Language: C++

#include<iostream>
#include<vector>
#include<complex>
#include<list>
#define rep(i,n) for(int i=0;i<n;i++)
#define foreach(i,c) for(__typeof(c.begin()) i=c.begin();i!=c.end();i++)
using namespace std;

const double EPS = 1e-8;
const double INF = 1e12;
typedef complex<double> P;
namespace std {
  bool operator < (const P& a, const P& b) {
    return real(a) != real(b) ? real(a) < real(b) : imag(a) < imag(b);
  }
}
double cross(const P& a, const P& b) {
  return imag(conj(a)*b);
}
double dot(const P& a, const P& b) {
  return real(conj(a)*b);
}
struct L : public vector<P> {
  L(const P &a, const P &b) {
    push_back(a); push_back(b);
  }
};
typedef vector<P> G;
struct C {
  P p; double r;
  C(const P &p, double r) : p(p), r(r) { }
};

int ccw(P a, P b, P c) {
  b -= a; c -= a;
  if (cross(b, c) > 0)   return +1;       // counter clockwise
  if (cross(b, c) < 0)   return -1;       // clockwise
  if (dot(b, c) < 0)     return +2;       // c--a--b on line
  if (norm(b) < norm(c)) return -2;       // a--b--c on line
  return 0;
}
bool intersectLL(const L &l, const L &m) {
  return abs(cross(l[1]-l[0], m[1]-m[0])) > EPS || // non-parallel
         abs(cross(l[1]-l[0], m[0]-l[0])) < EPS;   // same line
}
bool intersectLS(const L &l, const L &s) {
  return cross(l[1]-l[0], s[0]-l[0])*       // s[0] is left of l
         cross(l[1]-l[0], s[1]-l[0]) < EPS; // s[1] is right of l
}
bool intersectLP(const L &l, const P &p) {
  return abs(cross(l[1]-p, l[0]-p)) < EPS;
}
bool intersectSS(const L &s, const L &t) {
  return ccw(s[0],s[1],t[0])*ccw(s[0],s[1],t[1]) <= 0 &&
         ccw(t[0],t[1],s[0])*ccw(t[0],t[1],s[1]) <= 0;
}
bool intersectSP(const L &s, const P &p) {
  return abs(s[0]-p)+abs(s[1]-p)-abs(s[1]-s[0]) < EPS; // triangle inequality
}
P projection(const L &l, const P &p) {
  double t = dot(p-l[0], l[0]-l[1]) / norm(l[0]-l[1]);
  return l[0] + t*(l[0]-l[1]);
}
P reflection(const L &l, const P &p) {
	return p + P(2,0) * (projection(l, p) - p);
}
double distanceLP(const L &l, const P &p) {
  return abs(p - projection(l, p));
}
double distanceLL(const L &l, const L &m) {
  return intersectLL(l, m) ? 0 : distanceLP(l, m[0]);
}
double distanceLS(const L &l, const L &s) {
  if (intersectLS(l, s)) return 0;
  return min(distanceLP(l, s[0]), distanceLP(l, s[1]));
}
double distanceSP(const L &s, const P &p) {
  const P r = projection(s, p);
  if (intersectSP(s, r)) return abs(r - p);
  return min(abs(s[0] - p), abs(s[1] - p));
}
double distanceSS(const L &s, const L &t) {
  if (intersectSS(s, t)) return 0;
  return min(min(distanceSP(s, t[0]), distanceSP(s, t[1])),
             min(distanceSP(t, s[0]), distanceSP(t, s[1])));
}
P crosspoint(const L &l, const L &m) {
  double A = cross(l[1] - l[0], m[1] - m[0]);
  double B = cross(l[1] - l[0], l[1] - m[0]);
  if (abs(A) < EPS && abs(B) < EPS) return m[0]; // same line
  if (abs(A) < EPS) assert(false); // !!!PRECONDITION NOT SATISFIED!!!
  return m[0] + B / A * (m[1] - m[0]);
}

struct U{
	P p,dp; double r,v;
	U(P p,double r,double v):p(p),r(r),v(v){
		dp=p*v/P(abs(p),0);
	}
};
int main(){
	int r,n; P O(0,0);
	while(cin>>r>>n,n){
		list<U> u;
		double x,y,r_,v,mn;
		rep(i,n)cin>>x>>y>>r_>>v, u.push_back(U(P(x,y),r_,v));
		int t=1,ans=0;
		foreach(i,u){
			if(norm(i->p)<=r*r)i=u.erase(i),i--,ans++;
			else i->p-=i->dp;
		}
		while(!u.empty()){
			mn=INF; P closest;
			foreach(i,u){
				P prev=i->p+i->dp;
				if(distanceSP(L(i->p,prev),O)<=r)i=u.erase(i),i--,ans++;
				else if(norm(i->p)<mn)closest=i->p,mn=norm(i->p);
			}
			foreach(i,u){
				if(distanceSP(L(closest*P(INF,0),O),i->p)<=i->r)i=u.erase(i),i--;
				else i->p-=i->dp;
			}
		}
		cout<<ans<<endl;
	}
	return 0;
}

Compiler output:
a.cc: In function 'P crosspoint(const L&, const L&)':
a.cc:91:21: error: 'assert' was not declared in this scope
   91 |   if (abs(A) < EPS) assert(false); // !!!PRECONDITION NOT SATISFIED!!!
      |                     ^~~~~~
a.cc:5:1: note: 'assert' is defined in header '<cassert>'; this is probably fixable by adding '#include <cassert>'
    4 | #include<list>
  +++ |+#include <cassert>
    5 | #define rep(i,n) for(int i=0;i<n;i++)