;
                    continue;
                }
                if(min_d>d){
                    min_d = d;
                    min_i = i;
                }
            }
            if(count==N) break;
            ufo min_e = enemys[min_i];
            double abs_i = sqrt(min_e.x*min_e.x + min_e.y*min_e.y);
            for(int i=0;i<N;i++){
                if(!enemys[i].active) continue;
                if(min_e.x*enemys[i].x > -EPS && min_e.y*enemys[i].y > -EPS){
                    double d = (min_e.x*enemys[i].y - min_e.y*enemys[i].x) / abs_i;
                    if(d <= enemys[i].r+EPS){
                        //printf("break %d at %d\n",i,t);
                        enemys[i].active = false;
                        count++;
                    }
                }
            }
            t++;
        }
        cout << ans << endl;
    }

    return 0;
}