#include <bits/stdc++.h>
//#include "grader.cpp"
#include "dungeons.h"
using namespace std;
typedef long long ll;
const int N = 4e5 + 500;
ll sum_lose[N][30];
ll sum_win[N][30];
ll need_lose[N][30];
ll need_win[N][30];
int up_lose[N][30], up_win[N][30];
int n;
void init(int _n, vector <int> s, vector <int> p, vector <int> w, vector <int> l) {
n = _n;
for (int i = 0; i < n; i++) {
need_lose[i][0] = s[i]; need_win[i][0] = s[i];
sum_lose[i][0] = p[i]; sum_win[i][0] = s[i];
up_lose[i][0] = l[i]; up_win[i][0] = w[i];
}
for (int st = 1; st < 30; st++) {
for (int i = 0; i < n; i++) {
if (up_lose[i][st - 1] != n) {
int to = up_lose[i][st - 1];
need_lose[i][st] = min(need_lose[i][st - 1], need_lose[to][st - 1] - sum_lose[i][st - 1]);
sum_lose[i][st] = sum_lose[i][st - 1] + sum_lose[to][st - 1];
up_lose[i][st] = up_lose[to][st - 1];
} else {
up_lose[i][st] = n;
sum_lose[i][st] = sum_lose[i][st - 1];
need_lose[i][st] = need_lose[i][st - 1];
}
if (up_win[i][st - 1] != n) {
int to = up_win[i][st - 1];
need_win[i][st] = max(need_win[i][st - 1], need_win[to][st - 1] - sum_win[i][st - 1]);
sum_win[i][st] = sum_win[i][st - 1] + sum_win[to][st - 1];
up_win[i][st] = up_win[to][st - 1];
} else {
up_win[i][st] = n;
sum_win[i][st] = sum_win[i][st - 1];
need_win[i][st] = need_win[i][st - 1];
}
}
}
}
long long simulate(int x, int start) {
long long z = start;
while (x != n) {
for (int st = 29; st >= 0 && x != n; st--) {
if (z < need_lose[x][st]) {
z += sum_lose[x][st];
x = up_lose[x][st];
}
}
for (int st = 29; st >= 0 && x != n; st--) {
if (z >= need_win[x][st]) {
z += sum_win[x][st];
x = up_win[x][st];
}
}
}
return z;
}
