#include "shortcut.h"
#include <bits/stdc++.h>
#include <bits/extc++.h>
#define StarBurstStream ios_base::sync_with_stdio(false); cin.tie(0); cout.tie(0);
#define iter(a) a.begin(), a.end()
#define riter(a) a.rbegin(), a.rend()
#define lsort(a) sort(iter(a))
#define gsort(a) sort(riter(a))
#define pb(a) push_back(a)
#define eb(a) emplace_back(a)
#define pf(a) push_front(a)
#define ef(a) emplace_front(a)
#define pob pop_back()
#define pof pop_front()
#define mp(a, b) make_pair(a, b)
#define F first
#define S second
#define mt make_tuple
#define gt(t, i) get<i>(t)
#define tomax(a, b) ((a) = max((a), (b)))
#define tomin(a, b) ((a) = min((a), (b)))
#define topos(a) ((a) = (((a) % MOD + MOD) % MOD))
#define uni(a) a.resize(unique(iter(a)) - a.begin())
#define printv(a, b) {bool pvaspace=false; \
for(auto pva : a){ \
if(pvaspace) b << " "; pvaspace=true;\
b << pva;\
}\
b << "\n";}
using namespace std;
using namespace __gnu_pbds;
typedef long long ll;
typedef unsigned long long ull;
typedef long double ld;
using pii = pair<int, int>;
using pll = pair<ll, ll>;
using pdd = pair<ld, ld>;
using tiii = tuple<int, int, int>;
const ll MOD = 1000000007;
const ll MAX = 1LL << 60;
template<typename A, typename B>
ostream& operator<<(ostream& o, pair<A, B> p){
return o << '(' << p.F << ',' << p.S << ')';
}
ll ifloor(ll a, ll b){
if(b < 0) a *= -1, b *= -1;
if(a < 0) return (a - b + 1) / b;
else return a / b;
}
ll iceil(ll a, ll b){
if(b < 0) a *= -1, b *= -1;
if(a > 0) return (a + b - 1) / b;
else return a / b;
}
int n;
vector<ll> p, d, s;
ll c;
vector<ll> discr;
vector<ll> tmp;
vector<ll> pos;
int lowbit(int x){
return x & -x;
}
struct event{
ll x, y1, y2, ty;
bool operator<(event b){
return x < b.x;
}
};
bool check(ll t){
//cerr << "check " << t << "\n";
ll y1 = -MAX, y2 = MAX;
ll x1 = -MAX, x2 = MAX;
vector<pll> dq;
for(int a = n - 1; a >= 0; a--){
ll X = t - d[a] - c;
//cerr << "test " << a << " : " << p[a] - d[a] << " " << p[a] + d[a] << " " << t + p[a] - d[a] << "\n";
//printv(dq, cerr);
if(!dq.empty() && dq.front().S > t + p[a] - d[a]){
auto it = lower_bound(iter(dq), mp(0, t + p[a] - d[a]), [&](pll x, pll y){
return x.S > y.S;
} );
it--;
//cerr << "tmp " << dq.front().S << " " << it->F << "\n";
ll mny = -X + dq.front().S;
ll mxy = X + it->F;
if(mny > mxy) return false;
mny *= 2;
mxy *= 2;
ll midx = p[a] * 2;
ll midy = (mny + mxy) / 2;
ll r = mxy - midy;
ll mnx = midx - r;
ll mxx = midx + r;
//cerr << "rect " << midx << " " << midy << " " << r << "\n";
x1 = max(x1, mnx - midy);
x2 = min(x2, mxx - midy);
y1 = max(y1, mnx + midy);
y2 = min(y2, mxx + midy);
}
while(!dq.empty() && dq.back().S <= p[a] + d[a]) dq.pob;
if(dq.empty() || p[a] - d[a] < dq.back().F) dq.eb(mp(p[a] - d[a], p[a] + d[a]));
}
//cerr << "ok\n";
//cerr << "range " << x1 << " " << x2 << " " << y1 << " " << y2 << "\n";
if(x1 > x2 || y1 > y2) return false;
int b = n - 1;
for(int a = 0; a < n; a++){
ll x = p[a] * 2;
ll mny = max(y1 - x, x - x2);
ll mxy = min(y2 - x, x - x1);
while(b < n - 1 && p[b] * 2 < mny) b++;
while(b > 0 && p[b - 1] * 2 >= mny) b--;
if(p[b] * 2 >= mny && p[b] * 2 <= mxy) return true;
}
return false;
}
ll find_shortcut(int _n, vector<int> len, vector<int> _d, int _c){
n = _n;
c = _c;
p.resize(n);
s.resize(n);
d.resize(n);
for(int i = 0; i < n; i++) d[i] = _d[i];
for(int i = 0; i < n - 1; i++){
p[i + 1] = p[i] + len[i];
}
for(int i = 0; i < n; i++){
s[i] = p[i] + d[i];
}
discr = s;
tmp.resize(n);
pos.resize(n);
iota(iter(tmp), 0);
sort(iter(tmp), [&](int x, int y){ return s[x] < s[y]; });
for(int i = 0; i < n; i++){
pos[tmp[i]] = i;
}
lsort(discr);
ll l = 1, r = (ll)(1e9 + 5) * n + (ll)2e9 + 5;
while(l < r){
ll m = (l + r) / 2;
if(check(m)) r = m;
else l = m + 1;
}
return l;
}
