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>
#define int long long
using namespace std ;
const int maxn = 2e5 + 5 ;
int n, r, xi[maxn], xf[maxn], yi[maxn], yf[maxn] ;
vector<pair<int,int>> inter ;
bool test(int a, int b, int c, int x){ return (a*x*x + b*x + c <= 0) ; }
pair<int,int> bsk(int a, int b, int c){
int d = (b*b) - (4*a*c) ;
if(d < 0) return {1, 0} ;
double k = (-b - sqrt(d))*1.00/(2*a*1.00) ;
double k2 = (-b + sqrt(d))*1.00/(2*a*1.00) ;
if(k < 0 && k2 < 0) return {1, 0} ;
//cout << k << " " << k2 << "\n" ;
if(k < 0) k = 0LL ;
if(k2 < 0) k2 = 0LL ;
//cout << a << " " << b << " " << c << " " << d << " " << k2 << "\n" ;
return {k, k2} ;
}
int32_t main(){
cin >> n >> r ;
for(int i = 1 ; i <= n ; i++) cin >> xi[i] >> yi[i] >> xf[i] >> yf[i] ;
for(int i = 1 ; i <= n ; i++){
int dx = (xf[i]-xi[i]), dy = (yf[i]-yi[i]) ;
int a = ((dx*dx)+(dy*dy)) ;
int b = (2*xi[i]*dx) + (2*yi[i]*dy) ;
int c = (xi[i]*xi[i]) + (yi[i]*yi[i]) - (r*r) ;
//cout << a << " " << b << " " << c << "\n" ;
pair<int,int> x = bsk(a, b, c) ;
int tryy = x.first ;
pair<int,int> kk = {-1, -1} ;
for(int j = 0 ; j <= 3 ; j++) if(test(a, b, c, tryy + j)) kk.first = x.first + tryy ;
for(int j = 0 ; j <= 3 ; j++) if(test(a, b, c, tryy - j)) kk.first = x.first - tryy ;
tryy = x.second ;
for(int j = 0 ; j <= 3 ; j++) if(test(a, b, c, tryy - j)) kk.second = x.second - tryy ;
for(int j = 0 ; j <= 3 ; j++) if(test(a, b, c, tryy + j)) kk.second = x.second + tryy ;
//cout << x.first << " " << x.second << " " << kk.first << " " << kk.second << "\n" ;
if(kk.first > kk.second || kk.first == -1 || kk.second == -1 || x.first > x.second) continue ;
inter.push_back({kk.first, 0}) ; inter.push_back({kk.second, 1}) ;
}
int ans = 0, sm = 0 ;
sort(inter.begin(), inter.end()) ;
for(auto a : inter){
if(a.second) sm-- ;
else sm++ ;
ans = max(ans, sm) ;
}
cout << ans << "\n" ;
}
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