Language: C++

#include <cstdio>
#include <complex>
#include <vector>
#include <list>
#include <algorithm>
#include <cmath>
using namespace std;

#define EPS 1e-6
typedef complex<double> P;

struct L : public vector<P> {
  L(const P &a, const P &b) {
    push_back(a); push_back(b);
  }
};

struct C {
  P p; double r;
  C(const P &p, double r) : p(p), r(r) { }
};

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);
}

double dist(const P& a, const P& b)
{
	return sqrt((a.real()-b.real())*(a.real()-b.real())+(a.imag()-b.imag())*(a.imag()-b.imag()));
}

bool isIntoC(const P& p, const C& c)
{
	return dist(p, c.p) < c.r+EPS;
}

bool isIntoC(const L& l, const C& c)
{
	return dist(l[0], c.p) < c.r+EPS && dist(l[1], c.p) < c.r+EPS;
}

int CrossPtNum(const C& c, const L& l)
{
	P LV=l[0]-l[1];
	double A=(LV.real()*LV.real())+(LV.imag()*LV.imag());
	double B=(LV.real()*l[0].real())-(LV.real()*c.p.real())+(LV.imag()*l[0].imag())-(LV.imag()*c.p.imag());
	double C=(l[0].real()-c.p.real())*(l[0].real()-c.p.real())+(l[0].imag()-c.p.imag())*(l[0].imag()-c.p.imag())-(c.r*c.r);

	if(fabs(B*B-A*C) < EPS) return 1;
	if(B*B-A*C  > 0) return 2;
	
	return 0;
}

bool intersectSC(const L& l, const C& c)
{
	if(isIntoC(l, c)) return false;
	
	double vc=dot(l[1]-l[0], c.p-l[0]);
	if(vc<0)
	{
		double dif=c.r-dist(l[0], c.p);
		return dif+EPS > 0;
	}
	
	double vv=dot(l[1]-l[0], l[1]-l[0]);
	
	if(vc > vv)
	{
		double d=dist(l[1], c.p);
		double dif=c.r*c.r-d*d;
		
		return dif+EPS > 0;
	}
	
	double cc=dot(c.p-l[0], c.p-l[0]);
	double dif=c.r*c.r-(cc-(vc/vv)*vc);
	
	return dif+EPS > 0;
}

class UFO
{
	public:

		double x,y,r,v,d,dx,dy;

		UFO(int X, int Y, int R, int V)
		{
			x=X;
			y=Y;
			r=R;
			v=V;
			d=sqrt(x*x+y*y);
			dx=v*x/d;
			dy=v*y/d;
		}

		int move()
		{
			x-=dx;
			y-=dy;
			d=sqrt(x*x+y*y);
			return d;
		}
};

int main()
{
	int R,N,x,y,r,v;
	while(cin >> R >> N, (R||N))
	{
		list<UFO> ls;
		while(N--)
		{
			cin >> x >> y >> r >> v;
			ls.push_back(UFO(x,y,r,v));
		}

		int cnt = 0;
		while(true)
		{
			double md = 1e20;
			double mx,my;
			for(list<UFO>::iterator it=ls.begin(); it!=ls.end();)
			{
				it->move();
				if(it->d <= R)
				{
					it = ls.erase(it);
					cnt++;
				}
				else
				{
					if(md>it->d)
					{
						mx=it->x;
						my=it->y;
						md=it->d;
					}
					it++;
				}
			}
			if(ls.empty()) { cout << cnt << endl; break; }

			L laser(P(0,0),P(mx*1000,my*1000));
			for(list<UFO>::iterator it=ls.begin(); it!=ls.end();)
			{
				C ufo(P(it->x,it->y),it->r);
				if(intersectSC(laser,ufo))
				{
					it = ls.erase(it);
				}
				else
				{
					it++;
				}
			}
		}


	}

	return 0;
}

Compiler output:
a.cc: In function 'int main()':
a.cc:115:15: error: 'cin' was not declared in this scope
  115 |         while(cin >> R >> N, (R||N))
      |               ^~~
a.cc:7:1: note: 'std::cin' is defined in header '<iostream>'; this is probably fixable by adding '#include <iostream>'
    6 | #include <cmath>
  +++ |+#include <iostream>
    7 | using namespace std;
a.cc:148:42: error: 'cout' was not declared in this scope
  148 |                         if(ls.empty()) { cout << cnt << endl; break; }
      |                                          ^~~~
a.cc:148:42: note: 'std::cout' is defined in header '<iostream>'; this is probably fixable by adding '#include <iostream>'