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>

#define PI 3.141592653589793

using namespace std;

struct tagUFO{
	tagUFO*pBefore;
	tagUFO*pNext;
	double x;//??§?¨?x
	double y;//??§?¨?y
	int r;//UFO?????????
	int v;//UFO?????????(??????)
	double Distance;
};

void AddUFO(tagUFO*p);
tagUFO*DeleteUFO(tagUFO*pDelete);
int ShotUFO(tagUFO*pAimedUFO, tagUFO*pShotUFO, int R);

tagUFO*pFirst = NULL;
tagUFO*pLast = NULL;

int main() {
	while (true) {
		int R;//??¬?????¶???????¨???????????????????????????????
		int N;//UFO?????°
		tagUFO*p;
		int InvadingUFO = 0;

		cin >> R >> N;
		if (R == 0 && N == 0)break;//0 0?????\?????????????????????

		for (int i = 0; i < N; i++) {
			p = new tagUFO;
			cin >> p->x >> p->y >> p->r >> p->v;
			p->Distance = sqrt(p->x*p->x + p->y*p->y);
			//??????????????§??????R??????UFO?????????
			if (p->Distance < R) {
				InvadingUFO++;
				delete p;
			}
			else
				AddUFO(p);
		}

		p = pFirst;

		while (p!=NULL) {
			//UFO?????§?¨????1???????????´??°
			while (p != NULL) {
				p->x -= p->x*p->v / p->Distance;
				p->y -= p->y*p->v / p->Distance;
				p->Distance = sqrt(p->x*p->x + p->y*p->y);

				p = p->pNext;
			}

			//??????R??????UFO?????????
			p = pFirst;
			while (p != NULL) {
				if (p->Distance < R) {
					InvadingUFO++;
					p = DeleteUFO(p);
				}
				else
					p = p->pNext;
			}

			//UFO???????¢?
			p = pFirst;
			double Nearest = p->Distance;
			p = p->pNext;
			while (p != NULL) {
				if (p->Distance < Nearest)
					Nearest = p->Distance;

				p = p->pNext;
			}
			p = pFirst;
			while (p != NULL) {
				if (p->Distance == Nearest) {
					tagUFO tmp = *p;
					p = pFirst;
					while (p != 0) {
						if (ShotUFO(&tmp, p, R)) {
							p = DeleteUFO(p);
						}
						else {
							p = p->pNext;
						}
					}
					break;
				}
				p = p->pNext;
			}
			p = pFirst;
		}
		tagUFO*pNext = pFirst;
		while (pNext) {
			p = pNext;
			pNext = p->pNext;
			delete p;
		}
		pFirst = pLast = NULL;

		//??????????????????R???????????\??????UFO?????°?????????
		cout << InvadingUFO << endl;
	}

	return 0;
}

void AddUFO(tagUFO*pAdd) {
	if (!pFirst)
		pFirst = pAdd;
	if (pLast)
		pLast->pNext = pAdd;
	pAdd->pBefore = pLast;
	pAdd->pNext = NULL;
	pLast = pAdd;
}

tagUFO*DeleteUFO(tagUFO*pDelete) {
	tagUFO*pReturn = pDelete->pNext;
	if (pDelete->pBefore)
		pDelete->pBefore->pNext = pReturn;
	else
		pFirst = pReturn;
	if (pReturn)
		pReturn->pBefore = pDelete->pBefore;
	else
		pLast = pDelete->pBefore;
	delete pDelete;
	return pReturn;
}

int ShotUFO(tagUFO*pAimedUFO,tagUFO*pShotUFO,int R) {
	double AimedUFOAngle = atan(pAimedUFO->y / pAimedUFO->x);
	if (pAimedUFO->x < 0) {
		AimedUFOAngle += PI;
	}
	else if (pAimedUFO->y < 0) {
		AimedUFOAngle += 2 * PI;
	}

	double ShotUFOCenterAngle = atan(pShotUFO->y / pShotUFO->x);
	if (pShotUFO->x < 0) {
		ShotUFOCenterAngle += PI;
	}
	else if (pShotUFO->y < 0) {
		ShotUFOCenterAngle += 2 * PI;
	}

	double ShotUFORangeAngle;
	if ((pShotUFO->Distance*pShotUFO->Distance - pShotUFO->r*pShotUFO->r) > R*R) {
		ShotUFORangeAngle = asin(pShotUFO->r / pShotUFO->Distance);
	}
	else if (pShotUFO->Distance + R>pShotUFO->r) {
		ShotUFORangeAngle = acos((pShotUFO->r*pShotUFO->r + R*R - pShotUFO->Distance*pShotUFO->Distance) / (2 * pShotUFO->r*R));
	}
	else {
		return 1;
	}

	if (ShotUFOCenterAngle - ShotUFORangeAngle <= AimedUFOAngle&&AimedUFOAngle <= ShotUFOCenterAngle + ShotUFORangeAngle)
		return 1;
	else if (ShotUFOCenterAngle - ShotUFORangeAngle + PI <= AimedUFOAngle&&AimedUFOAngle <= ShotUFOCenterAngle + ShotUFORangeAngle + PI)
		return 1;
	else if (ShotUFOCenterAngle - ShotUFORangeAngle <= AimedUFOAngle + PI&&AimedUFOAngle + PI <= ShotUFOCenterAngle + ShotUFORangeAngle)
		return 1;
	else
		return 0;
}