#include "tree.h"
#include <bits/stdc++.h>
using namespace std;
using ll = long long;
int n;
vector<int> adj[200200];
ll a[200200];
void init(std::vector<int> P, std::vector<int> W) {
n = P.size();
for (int i=1;i<n;i++) adj[P[i]+1].push_back(i+1);
for (int i=0;i<n;i++) a[i+1] = W[i];
}
ll ofs[200200], len[200200];
priority_queue<array<ll, 2>, vector<array<ll, 2>>, greater<>> dp[200200];
void merge(int s, int v){
ofs[s] += ofs[v];
len[s] += len[v];
if (dp[s].size() < dp[v].size()) swap(dp[s], dp[v]);
while(!dp[v].empty()){
auto p = dp[v].top(); dp[v].pop();
dp[s].push(p);
}
}
void dfs(int s, int L, int R){
while(!dp[s].empty()) dp[s].pop();
ofs[s] = 0;
len[s] = 0;
if (adj[s].empty()){
ofs[s] = a[s] * L;
return;
}
for (auto &v:adj[s]){
dfs(v, L, R);
merge(s, v);
}
int d = adj[s].size();
ofs[s] += a[s] * L * (d - 1);
ofs[s] -= a[s] * (R-L);
len[s] += R-L;
dp[s].push({a[s], R-L});
while(len[s] > R-L){
auto [dy, cnt] = dp[s].top(); dp[s].pop();
ofs[s] += dy * cnt;
len[s] -= cnt;
if (len[s] >= R-L) continue;
ofs[s] -= dy * ((R-L) - len[s]);
len[s] = R-L;
dp[s].push({dy, (R-L) - len[s]});
break;
}
}
long long query(int L, int R) {
dfs(1, L, R);
return ofs[1];
}
