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 <bits/stdc++.h>
  
using namespace std;
  
#define rep(i,n) REP(i,0,n)
#define REP(i,s,e) for(int i=(s); i<(int)(e); i++)
#define pb push_back
#define all(r) (r).begin(),(r).end()
#define rall(r) (r).rbegin(),(r).rend()
#define fi first
#define se second
  
typedef long long ll;
typedef vector<int> vi;
typedef vector<ll> vl;
typedef pair<int, int> pii;
typedef pair<ll, ll> pll;
 
const double EPS = 1e-8;
const double INF = 1e12;
const double PI = acos(-1);
typedef complex<double> P;
typedef complex<double> point;
namespace std {
	bool operator < (const P& a, const P& b) {
		return real(a) != real(b) ? real(a) < real(b) : imag(a) < imag(b);
	}
}
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);
}

struct L : public vector<P> {
	L(const P &a, const P &b) {
		push_back(a); push_back(b);
	}
};

typedef vector<P> G;
typedef vector<P> polygon;

struct C {
	P p; double r;
	C(const P &p, double r) : p(p), r(r) { }
};
//??????????????????
int ccw(P a, P b, P c) {
	b -= a; c -= a;
	if (cross(b, c) > 0)   return +1;       // counter clockwise
	if (cross(b, c) < 0)   return -1;       // clockwise
	if (dot(b, c) < 0)     return +2;       // c--a--b on line
	if (norm(b) < norm(c)) return -2;       // a--b--c on line
	return 0;
}
bool intersectSP(const L &s, const P &p) {
	return abs(s[0]-p)+abs(s[1]-p)-abs(s[1]-s[0]) < EPS; // triangle inequality
}
P projection(const L &l, const P &p) {
	double t = dot(p-l[0], l[0]-l[1]) / norm(l[0]-l[1]);
	return l[0] + t*(l[0]-l[1]);
}
double distanceSP(const L &s, const P &p) {
	if(intersectSP(s, p)) return 0.0;
	const P r = projection(s, p);
	if (intersectSP(s, r)) return abs(r - p);
	return min(abs(s[0] - p), abs(s[1] - p));
}

//?????¢???rate???????????§???????°????
point spinPExtend(const point& p, double theta, double rate = 1.0){
	return p*complex<double>(rate*cos(theta),rate*sin(theta));
}

int main(){
	double r;
	int n;
	while(cin >> r>> n) {
		if((int)r == 0 && n == 0) break;
		C cir({0.0,0.0}, r);
		vector<C> cs;
		vector<double> v;
		vector<int> exist(n, 1);
		rep(i, n) {
			double x, y, _r, _v;
			cin >> x >> y >> _r >> _v;
			cs.pb({{x, y}, _r});
			v.pb(_v);
		}
		int ans = 0;
		while(1){
			int idx = -1;
			double mindist = INF, maxdist = 0.0;
			rep(i, n) if(exist[i] != 0) {
				double dist = abs(cs[i].p);
				if(dist < v[i] + EPS) {
					exist[i] = 0;
					ans++;
					continue;
				}
				cs[i].p *= (dist-v[i])/dist;
				dist = abs(cs[i].p);
				if(dist < r + EPS) {
					exist[i] = 0;
					ans++;
					continue;
				}
				if(dist < mindist - EPS) idx = i, mindist=dist;
				if(dist > maxdist + EPS) maxdist = dist;
			}
			if(idx == -1) break;
			L l(cs[idx].p * (maxdist + 500.0)/abs(cs[idx].p), cs[idx].p*r/abs(cs[idx].p));
			rep(i, n) if(exist[i] != 0) {
				if(distanceSP(l, cs[i].p) < cs[i].r+EPS) exist[i] = 0;
			}
		}
		//rep(i, n) if(exist[i]) ans++;
		rep(i, n) assert(exist[i] == 0);
		cout<<ans<<endl;
	}
}

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;
		double dis;
		ufo(P p, int r, P v, double dis):pos(p),r(r),v(v),dis(dis) {
			av = true;			
		}
		void move();
};

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

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

bool IntersectCL(P p0, int r, P p1) {
	double dis = abs(real(p0)*imag(p1)-imag(p0)*real(p1)) / sqrt(real(p1)*real(p1)+imag(p1)*imag(p1));
	return dis <= r;
}

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

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

void shot() {
	sort(dt.begin(), dt.end(), comp());
	P v(0,0);
	bool f=true;
	int i=0;
	while(i<N) {
		if (dt[i].av && R < dt[i].dis) {
			f = false;
			dt[i].av = false;
			v = dt[i].pos;
			break;
		}
		i++;
	}
	if (f) { fava = false; return; }
	for (int i=0; i<N; i++) {
		if (dt[i].av && R < dt[i].dis) {
			if (IntersectCL(dt[i].pos, dt[i].r, v))
				dt[i].av = false;
		}
	}
}

int main() {
	while(cin >> R >> N, (R||N)) {
		dt.clear();
		fava = true;
		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, abs(pos)));
		}
		while (fava) {
			move();
			shot();
		}
		int cnt = 0;
		for (int i=0; i<N; i++)
			if (dt[i].av) cnt++;
		cout << cnt << endl;
	}
	return 0;
}