#include "shortcut.h"
#include <bits/stdc++.h>
using namespace std;
const int N = 1000005;
const long long INF = 2e15;
int n, c;
int b[N];
int mn[N][2], mx[N][2];
bool visit[N];
long long a[N];
pair<long long, int> vec1[N], vec2[N];
bool check(long long dis) {
long long mn1, mx1, mn2, mx2;
mn1 = mn2 = -INF, mx1 = mx2 = INF;
int ptr = 0;
int opt[2][2];
memset(opt, -1, sizeof opt);
for (int i = 0; i < n; ++i) {
while (ptr < n && vec1[i].first - vec2[ptr].first > dis) {
int id = vec2[ptr].second;
if (opt[0][0] == -1 || a[opt[0][0]] + b[opt[0][0]] < a[id] + b[id]) {
opt[0][1] = opt[0][0], opt[0][0] = id;
}
else if (opt[0][1] == -1 || a[opt[0][1]] + b[opt[0][1]] < a[id] + b[id]) {
opt[0][1] = id;
}
if (opt[1][0] == -1 || b[opt[1][0]] - a[opt[1][0]] < b[id] - a[id]) {
opt[1][1] = opt[1][0], opt[1][0] = id;
}
else if (opt[1][1] == -1 || b[opt[1][1]] - a[opt[1][1]] < b[id] - a[id]) {
opt[1][1] = id;
}
ptr++;
}
int id = vec1[i].second;
int p0 = opt[0][0] == id ? opt[0][1] : opt[0][0];
int p1 = opt[1][0] == id ? opt[1][1] : opt[1][0];
if (p0 != -1) {
mn1 = max(mn1, -(dis - c) + (a[id] + b[id]) + (a[p0] + b[p0]));
mx2 = min(mx2, (dis - c) + (a[id] - b[id]) - (a[p0] + b[p0]));
}
if (p1 != -1) {
mn2 = max(mn2, -(dis - c) + (a[id] + b[id]) + (b[p1] - a[p1]));
mx1 = min(mx1, (dis - c) + (a[id] - b[id]) - (b[p1] - a[p1]));
}
}
// cout << mn1 << ' ' << mx1 << ' ' << mn2 << ' ' << mx2 << '\n';
ptr = -1;
for (int i = n - 1; i >= 0; --i) {
while (ptr + 1 < n && a[ptr + 1] <= mx1 - a[i]) ptr++;
mx[i][0] = ptr;
}
ptr = -1;
for (int i = 0; i < n; ++i) {
while (ptr + 1 < n && a[ptr + 1] <= a[i] - mn2) ptr++;
mx[i][1] = ptr;
}
ptr = n;
for (int i = 0; i < n; ++i) {
while (ptr - 1 >= 0 && a[ptr - 1] >= mn1 - a[i]) ptr--;
mn[i][0] = ptr;
}
ptr = n;
for (int i = n - 1; i >= 0; --i) {
while (ptr - 1 >= 0 && a[ptr - 1] >= a[i] - mx2) ptr--;
mn[i][1] = ptr;
}
for (int i = 0; i < n; ++i) {
if (max(mn[i][0], mn[i][1]) <= min(mx[i][0], mx[i][1])) return 1;
}
return 0;
}
long long find_shortcut(int _n, vector<int> l, vector<int> d, int _c) {
n = _n, c = _c;
for (int i = 1; i < n; ++i) {
a[i] = a[i - 1] + l[i - 1];
}
for (int i = 0; i < n; ++i) b[i] = d[i];
for (int i = 0; i < n; ++i) {
vec1[i] = {a[i] + b[i], i};
vec2[i] = {a[i] - b[i], i};
}
sort(vec1, vec1 + n);
sort(vec2, vec2 + n);
long long low = 0, high = INF;
while (low < high) {
long long mid = (low + high) >> 1;
if (check(mid)) high = mid; else low = mid + 1;
}
return low;
}
