#include "tree.h"
#include <bits/stdc++.h>
using namespace std;
#define vi vector<int>
#define pb push_back
#define pii pair<int,int>
#define ff first
#define ss second
#define all(x) x.begin(),x.end()
#define ll long long int
const int N = 2e5+100;
int n;
vector<int> p, w;
multiset<array<ll, 2>> S[N];
vi g[N];
ll dp[N], sum[N], extra[N];
ll L, R;
void dfs(int v){
S[v].clear();
int big = -1;
sum[v] = 0;
extra[v] = 0;
dp[v] = 0;
for(int u: g[v]){
dfs(u);
extra[v] += extra[u];
if(big == -1 || S[u].size() > S[big].size()) big = u;
dp[v] += dp[u];
sum[v] += sum[u];
}
if(big == -1){
sum[v] = L;
dp[v] += L * w[v];
return;
}
S[v].swap(S[big]);
for(int u: g[v]){
if(u != big) for(auto x: S[u]) S[v].insert(x);
}
if(sum[v] <= L){
dp[v] += (L-sum[v]) * w[v];
sum[v] = L;
}else if(sum[v] <= R){
S[v].insert({w[v], sum[v] - L});
extra[v] += sum[v] - L;
}else{
ll dif = sum[v] - R;
while(dif && S[v].size()){
auto it = S[v].begin();
auto [W, P] = *it;
if(W > w[v]) break;
if(P <= dif){
extra[v] -= P;
dp[v] += W * P;
S[v].erase(it);
dif -= P;
}else{
extra[v] -= dif;
dp[v] += dif * W;
S[v].erase(it);
S[v].insert({W, P - dif});
dif = 0;
}
}
if(dif > 0){
dp[v] += w[v] * dif;
}
sum[v] = R;
S[v].insert({w[v], R-L});
extra[v] += R-L;
}
ll max_extra = sum[v] - L;
while(extra[v] > max_extra && S[v].size()){
auto it = prev(S[v].end());
auto [W, P] = *it;
if(extra[v] - P >= max_extra){
S[v].erase(it);
extra[v] -= P;
}else{
S[v].erase(it);
S[v].insert({W, P - (extra[v] - max_extra)});
extra[v] = max_extra;
}
}
}
void init(std::vector<int> P, std::vector<int> W) {
p = P;
w = W;
n = (int)p.size();
for(int i = 1; i < n; ++i) g[P[i]].pb(i);
}
long long query(int l, int r) {
L = l, R = r;
dfs(0);
return dp[0];
}
