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 <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; }

bool sameDirection(double x1, double y1, double x2, double y2) {
	if (x1 < -eps && eps < x2) return false;
	if (x2 < -eps && eps < x1) return false;
	if (y1 < -eps && eps < y2) return false;
	if (y2 < -eps && eps < y1) return false;
	return true;
}

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 && sameDirection(x, y, p, q)) {
						shoot[i] = true;
					}
				}
			}
		}
		int res = 0;
		for (int i=0; i<N; ++i) {
			if ( ! shoot[i]) ++res;
		}
		cout << res << endl;
	}
	return 0;
}

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 xr = x[n] * cos(zt) + y[n] * sin(zt);
      double yr = x[n] * -sin(zt) + y[n] * cos(zt);
      if (yr > r[n] - EPS || yr < EPS - r[n]) {
        ++it;
        continue;
      }
      double dk = sqrt(r[n] * r[n] - yr * yr);
      double k1 = xr + dk;
      double k2 = xr - dk;
      if (k1 > R - EPS || k2 < EPS - R) {
        s.erase(it++);
      } else {
        ++it;
      }
    }
  }
  cout << ans << endl;
}

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