#include "overtaking.h"
#include <bits/stdc++.h>
using namespace std;
const long long INF=3e18;
typedef pair <long long, long long> pii;
typedef pair <pii, int> piii;
pii st[32000001];
vector <long long> ve;
vector <piii> v;
long long e[1001][1001],l[1001][1001],r[1001][1001],x,n,t[1001],w[1001],d;
void update(int node, int l, int r, int u, int v, pii p){
if (ve[l]>v||ve[r]<u||l>r||u>v)
return;
if (ve[l]>=u&&ve[r]<=v){
st[node]=min(st[node],p);
return;
}
int mid=(l+r)>>1;
update(node<<1,l,mid,u,v,p);
update(node<<1|1,mid+1,r,u,v,p);
}
pii get(int node, int l, int r, int i){
pii p={INF,i};
while (l<r&&ve[l]<=i&&ve[r]>=i){
p=min(p,st[node]);
int mid=(l+r)>>1;
if (ve[mid]>=i){
r=mid;
node<<=1;
}
else if (ve[mid+1]<=i){
l=mid+1;
node=node<<1|1;
}
else
break;
}
return min(p,st[node]);
}
void init(int L, int N, vector<long long> T, vector<int> W, int X, int m, vector<int> s)
{
d=L;
x=X;
for (int i=0;i<N;i++){
if (W[i]>x){
w[n]=W[i];
e[n][0]=t[n]=T[i];
n++;
}
}
for (int i=1;i<m;i++){
for (int j=0;j<n;j++)
v.push_back({{e[j][i-1],w[j]},j});
sort(v.begin(),v.end());
long long mx=0;
for (int it=0;it<v.size();it++){
int j=v[it].second;
mx=max(mx,e[j][i-1]+w[j]*(s[i]-s[i-1]));
e[j][i]=mx;
l[j][i-1]=e[j][i-1]+1;
r[j][i-1]=min((it==v.size()-1?INF:e[v[it+1].second][i-1]),mx-x*(s[i]-s[i-1]));
ve.push_back(l[j][i-1]+x*(d-s[i-1]));
ve.push_back(l[j][i-1]+x*(d-s[i-1])-1);
ve.push_back(l[j][i-1]+x*(d-s[i-1])+1);
ve.push_back(r[j][i-1]+x*(d-s[i-1]));
ve.push_back(r[j][i-1]+x*(d-s[i-1])-1);
ve.push_back(r[j][i-1]+x*(d-s[i-1])+1);
//cout << i-1 << ' ' << j << ' ' << l[j][i-1] << ' ' << r[j][i-1] << '\n';
}
v.clear();
}
for (int i=0;i<n;i++){
ve.push_back(e[i][m-1]);
ve.push_back(e[i][m-1]-1);
ve.push_back(e[i][m-1]+1);
}
ve.push_back(INF);
sort(ve.begin(),ve.end());
ve.resize(unique(ve.begin(),ve.end())-ve.begin());
for (int i=1;i<=ve.size()*4;i++)
st[i]={INF,INF};
for (int i=m-1;i;i--){
for (int j=0;j<n;j++)
v.push_back({{e[j][i],w[j]},j});
sort(v.begin(),v.end());
for (auto p:v){
int j=p.second;
auto q=get(1,0,ve.size()-1,e[j][i]+x*(d-s[i]));
update(1,0,ve.size()-1,l[j][i-1]+x*(d-s[i-1]),r[j][i-1]+x*(d-s[i-1]),{i,q.second});
}
v.clear();
}
return;
}
long long arrival_time(long long y)
{
int val=lower_bound(ve.begin(),ve.end(),y+x*d)-ve.begin();
auto res=get(1,0,ve.size()-1,ve[val]);
return (res.first==INF?y+x*d:res.second);
}
