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>;
int n, radius;
bool getSecs(int a, int b, int c, int d, ld& s1, ld& s2) {
i64 C = (i64)a * a + (i64)b * b - (i64)radius * radius;
i64 B = 2 * ((i64)a * c + (i64)b * d);
i64 A = (i64)c * c + (i64)d * d;
ld delta = 1.0L * B * B - 4.0L * A * C;
if(delta < -EPS) return false;
delta = sqrt(delta);
s1 = (-B - delta) / (2 * A);
s2 = (-B + delta) / (2 * A);
return true;
}
void solve() {
cin >> n >> radius;
set<pair<i64, int>> sweep;
int opening = 0, ans = 0;
for(int i = 1; i <= n; ++i) {
int a, b, c, d;
ld s1, s2;
cin >> a >> b >> c >> d;
if(!getSecs(a, b, c - a, d - b, s1, s2)) continue;
i64 l = max(0.0L, ceil(s1)), r = floor(s2);
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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