#include <bits/stdc++.h>
using namespace std;
#define int long long
signed main()
{
int n,R;
cin>>n>>R;
int a[n],b[n],c[n],d[n];
for (int i=0;i<n;i++)
cin>>a[i]>>b[i]>>c[i]>>d[i];
vector<int> v,v1;
set<int> se;
for (int i=0;i<n;i++)
{
if (b[i]<=R)
{
c[i]-=a[i];
int x=sqrtl(R*R-b[i]*b[i]);
if (c[i]<0)
{
int s=-1,e=1e9;
while (s+1<e)
{
int mid=(s+e)/2;
if (c[i]*mid+a[i]<=x)
e=mid;
else
s=mid;
}
int l=e;
s=0,e=1e9;
while (s+1<e)
{
int mid=(s+e)/2;
if (c[i]*mid+a[i]>=-x)
s=mid;
else
e=mid;
}
if (s>=l)
v.push_back(l),v1.push_back(s);
}
else
{
int s=-1,e=1e9;
while (s+1<e)
{
int mid=(s+e)/2;
if (c[i]*mid+a[i]>=-x)
e=mid;
else
s=mid;
}
int l=e;
s=0,e=1e9;
while (s+1<e)
{
int mid=(s+e)/2;
if (c[i]*mid+a[i]<=x)
s=mid;
else
e=mid;
}
if (s>=l)
v.push_back(l),v1.push_back(s);
}
if (!v.empty())
se.insert(v.back()),se.insert(v1.back());
}
}
sort(v.begin(),v.end());
sort(v1.begin(),v1.end());
int ans=0,id=0,id1=0;
for (int i:se)
{
while (id<v.size() && v[id]<=i)
id++;
while (id1<v1.size() && v1[id1]<i)
id1++;
ans=max(ans,id-id1);
}
cout<<ans<<endl;
return 0;
}
