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(x, y);
	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].x, data[i].y);
			float b = a + d;
			float c = a - d;
			if ((b > num&&num > c) || (b + 2 * PI > num&&num > c + 2 * PI)) {
				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;
		}
		x /= per;
		y /= per;
		x *= data[i].speed;
		y *= data[i].speed;
		data[i].x += x;
		data[i].y += y;
	}
}

C++: #include <algorithm>
#include <cctype>
#include <climits>
#include <cmath>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <functional>
#include <map>
#include <numeric>
#include <queue>
#include <set>
#include <string>
#include <vector>

using namespace std;

#define reps(i,f,n) for(int i=f; i<int(n); ++i)
#define rep(i,n) reps(i,0,n)

typedef long long ll;
typedef vector<int> vi;
typedef vector<vi> vvi;
typedef pair<int, int> pii;

const long double EPS = 1e-13;
const int INF = 1001001001;

struct UFO
{
	int r, v;
	long double a, arg;
	bool alive;
	UFO() : alive(true) {}
};

int main()
{
	int R, n;
	while(scanf("%d%d", &R, &n), n){
		UFO ufo[100];
		rep(i, n){
			int x0, y0;
			scanf("%d%d%d%d", &x0, &y0, &ufo[i].r, &ufo[i].v);
			ufo[i].a = hypot((long double)x0, (long double)y0);
			ufo[i].arg = atan2((long double)y0, (long double)x0);
		}
		
		int cnt = 0;
		for(;;){
			int nearest = -1;
			rep(i, n){
				if(ufo[i].alive){
					ufo[i].a -= ufo[i].v;
					if(ufo[i].a < R+EPS){
						ufo[i].alive = false;
						++cnt;
					}
					else if(nearest==-1 || ufo[nearest].a > ufo[i].a)
						nearest = i;
				}
			}
			if(nearest == -1)
				break;

			long double arg = ufo[nearest].arg;
			rep(i, n){
				if(!ufo[i].alive)
					continue;
				if(ufo[i].r+EPS > ufo[i].a)
					ufo[i].alive = false;
				else{
					long double diff = abs(arg - ufo[i].arg);
					if(cos(diff) < 0.0)
						continue;
					long double d = ufo[i].a*sin(diff);
					if(d < ufo[i].r+EPS)
						ufo[i].alive = false;
				}
			}
		}
		printf("%d\n", cnt);
	}
	return 0;
}