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 <complex>
#include <algorithm>
#include <cmath>
using namespace std;

typedef complex<double> P;

class ufo {
	public:
		P pos;
		int r;
		P v;
		bool av;
		bool in;
		ufo(P p, int r, P v):pos(p),r(r),v(v) {av = true; in = false;}
		void move();
};

class comp {
	public:
		bool operator() (const ufo& x, const ufo&y) const {
			return abs(x.pos) < abs(y.pos);
		}
};

vector<ufo> dt;
bool fava = true;
bool debug = false;
int R, N;

void ufo::move() {
	pos += v;
}

int ILimit (P x) {
	if (real(x) >= 0)
		if (imag(x) >= 0) return 1;
		else return 4;
	else
		if (imag(x) >= 0) return 2;
		else return 3;
}

bool IntersectCL(P p0, int r, P p1) {
	if (real(p1) == 0) return r*r >= real(p0)*real(p0);
	double a = imag(p1)/real(p1);
	return (2*a*real(p0)*imag(p0)+r*r) >= a*a*(real(p0)*real(p0)-imag(p0)*imag(p0));
}

void move() {
	for (int i=0; i<N; i++)
		dt[i].move();
}

void shot() {
	sort(dt.begin(), dt.end(), comp());
		if (debug) {
		cout << "debug\n";
		for (int i=0; i<N; i++) {
			if (dt[i].av)
			cout << '(' << real(dt[i].pos) << ',' << imag(dt[i].pos) << ')' << ',' << abs(dt[i].pos) << ',' << dt[i].in << endl;
		}
		}
	P v(0,0);
	bool f=true;
	int p=0;
	while(p<N) {
		if (dt[p].av && R < abs(dt[p].pos)) {
			f = false;
			dt[p].av = false;
			v = dt[p].pos;
			break;
		}
		p++;
	}
	if (f) { fava = false; return; }
	for (int i=0; i<N; i++) {
		if (R<abs(dt[i].pos)) {
			if (IntersectCL(dt[i].pos, dt[i].r, v) && ILimit(dt[i].pos)==ILimit(v))
				dt[i].av = false;
		} else  {
			 dt[i].in = true;
		}
	}
}

int main() {
	while(cin >> R >> N, (R||N)) {
		for (int i=0; i<N; i++) {
			int x, y, r, v;
			cin >> x >> y >> r >> v;
			P pos(x, y);
			P vr = - pos / abs(pos);
			vr *= (double)v;
			dt.push_back(ufo(pos, r, vr));
		}
		if (debug) {
		cout << "debug_m\n";
		for (int i=0; i<N; i++) {
			cout << '(' << real(dt[i].pos) << ',' << imag(dt[i].pos) << ')' << ',';
			cout << dt[i].r;
			cout << '(' << real(dt[i].v) << ',' << imag(dt[i].v) << ')' << '\n';
		}
		}
		while (fava) {
			move();
			shot();
		}
		int cnt = 0;
		for (int i=0; i<N; i++)
			if (dt[i].in) cnt++;
		cout << cnt << endl;
	}
	return 0;
}

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>
#include <complex>
using namespace std;

typedef complex<double> P;
const int INF = 1<<29;
const double EPS = 1e-8;

struct ufo{
    P pos,v;
    int r,id;
};

double cross(const P& a, const P& b) {
  return imag(conj(a)*b);
}

double dot(const P& a, const P& b) {
  return real(conj(a)*b);
}

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,vs;
            scanf("%d %d %d %d",&x,&y,&r,&vs);
            P pos = P(x,y);
            P v = -(double)vs * pos / abs(pos);
            enemys[i] = (ufo){pos,v,r,i};
        }

        int ans = 0;
        while(enemys.size()){
            double min_d = 1500;
            int min_i = -1;
            for(int i=0;i<enemys.size();i++){
                enemys[i].pos += enemys[i].v;
                double d = abs(enemys[i].pos);
                if(d <= R+EPS){
                    enemys.erase(enemys.begin()+i);
                    i--;
                    ans++;
                    continue;
                }
                if(min_d>d){
                    min_d = d;
                    min_i = i;
                }
            }
            if(enemys.size()==0) break;

            ufo min_e = enemys[min_i];
            double min_abs = abs(min_e.pos);
            for(int i=0;i<enemys.size();i++){
                double d = abs(cross(min_e.pos, enemys[i].pos)) / min_abs;
                if(d <= enemys[i].r+EPS){
                    P R_vec = (double)R * min_e.pos / min_abs;
                    P A = enemys[i].pos - R_vec;
                    if (dot(R_vec, A) > 0 || abs(A) < enemys[i].r){
                        enemys.erase(enemys.begin()+i);
                        i--;
                    }
                }
            }
        }
        cout << ans << endl;
    }

    return 0;
}