#pragma GCC optimize("O1,O2,O3,Ofast,unroll-loops")
#include "dungeons.h"
#include <bits/stdc++.h>
#include <string>
#include <iostream>
#include <cmath>
#include <numeric>
using namespace std;
typedef long long ll;
typedef unsigned long long ull;
typedef long double ld;
typedef pair<int, int> pi;
typedef pair<int, int> pl;
typedef pair<ld, ld> pd;
typedef vector<int> vi;
typedef vector<bool> vb;
typedef vector<vector<int>> vvi;
typedef vector<vector<ll>> vvl;
typedef vector<ld> vd;
typedef vector<ll> vl;
typedef vector<pi> vpi;
typedef vector<pl> vpl;
#define FOR(i, a, b) for (int i = a; i < (b); i++)
#define F0R(i, a) for (int i = 0; i < (a); i++)
#define FORd(i, a, b) for (int i = (b)-1; i >= a; i--)
#define F0Rd(i, a) for (int i = (a)-1; i >= 0; i--)
#define trav(a, x) for (auto &a : x)
#define uid(a, b) uniform_int_distribution<int>(a, b)(rng)
#define len(x) (int)(x).size()
#define mp make_pair
#define pb push_back
#define F first
#define nl endl
#define S second
#define lb lower_bound
#define ub upper_bound
#define aint(x) x.begin(), x.end()
#define raint(x) x.rbegin(), x.rend()
#define ins insert
const int MOD = 1000000007;
vi S,P,W,L,x;
vl dist;
vvl lost_pos,lost_hp;
int N;
ll INF = 1e18+10;
void init(int n, std::vector<int> s, std::vector<int> p, std::vector<int> w, std::vector<int> l) {
S = s;
P = p;
W = w;
L = l;
N = n;
dist = vl(n+1,-1);
dist[n] = 0;
lost_pos = vvl(n,vl(log2(n)+5,n-1));
lost_hp = vvl(n,vl(log2(n)+5,INF));
for(int i = n-1;i>=0;i--){
dist[i] = dist[W[i]] + 1;
}
FOR(i,0,n){
lost_pos[i][0] = L[i];
lost_hp[i][0] = P[i];
}
FOR(i,1,log2(n)+1){
FOR(j,0,n){
if(lost_hp[lost_pos[j][i-1]][i-1] == INF || lost_hp[j][i-1] == INF)continue;
lost_pos[j][i] = lost_pos[lost_pos[j][i-1]][i-1];
lost_hp[j][i] = lost_hp[lost_pos[j][i-1]][i-1] + lost_hp[j][i-1];
}
}
// cout << "###############" << endl;
// FOR(i,0,log2(n)+1){
// FOR(j,0,n){
// cout << lost_pos[j][i] << " ";
// }cout << endl;
// }cout << endl;
// FOR(i,0,log2(n)+1){
// FOR(j,0,n){
// cout << lost_hp[j][i] << " ";
// }cout << endl;
// }cout << endl;
// cout << "###############" << endl;
}
long long simulate(int x, int z) {
if(x == N)return z;
if(z < S[x]){
int pos = upper_bound(lost_hp[x].begin(),lost_hp[x].end(),S[x]-z) - lost_hp[x].begin();
if(pos == 0)return z+lost_hp[x][0]+S[x]*(dist[x]);
return simulate(lost_pos[x][pos-1],z+lost_hp[x][pos-1]);
}
return z+S[x]*(dist[x]);
}
