#include "shortcut.h"
#include<bits/stdc++.h>
using namespace std;
#include<ext/pb_ds/assoc_container.hpp>
#include<ext/pb_ds/tree_policy.hpp>
using namespace __gnu_pbds;
#define ll long long
#define fall(i,a,b) for(int i=a;i<=b;i++)
#define rfall(i,a,b) for(int i=a;i>=b;i--)
#define pb push_back
#define all(x) x.begin(),x.end()
#define sz(x) (int)x.size()
#define ordered_set tree<int,null_type,less<int>,rb_tree_tag,tree_order_statistics_node_update>
const ll inf=1e16;
const int MAXN=1e6+10;
typedef pair<ll,ll> pii;
struct node{
ll v1,v2,v3,v4;
};
map<ll,int> mp;
int val[MAXN];
node seg[4*MAXN];
node merge(node a,node b){
node c;
c.v1=min(a.v1,b.v1);
c.v2=min(a.v2,b.v2);
c.v3=max(a.v3,b.v3);
c.v4=max(a.v4,b.v4);
return c;
}
void add(int ind,int l,int r,int p,ll x,ll v){
if(l==r){
seg[ind].v1=x-v;
seg[ind].v2=-x-v;
seg[ind].v3=v-x;
seg[ind].v4=x+v;
return;
}
int m=(l+r)/2;
if(p<=m) add(2*ind,l,m,p,x,v);
else add(2*ind+1,m+1,r,p,x,v);
seg[ind]=merge(seg[2*ind],seg[2*ind+1]);
}
node query(int ind,int l,int r,int a,int b){
if(a>r || l>b) return{inf,inf,-inf,-inf};
if(a<=l && b>=r) return seg[ind];
int m=(l+r)/2;
return merge(query(2*ind,l,m,a,b),query(2*ind+1,m+1,r,a,b));
}
long long find_shortcut(int n, std::vector<int> pref, std::vector<int> d, int c){
vector<ll> l(n);
fall(i,1,n-1) l[i]=pref[i-1]+l[i-1];
vector<ll> lista;
fall(i,0,n-1){
lista.pb(d[i]-l[i]);
}
sort(all(lista));
int cur=0;
fall(i,0,n-1){
if(!mp[lista[i]]) mp[lista[i]]=++cur;
}
fall(i,0,n-1) val[i]=mp[d[i]-l[i]];
auto test=[&](ll k){
fall(i,1,4*cur) seg[i]={inf,inf,-inf,-inf};
ll mxs=1e16,mns=0,mxt=1e16,mnt=0;
fall(i,0,n-1){
auto it=mp.upper_bound(-l[i]-d[i]+k);
int qv=cur+1;
if(it!=mp.end()) qv=(*it).second;
node j=query(1,1,cur,qv,cur);
mxs=min(mxs,k+l[i]-d[i]-c+j.v1);
mxt=min(mxt,k+l[i]-d[i]-c+j.v2);
mnt=max(mnt,l[i]+d[i]-k+j.v3+c);
mns=max(mns,l[i]+d[i]-k+c+j.v4);
add(1,1,cur,val[i],l[i],d[i]);
}
fall(i,0,n-1){
int ini=i,fim=n-1;
while(ini<=fim){
int mei=(ini+fim)/2;
if(l[mei]+l[i]<=mxs && l[mei]-l[i]<=mxt && l[mei]-l[i]>=mnt && l[mei]+l[i]>=mns) return true;
else if(l[mei]+l[i]>mxs || l[mei]-l[i]>mxt) fim=mei-1;
else ini=mei+1;
}
}
return false;
};
ll ini=1,fim=3e15,ans=0;
while(ini<=fim){
ll mei=(ini+fim)/2;
if(test(mei)) ans=mei,fim=mei-1;
else ini=mei+1;
}
return ans;
}
