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 <stdio.h>
#include <stdlib.h>
#include <math.h>

#define PIE atan(1.0)*4

typedef struct nd{
	int id;
	//
	int x, y;
	int r;
	int v;
	//
	double polar_r;
	double polar_t;
	//
	int state;	// 0:接近中，1:撃破, 2:到達
	struct nd *next;
	struct nd *prev;
	bool dummy;
} node;

void initList(node **top, int num) {
	// 極座標変換
	for (int i = 0; i < num; i++) {
		top[i]->polar_r = sqrt((double)(top[i]->x*top[i]->x + top[i]->y*top[i]->y));
		top[i]->polar_t = acos((double)top[i]->x / top[i]->polar_r);
		if (top[i]->y < 0)
			top[i]->polar_t = 2*PIE-top[i]->polar_t;
		top[i]->prev = i!=0 ? top[i - 1] : NULL;
		top[i]->next = i!=num-1 ? top[i + 1] : NULL;
		top[i]->dummy = false;
	}
}

node *remove(node *target) {
	node *next = target->next;
	target->next->prev = target->prev;
	target->prev->next = target->next;
	free(target);
	return next;
}

void removeNodes(node *begin) {
	node *temp = begin->next;
	while (temp->next != NULL) {
		if (temp->state != 0)
			temp = remove(temp);
		else
			temp = temp->next;
	}
}

int main(int argc, char* argv[]) {

	while (true) {
		// データ読み込み
		int invaridR, ufoNum;
		fscanf_s(stdin, "%d %d", &invaridR, &ufoNum);
		if (invaridR == 0 && ufoNum == 0) break;
		node **ufos = (node**)malloc(sizeof(node*)*ufoNum);
		for (int i = 0; i < ufoNum; i++) {
			ufos[i] = (node*)malloc(sizeof(node));
			ufos[i]->id = i;
			fscanf_s(stdin, "%d %d %d %d", &(ufos[i]->x), &(ufos[i]->y), &(ufos[i]->r), &(ufos[i]->v));
			ufos[i]->next = ufos[i]->prev = NULL;
			ufos[i]->state = 0;
		}
		initList(ufos, ufoNum);
		node *begin = (node*)malloc(sizeof(node));
		begin->dummy = true;
		begin->id = -1;
		begin->prev = NULL;
		begin->next = ufos[0];
		ufos[0]->prev = begin;
		node *end = (node*)malloc(sizeof(node));
		end->dummy = true;
		end->id = -2;
		end->next = NULL;
		end->prev = ufos[ufoNum - 1];
		ufos[ufoNum - 1]->next = end;

		// 計算
		int t = 0;
		int count = 0;
		while (begin->next != end) {
			// 位置＆時刻更新
			t++;
			for (int i = 0; i < ufoNum; i++) {
				ufos[i]->polar_r -= ufos[i]->v;
			}
			// 照射方向決定
			double minR = 1500;
			double fireT = 0;
			for (node *temp = begin->next; temp != end; temp = temp->next) {
				if (temp->polar_r < minR && temp->polar_r>invaridR) {
					minR = temp->polar_r;
					fireT = temp->polar_t;
				}
			}
			// 照射
			for (node *temp = begin->next; temp != end; temp = temp->next) {
				double dt = fireT - temp->polar_t;
				if (dt > 2 * PIE) dt - 2 * PIE;
				if (dt < 0) dt += 2 * PIE;
				if (temp->polar_r < invaridR) {
					// 到達
					temp->state = 2;
					count++;
				}
				else if (fabs(temp->polar_r*sin(dt)) < temp->r){
					// 撃破
					temp->state = 1;
				}
			}
			// 不要ufo削除
			removeNodes(begin);
		}

		fprintf(stdout, "%d\n", count);
	}
}