#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
const ll N = 2e5+5, INF = 1e18, SQRINF = 1e9;
ll n, R;
ll a[N], b[N], c[N], d[N];
vector<pair<ll, ll>> events;
void read() {
cin >> n >> R;
for(int i = 0; i < n; i++)
cin >> a[i] >> b[i] >> c[i] >> d[i];
}
ll val(ll a, ll b, ll c, ll d, ll t) {
ll r1 = a + (c - a) * t;
ll r2 = b + (d - b) * t;
return min(INF, ((r1>=SQRINF || r1<=-SQRINF)?INF:(r1*r1)) + ((r2>=SQRINF || r2<=-SQRINF)?INF:(r2*r2)));
}
void solve() {
for(int i = 0; i < n; i++) {
pair<ll, ll> ans = {INF, INF};
ll x1, x2, l, r, xx;
ll nom = a[i] * (a[i] - c[i]) + b[i] * (b[i] - d[i]);
ll den = (a[i] - c[i]) * (a[i] - c[i]) + (b[i] - d[i]) * (b[i] - d[i]);
if(nom % den == 0) {
x1 = x2 = nom / den;
} else {
x1 = nom / den;
x2 = x1 + 1;
}
x1 = max(0ll, x1), x2 = max(0ll, x2);
if(val(a[i], b[i], c[i], d[i], x2) < val(a[i], b[i], c[i], d[i], x1)) x1 = x2;
if(val(a[i], b[i], c[i], d[i], x1) > R*R) continue;
xx = INF;
l = 0, r = x1;
while(l <= r) {
ll mid = (l+r)/2;
if(val(a[i], b[i], c[i], d[i], mid) <= R*R)
xx = mid, r = mid-1;
else
l = mid+1;
}
ans.first = xx;
xx = INF;
l = x1, r = 1e9;
while(l <= r) {
ll mid = (l+r)/2;
if(val(a[i], b[i], c[i], d[i], mid) <= R*R)
xx = mid, l = mid+1;
else
r = mid-1;
}
ans.second = xx;
if(ans.first == INF || ans.second == INF) continue;
events.push_back({ans.first, 1});
events.push_back({ans.second+1, -1});
}
sort(events.begin(), events.end());
ll ans = 0, cur = 0, prv = 0;
for(auto e : events) {
cur += e.second;
ans = max(ans, cur);
prv = e.first;
}
cout << ans << '\n';
}
int main() {
ios::sync_with_stdio(0); cin.tie(0);
read();
solve();
return 0;
}
