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 <vector>
#include <algorithm>
#include <complex>
#include <cmath>

using namespace std;

typedef complex<double> P;
const double PI = acos(-1);
const double EPS = 1e-9;

int cmp(double a, double b) {
    const double d = a-b;
    if(abs(d) < EPS) return 0;
    else if(d < 0) return -1;
    return 1;
}

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

struct line/*{{{*/
{
  P a, b;
  line() {}
  line(const P& p, const P& q) : a(p), b(q) {}

  // AOJ 1171 Laser Beam Reflections
  inline P perpendicular(const P& p) const
  {
    // 点 p から直線上に下ろした垂線の足
    const double t = dot(p-a, a-b) / dot(b-a, b-a);
    return a + t*(a-b);
  }

  inline double distance(const P& p) const {
      return abs(p - this->perpendicular(p));
  }
};/*}}}*/

struct circle/*{{{*/
{
  P o;
  double r;
  circle() {}
  circle(const P& p, double x) : o(p), r(x) {}

  inline bool intersects(const line& ln) const
  {
    return abs(ln.distance(o)) <= r;
  }

  pair<P,P> intersection(const line& ln) const
  {
    // assert(intersects(ln))
    const P h = ln.perpendicular(o);
    const double d = abs(h - o);
    P ab = ln.b - ln.a;
    ab /= abs(ab);
    const double l = sqrt(r*r - d*d);
    return make_pair(h + l*ab, h - l*ab);
  }
};/*}}}*/

struct UFO {
    P pos, dv;
    double r;

    UFO() {}
    UFO(const P &p, double r, double v) : pos(p), r(r) {
        dv = pos * v / abs(pos);
    }

    void move() {
        if(cmp(abs(dv), abs(pos)) >= 0) {
            pos = P(0, 0);
        } else {
            pos -= dv;
        }
    }
};

bool check(const P &p, const P &dir, double R) {
    if(dot(p, dir) < 0) return false;
    return cmp(abs(p), R) > 0;
}

bool solve() {
    int R, N;
    cin >> R >> N;
    if(!R && !N) return false;

    vector<UFO> ufos;
    for(int i = 0; i < N; ++i) {
        double x, y, r, v;
        cin >> x >> y >> r >> v;
        ufos.push_back(UFO(P(x, y), r, v));
    }
    int ans = 0;
    while(true) {
        const int M = ufos.size();
        double min_dist = 1e10;
        int min_idx = -1;
        for(int i = 0; i < M; ++i) {
            UFO &u = ufos[i];
            u.move();
            const double d = abs(u.pos);
            if(cmp(d, R) > 0 && d < min_dist) {
                min_dist = d;
                min_idx = i;
            }
        }
        if(min_idx == -1) break;
        //cout << ufos[min_idx].pos << endl;
        const line l(P(0, 0), ufos[min_idx].pos);
        const double angle = arg(l.b);
        auto pend = remove_if(ufos.begin(), ufos.end(), [&](const UFO &u) {
                const circle c(u.pos, u.r);
                if(!c.intersects(l)) return false;
                const auto tmp = c.intersection(l);
                return check(tmp.first, l.b, R) || check(tmp.second, l.b, R);
                });
        //cout << distance(pend, ufos.end()) << endl;
        ufos.erase(pend, ufos.end());
    }
    cout << ufos.size() << endl;
    return true;
}

int main() {
    cin.tie(0);
    ios::sync_with_stdio(0);

    while(solve()) ;
    return 0;
}