#include "dungeons.h"
#include <bits/stdc++.h>
using namespace std;
#pragma GCC optimize("O3")
typedef long long ll;
typedef long double ld;
#define sp <<" "<<
#define endl "\n"
const int MAXN = 4e5+5;
const int LOGN = 25;
int N;
vector<int> S, P, W, L, end, par;
vector<ll> trav, dep;
vector<vector<pair<int, int>>> adj;
vector<vector<int>> up;
vector<vector<ll>> sum;
int find(int u) {
if (u == par[u]) return u;
return par[u] = find(par[u]);
}
void unite(int u, int v) {
u = find(u), v = find(v);
if (u == v) return;
if (dep[u] > dep[v]) swap(u, v);
par[v] = u;
}
void init(int n, vector<int> s, vector<int> p, vector<int> w, vector<int> l) {
N = n, S = s, P = p, W = w, L = l;
trav.resize(N+1), adj.resize(N+1), dep.resize(N+1), par.resize(N+1);
up.assign(LOGN, vector<int>(N+1));
sum.assign(LOGN, vector<ll>(N+1));
iota(par.begin(), par.end(), 0);
using edge = tuple<ll, int, int>;
vector<edge> edges;
for (int i = 0; i < N; i++) {
adj[W[i]].emplace_back(i, S[i]);
edges.emplace_back(S[i], i, W[i]);
}
sort(edges.begin(), edges.end());
auto pre = [&](auto &&pre, int u, int p) -> void {
for (auto &[v, w] : adj[u]) {
if (v != p) {
trav[v] = trav[u] + w;
dep[v] = dep[u] + 1;
pre(pre, v, u);
}
}
};
pre(pre, N, -1);
vector<bool> proc(N+1);
int lo = 0, hi = 0;
while (lo < N) {
hi = lo;
while (hi < N and get<0>(edges[lo]) == get<0>(edges[hi])) hi++;
for (int i = lo; i < hi; i++) {
auto [w, u, v] = edges[i];
if (proc[u] or proc[v] or u == N or v == N) continue;
unite(u, v);
}
for (int i = lo; i < hi; i++) {
auto [w, u, v] = edges[i];
proc[u] = proc[v] = true;
}
lo = hi;
}
for (int i = 0; i <= N; i++) {
up[0][i] = (i != N ? L[i] : N);
sum[0][i] = (i != N ? P[i] : 0);
}
for (int j = 1; j < LOGN; j++) {
for (int i = 0; i <= N; i++) {
up[j][i] = up[j-1][ up[j-1][i] ];
sum[j][i] = sum[j-1][i] + sum[j-1][ up[j-1][i] ];
}
}
return;
}
ll simulate(int x, int z) {
ll at = x, ans = z;
cerr << endl << endl << endl;
while (true) {
for (int j = LOGN-1; j >= 0; j--) {
// cerr << at sp ans sp sum[j][at] sp S[find(at)] << endl;
if (up[j][at] != N and ans + sum[j][at] < S[find(at)]) {
ans += sum[j][at];
at = up[j][at];
}
}
// cerr << at sp ans << endl;
if (up[0][at] == N or ans < S[find(at)]) {
ans += sum[0][at];
at = up[0][at];
}
if (at == N) return trav[at] + ans;
if (ans >= S[find(at)]) {
ans += S[at];
at = W[at];
}
}
return trav[at] + ans;
}
