#include<bits/stdc++.h>
using namespace std;
#define int long long
typedef long double ld;
int n,r;
vector<pair<int,int>> timp;
map<int,int> mp,nrm;
int mars[1000005];
signed main()
{
cin>>n>>r;
int a,b,c,d;
for(int i=1;i<=n;i++)
{
cin>>a>>b>>c>>d;
vector<ld> v(4);
v[0] = (ld)(r-a-b)/(ld)(c+d-a-b);
v[1] = (ld)(r-a+b)/(ld)(c+b-a-d);
v[2] = (ld)(r+a-b)/(ld)(a+d-c-b);
v[3] = (ld)(r+a+b)/(ld)(a+b-c-d);
vector<ld> aux;
for(ld t:v)
{
if(abs((ld)a + (ld)(c-a)*t) + abs((ld)b + (ld)(d-b)*t) == r)
{
aux.push_back(t);
}
}
if((int)aux.size()==1)
aux.push_back(aux[0]);
if(!aux.empty())
{
if(aux[0]>aux[1])
swap(aux[0],aux[1]);
timp.push_back({ceil(aux[0]), floor(aux[1])});
}
}
for(auto [x,y]:timp)
{
mp[x]++;
mp[y]++;
}
int cate=0;
for(auto it:mp)
if(it.second)
nrm[it.first]=++cate;
for(int i=0;i<timp.size();i++)
{
mars[nrm[timp[i].first]]++;
mars[nrm[timp[i].second]+1]--;
}
int mxm=0;
for(int i=1;i<=cate;i++)
{
mars[i]+=mars[i-1];
mxm = max(mxm, mars[i]);
}
cout<<mxm;
return 0;
}
/**
a + (c-a)*t
b + (d-b)*t
a + (c-a)*t + b + (d-b)*t = r
t = (r-a-b)/(c+d-a-b)
a + (c-a)*t - b - (d-b)*t = r
t = (r-a+b)/(c+b-a-d)
-a - (c-a)*t + b + (d-b)*t = r
t = (r+a-b)/(a+d-c-b)
-a - (c-a)*t - b - (d-b)*t = r
t = (r+a+b)/(a+b-c-d)
*/
