This submission is migrated from previous version of oj.uz, which used different machine for grading. This submission may have different result if resubmitted.
#include "bits/stdc++.h"
using namespace std;
#define INF 1000000000
#define INFLL 1000000000000000000ll
#define EPS 1e-9
#define all(x) x.begin(),x.end()
#define rall(x) x.rbegin(),x.rend()
#define pb push_back
#define fi first
#define sc second
using i64 = long long;
using u64 = unsigned long long;
using ld = long double;
using ii = pair<int, int>;
#define double ld
int n, radius;
double closest(int a, int b, int c, int d) {
if(1ll*a*a+1ll*b*b <= 1ll * radius*radius) return 0;
double l = 0, r = 1e9;
while(fabs(l - r) > EPS) {
double L = (2 * l + r) / 3.0, R = (2 * r + l) / 3.0;
if(hypot(a + L * c, b + L * d) > hypot(a + R * c, b + R * d)) l = L;
else r = R;
}
return r;
}
double firstSec(int a, int b, int c, int d, double k) {
double l = 0, r = k;
while(fabs(l - r) > EPS) {
double m = (l + r) / 2;
if(hypot(a + m * c, b + m * d) <= radius) r = m;
else l = m;
}
return r;
}
double secondSec(int a, int b, int c, int d, double k) {
double l = k, r = 1e9;
while(fabs(l - r) > EPS) {
double m = (l + r) / 2;
if(hypot(a + m * c, b + m * d) > radius) r = m;
else l = m;
}
return r;
}
void solve() {
cin >> n >> radius;
set<ii> sweep;
int opening = 0, ans = 0;
for(int i = 1; i <= n; ++i) {
int a, b, c, d;
cin >> a >> b >> c >> d;
c -= a, d -= b;
double k = closest(a, b, c, d);
double l = firstSec(a, b, c, d, k);
double r = secondSec(a, b, c, d, k);
if(hypot(a + k * c, b + k * d) > radius) continue;
int L = (int)ceil(l), R = floor(r);
if(L > R) continue;
sweep.emplace(L, -i);
sweep.emplace(R, i);
}
for(auto [x, k] : sweep) {
opening += k < 0 ? 1 : -1;
ans = max(ans, opening);
}
cout << ans << '\n';
}
int main() {
ios_base :: sync_with_stdio(false);
cin.tie(0);
int t = 1;
//cin >> t;
while(t--) solve();
return 0;
}
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