#include "shortcut.h"
#include <bits/stdc++.h>
using namespace std;
typedef long long lint;
typedef pair<lint, lint> pi;
struct Fucking_locality{
lint arg1, arg2;
lint first;
int second;
bool operator<(const Fucking_locality &fuck)const{
return make_pair(first, second) < make_pair(fuck.first, fuck.second);
}
};
int n, c;
lint a[1000005], b[1000005];
Fucking_locality v[1000005], w[1000005];
bool trial(lint x){
lint ps = -1e18, pe = 1e18, ms = -1e18, me = 1e18;
lint mx = -1e18, mxp = -1, smx = -1e18;
lint mn = 1e18, mnp = -1, smn = 1e18;
int p = 0;
for(int i=0; i<n; i++){
while(p < n && w[p].first + x < v[i].first){
lint cmx = w[p].arg1;
lint cmn = w[p].arg2;
if(mx < cmx){
smx = mx;
mx = cmx;
mxp = w[p].second;
}
else if(smx < cmx) smx = cmx;
if(mn > cmn){
smn = mn;
mn = cmn;
mnp = w[p].second;
}
else if(smn > cmn) smn = cmn;
p++;
}
lint q1 = (v[i].second != mxp ? mx : smx);
lint q2 = (v[i].second != mnp ? mn : smn);
lint ca = v[i].arg1;
lint cb = v[i].arg2;
ps = max(ps, q1 - x + c + cb + ca);
pe = min(pe, q2 + x - c + cb - ca);
ms = max(ms, q1 - x + c - cb + ca);
me = min(me, q2 + x - c - cb - ca);
}
p = 0;
for(int i=0; i<n; i++){
lint s = max(ps - b[i], b[i] - me);
lint e = min(pe - b[i], b[i] - ms);
while(p < n && s > b[p]) p++;
while(p > 0 && s <= b[p-1]) p--;
while(p < n && b[p] <= e) return true;
}
return false;
}
long long find_shortcut(int n, std::vector<int> l, std::vector<int> d, int c)
{
::n = n;
::c = c;
for(int i=0; i<n; i++){
a[i] = d[i];
if(i >= 1) b[i] = b[i-1] + l[i-1];
}
for(int i=0; i<n; i++){
v[i] = (Fucking_locality){a[i], b[i], a[i] + b[i], i};
w[i] = (Fucking_locality){a[i] + b[i], -a[i] + b[i], -a[i] + b[i], i};
}
sort(v, v+n);
sort(w, w+n);
lint s = 0, e = 2e15;
while(s != e){
lint m = (s+e)/2;
if(trial(m)) e = m;
else s = m+1;
}
return s;
}
