/*
Author of all code: Pedro BIGMAN Dias
Last edit: 15/02/2021
*/
#pragma GCC optimization ("O3")
#pragma GCC optimization ("unroll-loops")
#pragma GCC optimize("Ofast")
#include <iostream>
#include <vector>
#include <cmath>
#include <algorithm>
#include <string>
#include <map>
#include <unordered_map>
#include <set>
#include <unordered_set>
#include <queue>
#include <deque>
#include <list>
#include <iomanip>
#include <stdlib.h>
#include <time.h>
#include <cstring>
#include "dungeons.h"
using namespace std;
typedef long long int ll;
typedef unsigned long long int ull;
typedef long double ld;
#define REP(i,a,b) for(ll i=(ll) a; i<(ll) b; i++)
#define pb push_back
#define mp make_pair
#define pl pair<ll,ll>
#define ff first
#define ss second
#define whole(x) x.begin(),x.end()
#define DEBUG(i) cout<<"Pedro Is The Master "<<i<<endl
#define INF 500000000LL
#define EPS 0.00000001
#define pi 3.14159
#define VV(vvvv,NNNN,xxxx); REP(i,0,NNNN) {vvvv.pb(xxxx);}
ll mod=1000000007LL;
template<class A=ll>
void Out(vector<A> a) {REP(i,0,a.size()) {cout<<a[i]<<" ";} cout<<endl;}
template<class A=ll>
void In(vector<A> &a, ll N) {A cur; REP(i,0,N) {cin>>cur; a.pb(cur);}}
ll n; vector<ll> s,pp,w,l;
class Tree
{
public:
ll N;
vector<ll> p;
vector<vector<ll> > sons;
vector<vector<ll> > adj;
ll root;
vector<ll> val; vector<ll> sumto;
vector<vector<ll> > f; vector<vector<ll> > f2;
Tree() {N=0;}
Tree(vector<vector<ll> > ad, ll r=0LL)
{
N=ad.size(); root=r; adj=ad;
vector<ll> xx; REP(i,0,N) {sons.pb(xx); p.pb(-1); sumto.pb(0);}
DFS_Build(r,r); DFS_Sumto(root); REP(i,0,n) {val.pb(s[i]+sumto[i]);} val.pb(INF);
VV(xx,log2(N)+1,0); VV(f,N,xx); VV(f2,N,xx); Conf2(0); Conf(0);
}
void DFS_Build(ll s, ll par)
{
p[s]=par;
REP(i,0,adj[s].size())
{
if(adj[s][i]==par) {continue;}
sons[s].pb(adj[s][i]);
DFS_Build(adj[s][i],s);
}
return;
}
void DFS_Sumto(ll x)
{
if(x==n) {sumto[x]=0;}
else {sumto[x]=sumto[p[x]]+s[x];}
REP(i,0,sons[x].size()) {DFS_Sumto(sons[x][i]);}
}
void Conf2(ll e) //O(NlogN)
{
if((1LL<<e)>N) {return;}
if(e==0) {REP(i,0,N) {f2[i][e]=p[i];} Conf2(e+1);}
else
{
REP(i,0,N)
{
f2[i][e]=f2[f2[i][e-1]][e-1];
}
}
Conf2(e+1);
}
void Conf(ll e) //O(NlogN)
{
if((1LL<<e)>N) {return;}
if(e==0) {REP(i,0,n) {f[i][e]=val[i];} f[n][e]=INF;}
else
{
REP(i,0,N)
{
f[i][e]=max(f[i][e-1],f[f2[i][e-1]][e-1]);
}
}
Conf(e+1);
}
ll Stop(ll v, ll nnode)
{
ll node = nnode;
ll e = log2(N);
while(e>=0)
{
if(f[node][e]<=v) {node=f2[node][e];}
e--;
}
return node;
}
};
Tree T;
void init(int nn, vector<int> ss, vector<int> ppp, vector<int> ww, vector<int> lll)
{
n=(ll) nn; REP(i,0,n) {s.pb((ll) ss[i]); pp.pb((ll) ppp[i]); w.pb((ll) ww[i]); l.pb((ll) lll[i]);}
vector<vector<ll> > adj; VV(adj,n+1,{});
REP(i,0,n) {adj[i].pb(w[i]); adj[w[i]].pb(i);}
Tree XX(adj,n); T=XX;
return;
}
long long simulate(int x, int z)
{
while(1>0)
{
ll nxt = T.Stop(z+T.sumto[x],x);
if(nxt==n) {return (z+T.sumto[x]);}
z+=(T.sumto[x]-T.sumto[nxt]); z+=pp[nxt];
x=l[nxt];
}
}
