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 <algorithm>
#include <complex>
#include <cmath>

using namespace std;

typedef complex<double> P;
const double PI = acos(-1);
const double EPS = 1e-9;

int cmp(double a, double b) {
    const double d = a-b;
    if(abs(d) < EPS) return 0;
    else if(d < 0) return -1;
    return 1;
}

inline double dot(const P& a, const P& b) { return a.real()*b.real() + a.imag()*b.imag(); }

struct line/*{{{*/
{
  P a, b;
  line() {}
  line(const P& p, const P& q) : a(p), b(q) {}

  // AOJ 1171 Laser Beam Reflections
  inline P perpendicular(const P& p) const
  {
    // 点 p から直線上に下ろした垂線の足
    const double t = dot(p-a, a-b) / dot(b-a, b-a);
    return a + t*(a-b);
  }

  inline double distance(const P& p) const {
      return abs(p - this->perpendicular(p));
  }
};/*}}}*/

struct UFO {
    P pos;
    double r;
    double v;

    UFO() {}
    UFO(const P &p, double r, double v) : pos(p), r(r), v(v) {}

    void move() {
        if(cmp(abs(pos), 0) == 0) return ;

        const P dv = pos / abs(pos)*v;
        if(cmp(abs(dv), abs(pos)) >= 0) {
            pos = P(0, 0);
        } else {
            pos -= dv;
        }
    }
};

bool solve() {
    int R, N;
    cin >> R >> N;
    if(!R && !N) return false;

    vector<UFO> ufos;
    for(int i = 0; i < N; ++i) {
        double x, y, r, v;
        cin >> x >> y >> r >> v;
        ufos.push_back(UFO(P(x, y), r, v));
    }
    int ans = 0;
    while(true) {
        const int M = ufos.size();
        double min_dist = 1e10;
        int min_idx = -1;
        for(int i = 0; i < M; ++i) {
            UFO &u = ufos[i];
            u.move();
            const double d = abs(u.pos);
            if(cmp(d, R) > 0 && d < min_dist) {
                min_dist = d;
                min_idx = i;
            }
        }
        if(min_idx == -1) break;
        //cout << ufos[min_idx].pos << endl;
        const line l(P(0, 0), ufos[min_idx].pos);
        auto pend = remove_if(ufos.begin(), ufos.end(), [&](const UFO &u) {
                return dot(ufos[min_idx].pos, u.pos) >= 0 && cmp(abs(u.pos), R) > 0 && cmp(l.distance(u.pos), u.r) <= 0;
                });
        //cout << distance(pend, ufos.end()) << endl;
        ufos.erase(pend, ufos.end());
    }
    cout << ufos.size() << endl;
    return true;
}

int main() {
    cin.tie(0);
    ios::sync_with_stdio(0);

    while(solve()) ;
    return 0;
}

C++: #include <iostream>
#include <string>
#include <vector>
#include <cstring>
#include <climits>
#include <algorithm>
#include <map>
#include <cmath>
using namespace std;

const double eps = 1e-7;
int xs[100], ys[100], rs[100], vs[100];
bool shoot[100];

inline int sq(int x) { return x*x; }
inline double sq(double x) { return x*x; }

int main() {
	int R, N;
	while (cin >> R >> N, (R || N)) {
		for (int i=0; i<N; ++i) {
			cin >> xs[i] >> ys[i] >> rs[i] >> vs[i];
		}
		memset(shoot, false, sizeof shoot);
		for (int m=1; ; ++m) {
			int k = -1, minDist = INT_MAX;
			for (int i=0; i<N; ++i) {
				int dist = sq(xs[i])+sq(ys[i]) - sq(R+vs[i]*m);
				if ( ! shoot[i] && 0 < dist && dist < minDist) {
					minDist = dist;
					k = i;
				}
			}
			if (k == -1) break;
			shoot[k] = true;
			for (int i=0; i<N; ++i) {
				int dist = sq(xs[i])+sq(ys[i]) - sq(R+vs[i]*m);
				if ( ! shoot[i] && 0 < dist) {
					double x = xs[k] - vs[k] * cos(atan2(ys[k], xs[k]));
					double y = ys[k] - vs[k] * sin(atan2(ys[k], xs[k]));
					double p = xs[i] - vs[i] * cos(atan2(ys[i], xs[i]));
					double q = ys[i] - vs[i] * sin(atan2(ys[i], xs[i]));
					double a = y/x;
					double t = sq(a*p-q)/(1+a*a);
					if (t <= sq(rs[i]) + eps) {
						shoot[i] = true;
					}
				}
			}
		}
		int res = 0;
		for (int i=0; i<N; ++i) {
			if ( ! shoot[i]) ++res;
		}
		cout << res << endl;
	}
	return 0;
}