#include "shortcut.h"
#include <bits/stdc++.h>
using namespace std;
#define ff first
#define ss second
#define bl ' '
#define endl '\n'
#define all(v) (v).begin(), (v).end()
#define comp(v) (v).erase(unique(all(v)), (v).end())
#define lbd(v,x) lower_bound(all(v), (x))-(v).begin()
#define ubd(v,x) upper_bound(all(v), (x))-(v).begin()
typedef long long ll;
typedef pair<int, int> pi;
typedef pair<pi, int> pii;
typedef pair<int, pi> ipi;
typedef pair<pi, pi> pipi;
typedef pair<ll, ll> pll;
const int MAXN = 100100*10;
const ll MOD = 998244353;
const ll INF = 2e9;
ll sum[MAXN], w[MAXN];
int N, C;
vector<ll> v;
int sz;
struct MinSeg {
ll tree[MAXN*4];
void init() {
fill(tree, tree+4*N, LLONG_MAX);
}
void update(int node, int s, int e, int idx, ll val) {
if(idx < s || e < idx) return;
if(s == e) {
tree[node] = min(tree[node], val);
return;
}
int mid = s+e>>1;
update(node<<1, s, mid, idx, val); update(node<<1|1, mid+1, e, idx, val);
tree[node] = min(tree[node<<1], tree[node<<1|1]);
}
ll solve(int node, int s, int e, int l, int r) {
if(e < l || r < s) return LLONG_MAX;
if(l <= s && e <= r) return tree[node];
int mid = s+e>>1;
return min(solve(node<<1, s, mid, l, r), solve(node<<1|1, mid+1, e, l, r));
}
} mnseg;
bool solve(ll L) {
ll mnsum, mxsum, mndif, mxdif;
mnsum = mndif = LLONG_MIN, mxsum = mxdif = LLONG_MAX;
mnseg.init(); ll mx = LLONG_MIN;
for(int i=0; i<N; i++) {
int it = lbd(v, sum[i]+w[i]);
mnseg.update(1, 0, sz-1, it, sum[i]-w[i]);
mx = max(mx, sum[i]+w[i]);
}
for(int i=N-2; i>=0; i--) {
int it = ubd(v, L+sum[i]-w[i]);
ll mn = mnseg.solve(1, 0, sz-1, it, sz-1);
if(mn != LLONG_MAX) {
mn += L-w[i]-C; mx += -L+w[i]+C;
mnsum = max(mnsum, sum[i]+mx); mxsum = min(mxsum, sum[i]+mn);
mndif = max(mndif, mx-sum[i]); mxdif = min(mxdif, mn-sum[i]);
mx -= -L+w[i]+C;
}
}
for(int i=0; i<N-1; i++) {
ll mn = max(mnsum-sum[i], mndif+sum[i]);
ll mx = min(mxsum-sum[i], mxdif+sum[i]);
int it = lower_bound(sum+i+1, sum+N, mn)-sum;
if(it < N && sum[it] <= mx) return true;
} return false;
}
long long find_shortcut(int n, std::vector<int> l, std::vector<int> d, int c)
{
for(int i=1; i<n; i++) sum[i] = sum[i-1]+l[i-1];
for(int i=0; i<n; i++) w[i]=d[i];
N = n, C = c;
for(int i=0; i<n; i++) v.push_back(w[i]+sum[i]);
sort(all(v)); comp(v); sz = v.size();
ll lb = 0, ub = 1e16, mid;
while(lb < ub) {
mid = lb+ub>>1;
if(solve(mid)) ub = mid;
else lb = mid+1;
}
return lb;
}
