#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, dep;
vector<vector<int>> adj, up;
vector<vector<ll>> sum;
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;
dep.resize(N+1), adj.resize(N+1);
up.assign(LOGN, vector<int>(N+1));
sum.assign(LOGN, vector<ll>(N+1));
for (int i = 0; i < N; i++) {
adj[W[i]].push_back(i);
}
auto dfs = [&](auto &&dfs, int u, int p) -> void {
for (auto &v : adj[u]) {
if (v != p) {
dep[v] = dep[u] + 1;
dfs(dfs, v, u);
}
}
};
dfs(dfs, N, -1);
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;
for (int j = LOGN-1; j >= 0; j--) {
if (up[j][at] != N and ans + sum[j][at] < S[at]) {
ans += sum[j][at];
at = up[j][at];
}
}
if (ans >= S[at]) return 1LL * dep[at] * S[at] + ans;
ans += sum[0][at];
at = up[0][at];
if (!(ans >= S[at] or at == N)) {
cerr << x sp z sp ans sp S[at] sp at sp N << endl;
}
assert(ans >= S[at] or at == N);
return 1LL * dep[at] * S[at] + ans;
}
