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 <stack>
#include <tuple>
#include <functional>
#include <type_traits>
#include <cmath>
#include <algorithm>
constexpr long double pi = 3.14159265359;
template <typename F, typename Func>
auto map(Func func, const F &vec) -> std::vector<typename decltype(func(*vec.begin()))>{
	std::vector<decltype(func(*vec.begin()))> res(vec.size());
	int idx{ 0 };
	for (const auto &v : vec) {
		res[idx++] = func(v);
	}
	return res;
}
template <typename F, typename Func>
auto filter(Func func, const F &traversable)->std::vector<typename std::remove_reference<decltype(*traversable.begin())>::type> {
	std::vector<typename std::remove_reference<decltype(*traversable.begin())>::type> res;
	for (const auto &v : traversable) {
		if (func(v))
			res.push_back(v);
	}
	return res;
}
template<typename F, typename Func>
void inner_filter(Func func, std::vector<F> &traversable) {
	int idx{ 0 };
	for (unsigned int i = 0; i < traversable.size(); ++i) {
		if (func(traversable[i])) {
			traversable[idx++] = std::move(traversable[i]);
		}
	}
	traversable.resize(idx);
}
struct Point {
	long double x, y;
	 Point(long double ax, long double ay) :x{ ax }, y{ ay } {}
	 Point() {}
};
struct Angle {
	long double sin, cos;
	Angle(long double s, long double c) :sin{ (s > 1) ? 1 : (s < -1) ? -1 : s }, cos{ (c > 1) ? 1 : (c < -1) ? -1 : c } {};
	static  Angle to_angle(long double x, long double y);
	 Angle operator+(const Angle other) const;
	 Angle operator-(const Angle other) const;
	 long double to_radian() const;
};
struct Vector {
	long double x, y;
	long double length() const;
	 Angle angle() const;
	 Vector(const Point from, const Point to);
	 Vector(const long double ax, const long double ay) :x{ ax }, y{ ay } {}
	 Vector(const Point p) :x{ p.x }, y{ p.y } {}
	 Vector() {}
	 Point end_point() const;
};
struct UFO {
	Point center;
	long double radius, velocity;
	 UFO(long double x, long double y, long double r, long double v);
	 UFO() { };
	 Point position(int time) const;
	 Angle angle() const;
};

 Angle Angle::to_angle(long double x, long double y)
{
	return Angle(y / std::sqrt(x * x + y * y), x / std::sqrt(x * x + y * y));
}

 Angle Angle::operator+(const Angle other) const
{
	return Angle(sin * other.cos + cos * other.sin, cos * other.cos - sin * other.sin);
}

 Angle Angle::operator-(const Angle other) const
{
	return Angle(sin * other.cos - cos * other.sin, cos * other.cos + sin * other.sin);
}

 long double Angle::to_radian() const
 {
	 return (sin >= 0) ? std::acos(cos) : 2 * pi - std::acos(cos);
 }

long double Vector::length() const
{
	return std::sqrt(x * x + y * y);
}

 Angle Vector::angle() const
{
	return Angle::to_angle(x, y);
}

 Vector::Vector(const Point from, const Point to) :x{ to.x - from.x }, y{ to.y - from.y }
{
}
 Point Vector::end_point() const
 {
	 return Point(x, y);
 }
 Point operator+(const Point p, const Vector v) {
	 return Point{ p.x + v.x, p.y + v.y };
 }
 
 Point operator-(const Point p, const Vector v)
{
	return Point{ p.x - v.x, p.y - v.y };
}
 Vector operator*(const Vector v, const long double d) {
	 return Vector{ v.x * d, v.y * d };
 }
 Vector operator*(const Vector v, const int d)
{
	return Vector{ v.x * d, v.y * d };
}

 Vector operator*(const long double d, const Vector v) {
	 return Vector{ v.x * d, v.y * d };
 }
 Vector operator*(const int d, const Vector v)
{
	return Vector(d * v.x, d * v.y);
}

 UFO::UFO(long double x, long double y, long double r, long double v) :center{ x, y }, radius{ r }, velocity{ v }
{
}

 Point UFO::position(int time) const
 {
	 auto reach_time = Vector(center).length() / velocity;
	 if (reach_time <= time) return Point(0, 0);
	 return ((reach_time - time) / reach_time * Vector(center)).end_point();
 }

 Angle UFO::angle() const
 {
	 return Angle::to_angle(center.x, center.y);
 }

bool is_shooted(const UFO ufo, const Angle razer, int time) {
	auto ufo_pos = ufo.position(time);
	auto relative_razer = razer - ufo.angle();
	auto sin = ufo.radius / Vector(ufo_pos).length();
	auto projection_ufo = Angle(sin, std::sqrt(1 - sin * sin));
	return !(projection_ufo.to_radian() < relative_razer.to_radian() && relative_razer.to_radian() < Angle(-projection_ufo.sin, projection_ufo.cos).to_radian());
}
int solve(std::vector<UFO> &ufos, int rad, int time = 1) {
	if (ufos.size() == 0) return 0;
	auto ufo_count = ufos.size();
	inner_filter([time, rad](const UFO ufo) {return Vector(ufo.position(time)).length() >= rad; }, ufos);
	auto through = ufo_count - ufos.size();
	std::sort(ufos.begin(), ufos.end(), [time](const UFO a, const UFO b) {return Vector(a.position(time)).length() > Vector(b.position(time)).length(); });
	auto target = ufos.back();
	inner_filter([time, target](const UFO ufo) {return !is_shooted(ufo, target.angle(), time); }, ufos);
	return through + solve(ufos, rad, time + 1);
}
void f(int rad, int n) {
	if (n != 0 && rad != 0) {
		std::vector<UFO> ufos(n);
		{
			int x, y, r, v;
			for (auto &ufo : ufos) {
				std::cin >> x >> y >> r >> v;
				ufo = UFO(x, y, r, v);
			}
		}
		std::cout << solve(ufos, rad) << std::endl;
		std::cin >> rad >> n;
		f(rad, n);
	}
}
int main() {
	int r, n;
	std::cin >> r >> n;
	f(r, n);
}