#include "dungeons.h"
#include <bits/stdc++.h>
using namespace std;
using ll = long long;
vector<int> S, P, W, L;
int N;
const int MAXN = 5e4 + 1;
vector<int> adj[MAXN + 1];
int lift[6][MAXN + 1][20];
ll to_root[MAXN + 1];
ll cost[6][MAXN + 1][20];
vector<int> vals;
void init(int n, std::vector<int> s, std::vector<int> p, std::vector<int> w, std::vector<int> l) {
N = n;
S = s;
P = p;
W = w;
L = l;
S.push_back(0);
for (int i = 0; i <= n; ++i) {
vals.push_back(S[i]);
}
sort(begin(vals), end(vals));
vals.erase(unique(begin(vals), end(vals)), end(vals));
// cout << vals.size() << endl;
for (int i = 0; i < n; ++i) {
adj[w[i]].push_back(i);
}
auto dfs = [&](auto& dfs, int i, ll now) -> void {
now += S[i];
to_root[i] = now;
for (auto& u : adj[i]) {
dfs(dfs, u, now);
}
};
dfs(dfs, n, 0);
// for (int i = 0; i < n; ++i) {
// cerr << cost[i] << " ";
// }
// cerr << "\n";
for (int i = 0; i <= n; ++i) {
for (int j = 0; j < 20; ++j) {
for (int k = 0; k < 6; ++k) {
lift[k][i][j] = -1;
cost[k][i][j] = 1e18;
}
}
}
// for (int i = 0; i < n; ++i) {
// if (cycle[i]) {
// cerr << i << " ";
// }
// }
// cerr << "\n";
for (int i = 0; i < n; ++i) {
for (int k = 0; k < vals.size(); ++k) {
if (vals[k] < S[i]) {
lift[k][i][0] = L[i];
cost[k][i][0] = P[i];
} else {
lift[k][i][0] = W[i];
cost[k][i][0] = S[i];
}
}
}
for (int j = 1; j < 20; ++j) {
for (int i = 0; i < n; ++i) {
for (int k = 0; k < 6; ++k) {
if (lift[k][i][j - 1] == -1) continue;
// cerr << i << "!\n";
lift[k][i][j] = lift[k][lift[k][i][j - 1]][j - 1];
cost[k][i][j] = cost[k][i][j - 1] + cost[k][lift[k][i][j - 1]][j - 1];
}
}
}
// for (int k = 0; k < (int)vals.size(); ++k) {
// cout << k << ":\n";
// for (int j = 0; j < 5; ++j) {
// for (int i = 0; i <= n; ++i) {
// cout << lift[k][i][j] << " ";
// }
// cout << "\n";
// }
// }
// for (int k = 0; k < (int)vals.size(); ++k) {
// cout << k << ":\n";
// for (int j = 0; j < 5; ++j) {
// for (int i = 0; i <= n; ++i) {
// cout << cost[k][i][j] << " ";
// }
// cout << "\n";
// }
// }
// for (int j = 0; j < 5; ++j) {
// for (int i = 0; i <= n; ++i) {
// cout << cost1[i][j] << " ";
// }
// cout << "\n";
// }
// for (int i = 0; i <= n; ++i) {
// cout << cycle[i] << " ";
// }
// cout << "\n";
return;
}
long long simulate(int x, int z) {
ll res = z;
ll tot = 0;
// cout << x << " -> ";
int k = 0;
while (k < vals.size() && res >= vals[k]) k += 1;
// cout << k << " " << res << " " << vals[k] << "\n";
while (k < vals.size() && res < vals[k] && x != N) {
int nk = k - 1;
for (int i = 19; i >= 0; --i) {
if (lift[nk][x][i] == -1) continue;
if (cost[nk][x][i] + res >= vals[k]) continue;
res += cost[nk][x][i];
x = lift[nk][x][i];
}
if (x == N) break;
res += cost[nk][x][0];
x = lift[nk][x][0];
while (k < vals.size() && res >= vals[k]) k += 1;
}
res += to_root[x];
return res;
}
