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 <sstream>
#include <iomanip>
#include <algorithm>
#include <cmath>
#include <string>
#include <vector>
#include <list>
#include <queue>
#include <stack>
#include <set>
#include <map>
#include <bitset>
#include <numeric>
#include <climits>
#include <cfloat>
using namespace std;

const double EPS = 1.0e-10;

class Point
{
public:
    double y, x;
    Point(){
        y = x = 0.0;
    }
    Point(double y0, double x0){
        y = y0;
        x = x0;
    }
    Point operator+(const Point& p) const{
        return Point(y + p.y, x + p.x);
    }
    Point operator-(const Point& p) const{
        return Point(y - p.y, x - p.x);
    }
    Point operator*(double a) const{
        return Point(y * a, x * a);
    }
    Point operator/(double a) const{
        return Point(y / a, x / a);
    }
    double length() const{
        return sqrt(y * y + x * x);
    }
    double dist(const Point& p) const{
        return sqrt(pow(y - p.y, 2) + pow(x - p.x, 2));
    }
    double dot(const Point& p) const{
        return y * p.y + x * p.x; // |a|*|b|*cosÆ
    }
    double cross(const Point& p) const{
        return x * p.y - y * p.x; // |a|*|b|*sinÆ
    }
};

class Line
{
public:
    double a, b, c; // a*x + b*y + c = 0
    Line(){
        a = c = 0.0;
        b = 1.0;
    }
    Line(double a0, double b0, double c0){
        a = a0;
        b = b0;
        c = c0;
    }
    Line(const Point& p1, const Point& p2){ // 2_ðÔ¼ü
        double dy = p2.y - p1.y;
        double dx = p2.x - p1.x;
        if(abs(dy / dx) < EPS){
            a = 0.0;
            b = 1.0;
            c = -p1.y;
        }else if(abs(dx / dy) < EPS){
            a = 1.0;
            b = 0.0;
            c = -p1.x;
        }else{
            a = - dy / dx;
            b = 1.0;
            c = dy / dx * p1.x - p1.y;
        }
    }
};

int circleLineIntersection(const Point& p, double r, const Line& l, vector<Point>& intersection)
{
    double s = l.a * p.x + l.b * p.y + l.c;
    double t = (l.a*l.a + l.b*l.b) * r*r - s*s;

    if(t < -EPS){
        intersection.resize(0);
        return 0;
    }
    if(t < EPS){
        intersection.assign(1, Point(l.b, l.a) * (-s / (l.a*l.a + l.b*l.b)) + p);
        return 1;
    }

    intersection.assign(2, Point(l.a, -l.b) * sqrt(t));
    intersection[1] = intersection[1] * -1;
    for(int i=0; i<2; ++i)
        intersection[i] = (intersection[i] - Point(l.b, l.a) * s) / (l.a*l.a + l.b*l.b) + p;
    return 2;
}

int main()
{
    for(;;){
        int d, n;
        cin >> d >> n;
        if(d == 0)
            return 0;

        vector<Point> p(n);
        vector<int> r(n), v(n);
        for(int i=0; i<n; ++i)
            cin >> p[i].x >> p[i].y >> r[i] >> v[i];

        vector<bool> check(n, false);
        int ret = 0;
        for(;;){
            for(int i=0; i<n; ++i){
                if(!check[i]){
                    if(p[i].length() - v[i] < d + EPS){
                        check[i] = true;
                        ++ ret;
                    }else{
                        p[i] = p[i] - p[i] / p[i].length() * v[i];
                    }
                }
            }

            int j = -1;
            double minDist = DBL_MAX;
            for(int i=0; i<n; ++i){
                if(!check[i] && p[i].length() < minDist){
                    minDist = p[i].length();
                    j = i;
                }
            }
            if(j == -1)
                break;

            Line line(Point(0,0), p[j]);
            for(int i=0; i<n; ++i){
                vector<Point> tmp;
                if(!check[i] && p[i].dot(p[j]) > 0 && circleLineIntersection(p[i], r[i], line, tmp) > 0)
                    check[i] = true;
            }
        }

        cout << ret << endl;
    }
}