#include <bits/stdc++.h>
#define point pair<long long, long long>
#define pii pair<int, bool>
using namespace std;
const long long limit = 2e8;
int N;
long long R;
long long a, b, c, d;
vector<pii> seg;
//a*x + b*y = c
//m = p/q
long long x_1, y_1, x_2, y_2, vx, vy;
long long p, q;
long double xx, yy;//terdekat
bool check(long long mid) {
long long a = x_1 + mid * vx, b = y_1 + mid * vy;
if(a > limit || a < -limit || b > limit || b < -limit) return 0;
return a * a + b * b <= R * R;
}
int main() {
ios_base::sync_with_stdio(0);
cin >> N >> R;
long long l, r, res, mid;
long long lb, ub;
for(int i = 1; i <= N; i++) {
cin >> x_1 >> y_1 >> x_2 >> y_2;
if(x_1 == x_2) swap(x_1, y_1), swap(x_2, y_2);
p = y_2 - y_1, q = x_2 - x_1;
vx = q, vy = p;
// cout << i << " " << p << " " << q << "\n";
xx = (long double)(q * y_1 - p * x_1) * -p / (q * q + p * p);
yy = (long double)(q * y_1 - p * x_1) * q / (q * q + p * p);
// cout << xx << " " << yy << "\n";
//kalau tedekat > R
if(xx * xx + yy * yy > R * R) continue;
//kalau ga bakal ketemu yang terdekat
if(((x_1 > x_2) ^ (x_1 > xx)) || ((y_1 > y_2) ^ (y_1 > yy)) || (x_1 == xx)) {
// cout << "A\n";
if(x_1 * x_1 + y_1 * y_1 > R * R) continue;
else {
l = 0, r = limit;
while(l <= r) {
mid = (l + r) >> 1;
if(check(mid)) {
l = mid + 1;
res = mid;
}else r = mid - 1;
}
seg.emplace_back(0, 1);
seg.emplace_back(res + 1, 0);
}
}else {
// cout << "B\n";
//cari yang bawah dulu
l = 0, r = floor((x_1 - xx) / (x_1 - x_2)), lb = -1;
while(l <= r) {
mid = (l + r) >> 1;
if(check(mid)) {
r = mid - 1;
lb = mid;
}else l = mid + 1;
}
l = lb, r = limit, ub = -1;
if(lb == -1) l = ceil((x_1 - xx) / (x_1 - x_2));
while(l <= r) {
mid = (l + r) >> 1;
if(check(mid)) {
l = mid + 1;
ub = mid;
}else r = mid - 1;
}
if(ub == -1 && lb == -1) continue;
if(ub == -1) ub = floor((x_1 - xx) / (x_1 - x_2));
if(lb == -1) lb = ceil((x_1 - xx) / (x_1 - x_2));
seg.emplace_back(lb, 1);
seg.emplace_back(ub + 1, 0);
}
}
sort(seg.begin(), seg.end());
seg.emplace_back(limit, 1);
//linesweep
long long now;
int cnt = 0, ans = 0;
for(int i = 0; i < seg.size() - 1;) {
now = seg[i].first;
while(now == seg[i].first) {
if(seg[i].second) cnt++;
else cnt--;
i++;
}
ans = max(ans, cnt);
}
cout << ans << "\n";
cin >> N;
}
