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++: from sys import stdin
from math import sqrt,fabs

class Game:
	class Ufo:
		def __init__(self,x,y,r,v):
			self.x = x*1.0
			self.y = y*1.0
			self.r = r*1.0
			self.v = v*1.0
			self.d = sqrt(x**2+y**2)
			self.cs = self.x / self.d
			self.si = self.y / self.d
			self.vx = -self.v*self.cs
			self.vy = -self.v*self.si

		def __str__(self):
			return "ufo x = " + str(self.x) + ", y = " + str(self.y) + ", r = " + str(self.r) + ", v = " + str(self.v)

		def oneMinMove(self):
			self.x += self.vx
			self.y += self.vy
			self.d -= self.v

	class Laser:
		def __init__(self,cs,si):
			self.cs = cs
			self.si = si

	ufos = []
	laser = Laser(0,0)
	gameend = False
	inrl = 0
	def __init__(self,R):
		self.R = R

	def hit(self,laser,ufo):
		temp1 = ufo.r**2 - (laser.si*ufo.x - laser.cs*ufo.y)**2
		if temp1 >= 0:
			temp2 = laser.cs*ufo.x + laser.si*ufo.y
			d1 = temp2 + sqrt(temp1)
			d2 = temp2 - sqrt(temp1)
			if d1>=0 or d2>=0: return True
			else: return False
		else: return False

	def isInvaded(self,ufo):
		return (ufo.d<= self.R)
	
	def gameOneMinMove(self):
		curInrs = []
		for ufo in self.ufos:
			ufo.oneMinMove()
			if self.isInvaded(ufo): curInrs.append(ufo)
		self.inrl += len(curInrs)
		#print str(len(curInrs)) + " ufos invaded!"
		for ufo in curInrs:
			self.ufos.remove(ufo)
			#print ufo
		del curInrs
		if self.ufos == []:
			self.gameend = True

	def setLaser(self):
		nearestUfo = self.ufos[0]
		for ufo in self.ufos:
			if nearestUfo.d > ufo.d :
				nearestUfo = ufo
		self.laser = self.Laser(nearestUfo.cs,nearestUfo.si)

	def fireLaser(self):
		curDeads = []
		for ufo in self.ufos:
			if self.hit(self.laser,ufo):
				curDeads.append(ufo)
		#print str(len(curDeads)) +" ufos burned!"
		for ufo in curDeads:
			self.ufos.remove(ufo)
			#print ufo
		del curDeads

	def oneLogic(self):
		self.gameOneMinMove()
		if self.gameend:
			pass
		else:
			self.setLaser()
			self.fireLaser()

	def allLogic(self):
		while not self.gameend:
			self.oneLogic()


for inp in stdin:
#for inp in open("input.txt"):
	inp = map(int,inp.split())
	if len(inp) == 2:
		if inp == (0,0): break
		game = Game(inp[0])
		N = inp[1]
	else:
		game.ufos.append(game.Ufo(inp[0],inp[1],inp[2],inp[3]))
		if len(game.ufos) == N:
			game.allLogic()
			print game.inrl

C++: #include <iostream>
#include <stdio.h>
#include <sstream>
#include <string>
#include <vector>
#include <map>
#include <queue>
#include <algorithm>
#include <set>
#include <math.h>
#include <utility>
#include <stack>
#include <string.h>
using namespace std;
typedef pair<int,int> P;
const int INF = 1<<29;
const double EPS = 1e-8;

struct ufo{
    int x,y,r,v;
    bool active;
};

double dist(ufo &a, int t){
    return sqrt(a.x*a.x+a.y*a.y) - a.v*t;
}

int main(){
    while(1){
        int R,N;
        scanf("%d %d",&R,&N);
        if(N==0)break;

        vector<ufo> enemys(N);
        for(int i=0;i<N;i++){
            int x,y,r,v;
            scanf("%d %d %d %d",&x,&y,&r,&v);
            enemys[i] = (ufo){x,y,r,v,true};
        }

        int count = 0, t = 1, ans = 0;
        while(count!=N){
            double min_d = 1500;
            int min_i = -1;
            for(int i=0;i<N;i++){
                if(!enemys[i].active) continue;
                double d = dist(enemys[i], t);
                if(d <= R+EPS){
                    //printf("goal %d at %d\n",i,t);
                    enemys[i].active = false;
                    ans++;
                    count++;
                    continue;
                }
                if(min_d>d){
                    min_d = d;
                    min_i = i;
                }
            }
            if(count==N) break;
            ufo min_e = enemys[min_i];
            double abs_i = sqrt(min_e.x*min_e.x + min_e.y*min_e.y);
            for(int i=0;i<N;i++){
                if(!enemys[i].active) continue;
                if(min_e.x*enemys[i].x > -EPS && min_e.y*enemys[i].y > -EPS){
                    double d = abs(min_e.x*enemys[i].y - min_e.y*enemys[i].x) / abs_i;
                    if(d <= enemys[i].r+EPS){
                        //printf("break %d at %d\n",i,t);
                        enemys[i].active = false;
                        count++;
                    }
                }
            }
            t++;
        }
        cout << ans << endl;
    }

    return 0;
}