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

double dist(double a, double b){ return sqrt(a*a + b*b);
}

struct UFO{
    double x;
    double y;
    double r;
    double v;
    double cos;
    double sin;
    int disabled;
    int signx;
    int signy;
    UFO(){}
    ~UFO(){}
    UFO(int a, int b, int c, int d){
        x = a;
        y = b;
        r = c;
        v = d;
        disabled = 0;
        signx = x;
        signy = y;
        cos = x / dist(x, y);
        sin = y / dist(x, y);
    }
    UFO(const UFO& z){
        x = z.x; y = z.y; r = z.r; v = z.v;
        disabled = z.disabled;
        signx = z.signx;
        signy = z.signy;
        cos = z.cos;
        sin = z.sin;
    }
    bool operator<(const UFO& z) const {
        if( disabled - z.disabled ) return disabled < z.disabled;
        if( dist(x, y)-dist(z.x, z.y) ) return dist(x, y) < dist(z.x, z.y);
        return r < z.r;
    }
    void step(){
        double t1, t2;
        t1 = x - v * cos;
        t2 = y - v * sin;
        if( t1 * signx <= 0 ){ x = 0; }
        else{ x = t1; }
        if( t2 * signy <= 0 ){ y = 0; }
        else{ y = t2; }
    }
};

typedef vector<UFO> VU;

int main(){
    int N;
    double R;
    for(;cin >> R >> N, R||N;){
        VU u;
        for(int i = 0; i < N; i++){
            double a, b, c, d;
            cin >> a >> b >> c >> d;
            u.push_back( UFO(a, b, c, d) );
        }
        int ans = 0, count = 0;
        while(true){
            for(int i = 0; i < u.size(); i++){
                if( u[i].disabled ) continue;
                u[i].step();
                if( dist(u[i].x, u[i].y) <= R ){
                    u[i].disabled = 1;
                    ans++;
                }
            }
            sort(u.begin(), u.end());
            if( u[0].disabled ) break;
            double a = -u[0].y, b = u[0].x;
            for(VU::iterator it = u.begin(); it != u.end(); it++){
                if( it->disabled ) continue;
                if( dist(it->x-u[0].x, it->y-u[0].y) <= it->r ){
                    it->disabled = 1;
                }
                if( u[0].x*it->x+u[0].y*it->y >= 0 &&
                    abs(a*it->x+b*it->y)/dist(a, b) <= it->r ){
                    it->disabled = 1;
                }
            }
            sort(u.begin(), u.end());
        }
        cout << ans << endl;
    }
    return 0;
}