#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;
vl dist;
int N;
vvl loop_ends,loop_sums;
void dfs(int start,int pos,ll sum){
if(sum >= S[0])return;
sum += P[pos];
loop_ends[start].pb(pos);
loop_sums[start].pb(sum);
dfs(start,L[pos],sum);
}
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);
loop_ends = vvl(n+1,vl());
loop_sums = vvl(n+1,vl());
dist[n] = 0;
for(int i = n-1;i>=0;i--){
dist[i] = dist[W[i]] + 1;
}
FOR(i,0,n){
dfs(i,i,0);
}
}
long long simulate(int x, int z) {
if(x == N)return z;
if(z < S[x]){
ll ans = z;
ll need = S[x] - z;
int n = loop_ends[x].size();
if(n<2)simulate(L[x],z+P[x]);
// if(need > loop_sums[x][n-2]){
// if(loop_ends[x][0] != loop_ends[x][n-2]){
// return simulate(loop_ends[x][n-2],z+loop_sums[x][n-2]);
// }
// ll counter = need/loop_sums[x][n-2];
// ans += loop_sums[x][n-2] * counter;
// need -= loop_sums[x][n-2] * counter;
// }
int pos = lower_bound(loop_sums[x].begin(),loop_sums[x].end(),need) - loop_sums[x].begin();
if(pos == n){
return simulate(loop_ends[x][n-1],ans+loop_sums[x][n-1]);
}
if(loop_sums[x][pos] > need){
return simulate(loop_ends[x][pos-1],ans+loop_sums[x][pos-1]);
}
return simulate(loop_ends[x][pos],ans+loop_sums[x][pos]);
}
return z+S[x]*(dist[x]);
}
