#include "bits/stdc++.h"
#define st first
#define nd second
using lint = int64_t;
constexpr int MOD = int(1e9) + 7;
constexpr int INF = 0x3f3f3f3f;
constexpr int NINF = 0xcfcfcfcf;
constexpr lint LINF = 0x3f3f3f3f3f3f3f3f;
const long double PI = acosl(-1.0);
// Returns -1 if a < b, 0 if a = b and 1 if a > b.
int cmp_double(double a, double b = 0, double eps = 1e-9) {
return a + eps > b ? b + eps > a ? 0 : 1 : -1;
}
using namespace std;
using ld = double;
bool inCircle(ld x, ld y, ld dx, ld dy, ld r, ld t){
return ( (x + dx*t)*(x + dx*t) + (y + dy*t)*(y + dy*t) ) <= r*r;
}
pair<bool, lint> firstInCircle(ld x, ld y, ld dx, ld dy, ld r, ld dbt){
lint s = ld(dbt) - 2;
lint e = s + 4;
for(ld t = s; t<=e; t++)
if(inCircle(x,y,dx,dy,r, t)) return {true,t};
return {false, -1};
}
pair<bool, lint> lastInCircle(ld x, ld y, ld dx, ld dy, ld r, ld dbt){
lint s = ld(dbt) + 2;
lint e = s - 4;
for(ld t = s; t>=e; t--)
if(inCircle(x,y,dx,dy,r, t)) return {true,t};
return {false, -1};
}
vector<lint> intersection(ld x, ld y, ld dx, ld dy, ld r){
vector<lint> answer;
ld a = (dx*dx + dy*dy);
ld b = (2ll*x*dx + 2ll*y*dy);
ld c = -(r*r - x*x - y*y);
ld delta = b*b - 4ll*a*c;
if(delta < 0) return answer;
if(delta == 0){
ld t = ld(-b) / ld(2*a);
auto left = firstInCircle(x,y,dx,dy,r,t);
if(!left.first) return {};
auto right = lastInCircle(x,y,dx,dy,r,t);
if(!right.first) return {};
answer = {left.second, right.second};
}else{
auto left = firstInCircle(x,y,dx,dy,r, ( ld(-b) - sqrtl((ld)delta))/ ld(2*a) );
if(!left.first) return {};
auto right = lastInCircle(x,y,dx,dy,r, (ld(-b) + sqrtl((ld)delta))/ ld(2*a) );
if(!right.first) return {};
answer = {left.second, right.second};
}
if(answer[0] < 0) answer[0] = 0;
if(answer[0] > answer[1]) answer = {};
else if(answer.back() < 0) answer = {};
return answer;
}
vector<ld> comprTime;
int main() {
cin.tie(nullptr)->sync_with_stdio(false);
comprTime = {-1};
int n;
lint r; cin>>n>>r;
vector<vector<lint>> stars;
for(int i=0; i<n; i++){
lint x1, y1, x2, y2;
cin>>x1>>y1>>x2>>y2;
auto v = intersection(x1, y1, x2-x1, y2-y1, r);
if(!v.empty()){
stars.push_back(v);
comprTime.push_back(v[0]);
comprTime.push_back(v[1]);
}
}
sort(comprTime.begin(), comprTime.end());
comprTime.resize(distance(
comprTime.begin(),
unique(comprTime.begin(), comprTime.end())
));
comprTime.push_back(comprTime.back()+1);
vector<int> pref(comprTime.size());
for(auto star : stars){
int l = lower_bound(comprTime.begin(),comprTime.end(), star[0]) - comprTime.begin();
int r = upper_bound(comprTime.begin(),comprTime.end(), star[1]) - comprTime.begin();
pref[l]++;
pref[r]--;
}
for(int i=1; i<int(comprTime.size()); i++)
pref[i] += pref[i-1];
cout<<*max_element(pref.begin(), pref.end())<<"\n";
return 0;
}
/*
[ ]Leu o problema certo???
[ ]Ver se precisa de long long
[ ]Viu o limite dos fors (é n? é m?)
[ ]Tamanho do vetor, será que é 2e5 em vez de 1e5??
[ ]Testar sample
[ ]Testar casos de borda
[ ]1LL no 1LL << i
[ ]Testar mod (é 1e9+7, mesmo?, será que o mod não ficou negativo?)
*/
