Language: C++

define _USE_MATH_DEFINES
#include <iostream>
#include <complex>
#include <algorithm>
#include <vector>
#include <stack>
#include <string>
#include <queue>
#include <cmath>
#include <math.h>
#include <numeric>
#include <list>
#include <sstream>
#include <fstream>
#include <iomanip>
#include <climits>
#include <set>
#include <memory.h>
#include <memory>
#include <cstdio>
#include <cstdlib>
#include <cctype>
#include <cassert>
#include <map>
#include <cassert>
#include <time.h>
#include <ctime>

using namespace std;

typedef complex<double> xy_t;
typedef pair<xy_t, xy_t> line;
typedef long long ll;
typedef pair<int, int> P;
typedef pair<int , P> PP;
typedef pair<int, string> Ps;
typedef vector<int> vec;
typedef vector<vec> mat;
const int INF = 1 << 27;
const double EPS = 1e-12;
const double PI = 3.1415926535897932384626433832795;
const int CLK = CLOCKS_PER_SEC;

#define rep(i, n) for(int i = 0; i < n; i++)
#define rep2(i, m, n) for(int i = m; i < n; i++)

int R;
double x[200], y[200], r[200], v[200];
double dis[200];
bool used[200];

double dot(const xy_t &a, const xy_t &b){
	return real(conj(a) * b);
}

xy_t projection(const line &l, const xy_t &p){
	double t = dot(l.second - l.first, p - l.first) / norm(l.second - l.first);
	return l.first + t * (l.second - l.first);
}

bool intersectSP(const line &l, const xy_t &p){
	return abs(l.first - p) + abs(l.second - p) - abs(l.second - l.first) < EPS;
}

double distanceSP(const line &l, const xy_t &p){
	xy_t r = projection(l, p);
	if(intersectSP(l, r)) return abs(r - p);
	else return min(abs(l.first - p), abs(l.second - p));
}
int main(){
	int n, cnt;
	while(cin >> R >> n && (R || n)){
		cnt = 0;
		memset(used, false, sizeof(used));

		rep(i, n){
			cin >> x[i] >> y[i] >> r[i] >> v[i];
			dis[i] = sqrt((double)x[i]*x[i]+y[i]*y[i]);
		}

		rep(i, n){

			rep(j, n){
				if(used[j]) continue;
				dis[j] -= v[j];
				double ang = atan2(y[j], x[j]);
				y[j] -= v[j] * sin(ang);
				x[j] -= v[j] * cos(ang);
//				cout << j << " " <<  "( " << x[j] << ", " << y[j] << ")" << endl;
			}
//			cout << cnt << endl;

			rep(j, n){
				if(!used[j]){
					if(dis[j] < R + EPS){
						cnt++;
						used[j] = true;
					}
				}
			}

			int id = 0;
			double best = 1e10;
			rep(j, n){
				if(!used[j] && dis[j] < best){
					best = dis[j];
					id = j;
				}
			}

			double ang = atan2(y[id], x[id]);
			line l = line(xy_t(R * cos(ang), R*sin(ang)), xy_t(cos(ang), sin(ang)) * 1e10);
			
			rep(j, n){
				if(!used[j] && distanceSP(l, xy_t(x[j], y[j])) < r[j] + EPS){
					used[j] = true;
				}
			}
		}
		cout << cnt << endl;
	}
	return 0;
}

Compiler output:
a.cc:1:1: error: 'define' does not name a type
    1 | define _USE_MATH_DEFINES
      | ^~~~~~
In file included from /usr/include/c++/14/iosfwd:42,
                 from /usr/include/c++/14/ios:40,
                 from /usr/include/c++/14/ostream:40,
                 from /usr/include/c++/14/iostream:41,
                 from a.cc:2:
/usr/include/c++/14/bits/postypes.h:68:11: error: 'ptrdiff_t' does not name a type
   68 |   typedef ptrdiff_t     streamsize; // Signed integral type
      |           ^~~~~~~~~
/usr/include/c++/14/bits/postypes.h:41:1: note: 'ptrdiff_t' is defined in header '<cstddef>'; this is probably fixable by adding '#include <cstddef>'
   40 | #include <cwchar> // For mbstate_t
  +++ |+#include <cstddef>
   41 | 
In file included from /usr/include/c++/14/bits/exception_ptr.h:38,
                 from /usr/include/c++/14/exception:166,
                 from /usr/include/c++/14/ios:41:
/usr/include/c++/14/new:131:26: error: declaration of 'operator new' as non-function
  131 | _GLIBCXX_NODISCARD void* operator new(std::size_t) _GLIBCXX_THROW (std::bad_alloc)
      |                          ^~~~~~~~
/usr/include/c++/14/new:131:44: error: 'size_t' is not a member of 'std'; did you mean 'size_t'?
  131 | _GLIBCXX_NODISCARD void* operator new(std::size_t) _GLIBCXX_THROW (std::bad_alloc)
      |                                            ^~~~~~
In file included from /usr/include/wchar.h:35,
                 from /usr/include/c++/14/cwchar:44,
                 from /usr/include/c++/14/bits/postypes.h:40:
/usr/lib/gcc/x86_64-linux-gnu/14/include/stddef.h:214:23: note: 'size_t' declared here
  214 | typedef __SIZE_TYPE__ size_t;
      |                       ^~~~~~
/usr/include/c++/14/new:132:41: error: attributes after parenthesized initializer ignored [-fpermissive]
  132 |   __attribute__((__externally_visible__));
      |                                         ^
/usr/include/c++/14/new:133:26: error: declaration of 'operator new []' as non-function
  133 | _GLIBCXX_NODISCARD void* operator new[](std::size_t) _GLIBCXX_THROW (std::bad_alloc)
      |                          ^~~~~~~~
/usr/include/c++/14/new:133:46: error: 'size_t' is not a member of 'std'; did you mean 'size_t'?
  133 | _GLIBCXX_NODISCARD void* operator new[](std::size_t) _GLIBCXX_THROW (std::bad_alloc)
      |                                              ^~~~~~
/usr/lib/gcc/x86_64-linux-gnu/14/include/stddef.h:214:23: note: 'size_t' declared here
  214 | typedef __SIZE_TYPE__ size_t;
      |                       ^~~~~~
/usr/include/c++/14/new:134:41: error: attributes after parenthesized initializer ignored [-fpermissive]
  134 |   __attribute__((__externally_visible__));
      |                                         ^
/usr/include/c++/14/new:140:29: error: 'std::size_t' has not been declared
  140 | void operator delete(void*, std::size_t) _GLIBCXX_USE_NOEXCEPT
      |                             ^~~
/usr/include/c++/14/new:142:31: error: 'std::size_t' has not been declared
  142 | void operator delete[](void*, std::size_t) _GLIBCXX_USE_NOEXCEPT
      |                               ^~~
/usr/include/c++/14/new:145:26: error: declaration of 'operator new' as non-function
  145 | _GLIBCXX_NODISCARD void* operator new(std::size_t, const std::nothrow_t&) _GLIBCXX_USE_NOEXCEPT
      |                          ^~~~~~~~
/usr/include/c++/14/new:145:44: error: 'size_t' is not a member of 'std'; did you mean 'size_t'?
  145 | _GLIBCXX_NODISCARD void* operator new(std::size_t, const std::nothrow_t&) _GLIBCXX_USE_NOEXCEPT
      |                                            ^~~~~~
/usr/lib/gcc/x86_64-linux-gnu/14/include/stddef.h:214:23: note: 'size_t' declared here
  214 | typedef __SIZE_TYPE__ size_t;
      |                       ^~~~~~
/usr/include/c++/14/new:145:52: error: expected primary-expression before 'const'
  145 | _GLIBCXX_NODISCARD void* operator new(std::size_t, const std::nothrow_t&) _GLIBCXX_USE_NOEXCEPT
      |                                                    ^~~~~
/usr/include/c++/14/new:147:26: error: declaration of 'operator new []' as non-function
  147 | _GLIBCXX_NODISCARD void* operator new[](std::size_t, const std::nothrow_t&) _GLIBCXX_USE_NOEXCEPT
      |                          ^~~~~~~~
/usr/include/c++/14/new:147:46: error: 'size_t' is not a member of 'std'; did you mean 'size_t'?
  147 | _GLIBCXX_NODISCARD void* operator new[](std::size_t, const std::nothrow_t&) _GLIBCXX_USE_NOEXCEPT
      |                                              ^~~~~~
/usr/lib/gcc/x86_64-linux-gnu/14/include/stddef.h:214:23: note: 'size_t' declared here
  214 | typedef __SIZE_TYPE__ size_t;
      |                       ^~~~~~
/usr/include/c++/14/new:147:54: error: expected primary-expression before 'const'
  147 | _GLIBCXX_NODISCARD void* operator new[](std::size_t, const std::nothrow_t&) _GLIBCXX_USE_NOEXCEPT
      |                                                      ^~~~~
/usr/include/c++/14/new:154:26: error: declaration of 'operator new' as non-function
  154 | _GLIBCXX_NODISCARD void* operator new(std::size_t, std::align_val_t)
      |                          ^~~~~~~~
/usr/include/c++/14/new:154:44: error: 'size_t' is not a member of 'std'; did you mean 'size_t'?
  154 | _GLIBCXX_NODISCARD void* operator new(std::size_t, std::align_val_t)
      |                                            ^~~~~~
/usr/lib/gcc/x86_64-linux-gnu/14/include/stddef.h:214:23: note: 'size_t' declared here
  214 | typedef __SIZE_TYPE__ size_t;
      |                       ^~~~~~
/usr/include/c++/14/new:154:68: error: expected primary-expression before ')' token
  154 | _GLIBCXX_NODISCARD void* operator new(std::size_t, std::align_val_t)
      |                                                                    ^
/usr/include/c++/14/new:155:73: error: attributes after parenthesized initializer ignored [-fpermissive]
  155 |   __attribute__((__externally_visible__, __alloc_size__ (1), __malloc__));
      |                                                                         ^
/usr/include/c++/14/new:156:26: error: declaration of 'operator new' as non-function
  156 | _GLIBCXX_NODISCARD void* operator new(std::size_t, std::align_val_t, const std::nothrow_t&)
      |                          ^~~~~~~~
/usr/include/c++/14/new:156:44: error: 'size_t' is not a member of 'std'; did you mean 'size_t'?
  156 | _GLIBCXX_NODISCARD void* operator new(std::size_t, std::align_val_t, const std::nothrow_t&)
      |                                            ^~~~~~
/usr/lib/gcc/x86_64-linux-gnu/14/include/stddef.h:214:23: note: 'size_t' declared here
  214 | typedef __SIZE_TYPE__ size_t;
      |                       ^~~~~~
/usr/include/c++/14/new:156:68: error: expected primary-expression before ',' token
  156 | _GLIBCXX_NODISCARD void* operator new(std::size_t, std::align_val_t, const std::nothrow_t&)
      |                                                                    ^
/usr/include/c++/14/new:156:70: error: expected primary-expression before 'const'
  156 | _GLIBCXX_NODISCARD void* operator new(std::size_t, std::align_val_t, const std::nothrow_t&)
      |                                                                      ^~~~~
/usr/include/c++/14/new:162:26: error: declaration of 'operator new []' as non-function
  162 | _GLIBCXX_NODISCARD void* operator new[](std::size_t, std::align_val_t)
      |                          ^~~~~~~~
/usr/include/c++/14/new:162:46: error: 'size_t' is not a member of 'std'; did you mean 'size_t'?
  162 | _GLIBCXX_NODISCARD void* operator new[](std::size_t, std::align_val_t)
      |                                              ^~~~~~
/usr/lib/gcc/x86_64-linux-gnu/14/include/stddef.h:214:23: note: 'size_t' declared here
  214 | typedef __SIZE_TYPE__ size_t;
      |                       ^~~~~~
/usr/include/c++/14/new:162:70: error: expected primary-expression before ')' token
  162 | _GLIBCXX_NODISCARD void* operator new[](std::size_t, std::align_val_t)
      |                                                                      ^
/usr/include/c++/14/new:163:73: error: attributes after parenthesized initializer ignored [-fpermissive]
  163 |   __attribute__((__externally_visible__, __alloc_size__ (1), __malloc__));
      |                                                                         ^
/usr/include/c++/14/new:164:26: error: declaration of 'operator new []' as non-function
  164 | _GLIBCXX_NODISCARD void* operator new[](std::size_t, std::align_val_t, const std::nothrow_t&)
      |                          ^~~~~~~~
/usr/include/c++/14/new:164:46: error: 'size_t' is not a member of 'std'; did you mean 'size_t'?
  164 | _GLIBCXX_NODISCARD void* operator new[](std::size_t, std::align_val_t, const std::nothrow_t&)
      |                                              ^~~~~~
/usr/lib/gcc/x86_64-linux-gnu/14/include/stddef.h:214:23: note: 'size_t' declared here
  214 | typedef __SIZE_TYPE__ size_t;
      |                       ^~~~~~
/usr/include/c++/14/new:164:70: error: expected primary-expression before ',' token
  164 | _GLIBCXX_NODISCARD void* operator new[](std::size_t, std::align_val_t, const std::nothrow_t&)
      |                                                                      ^
/usr/include/c++/14/new:164:72: error: expected primary-expression before 'const'
  164 | _GLIBCXX_NODISCARD void* operator new[](std::size_t, std::align_val_t, const std::nothrow_t&)
      |                                                                        ^~~~~
/usr/include/c++/14/new:171:29: error: 'std::size_t' has not been declared
  171 | void operator delete(void*, std::size_t, std::align_val_t)
      |                             ^~~
/usr/include/c++/14/new:173:31: error: 'std::size_t' has not been declared
  173 | void operator delete[](void*, std::size_t, std::align_val_t)
      |                               ^~~
/usr/include/c++/14/new:179:33: error: declaration of 'operator new' as non-function
  179 | _GLIBCXX_NODISCARD inline void* operator new(std::size_t, void* __p) _GLIBCXX_USE_NOEXCEPT
      |                                 ^~~~~~~~
/usr/include/c++/14/new:179:51: error: 'size_t' is not a member of 'std'; did you mean 'size_t'?
  179 | _GLI