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<algorithm>
#include<vector>
#include<cmath>
#define PI 3.141592
using namespace std;
class ufo {
public:
	float x;
	float y;
	float radius;
	float speed;
};

void move(vector<ufo> &);

int goal(vector<ufo>&,float);

void shot(vector<ufo>&, float, float);

int main() {
	float radius;
	int num;
	while (cin >> radius >> num&&num != 0) {
		vector<ufo> data(num);
		for (int i = 0; i < num; ++i) {
			cin >> data[i].x >> data[i].y >> data[i].radius >> data[i].speed;
		}
		int ans = 0;
		while (!data.empty()) {
			move(data);
			ans += goal(data, radius);
			if (data.empty())break;
			float fast;
			int place;
			fast = pow(data[0].x, 2.0) + pow(data[0].y, 2.0);
			place = 0;
			for (int i = 1; i < data.size(); ++i) {
				float di = pow(data[i].x, 2.0) + pow(data[i].y, 2.0);
				if (fast > di) {
					fast = di;
					place = i;
				}
			}
			shot(data, data[place].x, data[place].y);
		}
		cout << ans << endl;
	}
	return 0;
}

void shot(vector<ufo>& data, float x, float y) {
	float num = atan2(y, x);
	if (num < 0)num = PI * 2 + num;
	for (int i = 0; i < data.size(); ++i) {
		if (pow(data[i].x, 2.0) + pow(data[i].y, 2.0) <= data[i].radius) {
			swap(data[i], data.back());
			data.pop_back();
			--i;
		}
		else {
			float distance = sqrt(pow(data[i].x, 2.0) + pow(data[i].y, 2.0));
			float d = asin(data[i].radius / distance);
			float a = atan2(data[i].y, data[i].x);
			if (a < 0)a = PI * 2 + a;
			float b = a + d;
			float c = a - d;
			if (b < 0)b = PI * 2 + b;
			if (c < 0)c = PI * 2 + c;
			if ((b > num&&num > c) || (b<c&&PI*2+b>num&&num>c)||(b<c&&b>num&&num>c-PI*2)) {
				swap(data[i], data.back());
				data.pop_back();
				--i;
			}
		}
	}
}

int goal(vector<ufo>&data,float radius) {
	int res = 0;
	for (int i = 0; i < data.size(); ++i) {
		float x = data[i].x;
		float y = data[i].y;
		if (pow(x, 2.0) + pow(y, 2.0) <= pow(radius, 2.0)) {
			swap(data[i], data.back());
			data.pop_back();
			--i;
			++res;
		}
	}
	return res;
}

void move(vector<ufo>&data) {
	for (int i = 0, nmax = data.size(); i < nmax; ++i) {
		float x = -data[i].x;
		float y = -data[i].y;
		float per = sqrt(pow(x, 2.0) + pow(y, 2.0));
		if (per <= data[i].speed) {
			data[i].x = data[i].y = 0;
			continue;
		}
		x /= per;
		y /= per;
		x *= data[i].speed;
		y *= data[i].speed;
		data[i].x += x;
		data[i].y += y;
	}
}

C++: #include <iostream>
#include <set>
#include <cmath>
using namespace std;

typedef set<int> S;

const int NMAX = 500;
const double EPS = 1.0e-6;
const double INF = 1.0e10;

int N;
double R;
double x[NMAX];
double y[NMAX];
double r[NMAX];
double v[NMAX];

bool input() {
  cin >> R >> N;
  if (!R && !N) {
    return false;
  }
  for (int i = 0; i < N; ++i) {
    cin >> x[i] >> y[i] >> r[i] >> v[i];
  }
  return true;
}

void solve() {
  S s;
  for (int i = 0; i < N; ++i) {
    s.insert(i);
  }

  int ans = 0;
  while (!s.empty()) {
    int t = -1;
    double td = INF;
    for (S::iterator it = s.begin(); it != s.end();) {
      int n = *it;
      double d = sqrt(x[n] * x[n] + y[n] * y[n]);
      double nd = d - v[n];
      if (nd < R - EPS) {
        s.erase(it++);
        ++ans;
        continue;
      }
      if (td > nd) {
        td = nd;
        t = n;
      }
      x[n] *= nd / d;
      y[n] *= nd / d;
      ++it;
    }
    if (t == -1) {
      break;
    }
    double zt = atan2(y[t], x[t]);
    for (S::iterator it = s.begin(); it != s.end();) {
      int n = *it;
      double d2 = x[n] * x[n] + y[n] * y[n];
      double d = sqrt(d2);
      double z1 = atan2(y[n], x[n]);
      double z2;
      if (d - r[n] < -R) {
        z2 = M_PI;
      } else if (d - r[n] < 0) {
        double k = (r[n] * r[n] - R * R - d * d) / (2 * d);
        z2 = atan2(k, sqrt(R * R - k * k)) + M_PI / 2;
      } else if (d - r[n] < R) {
        double k = (d * d + R * R - r[n] * r[n]) / (2 * d);
        z2 = atan2(k, sqrt(R * R - k * k));
      } else {
        z2 = atan2(r[n], sqrt(d2 - r[n] * r[n]));
      }
      double zu = z1 + z2;
      double zl = z1 - z2;
      bool hit;
      if (zu > M_PI) {
        hit = ((zl - EPS < zt && zt <= M_PI)
            || (-M_PI <= zt && zt < zu + EPS - 2 * M_PI));
      } else if (zl < -M_PI) {
        hit = ((zl + 2 * M_PI - EPS < zt && zt <= M_PI)
            || (-M_PI <= zt && zt < zu + EPS));
      } else {
        hit = (zl - EPS < zt && zt < zu + EPS);
      }
      if (hit) {
        s.erase(it++);
      } else {
        ++it;
      }
    }
  }
  cout << ans << endl;
}

int main() {
  while (input()) {
    solve();
  }
}