#include <bits/stdc++.h>
#include "tree.h"
using namespace std;
using ll = long long;
const int mxN = 2e5+10;
vector<int> adj[mxN];
ll w[mxN], st[4*mxN], lazy[4*mxN], st1[mxN*4], lazy1[mxN*4];
int tin[mxN], tout[mxN], timer = -1, n;
set<array<int, 2>> mn[mxN];
ll ans = 0, l, r;
void build(int node, int l, int r) {
if(l == r) {
st[node] = 0; lazy[node] = 0; st1[node] = 0;
return ;
}
int mid = (l+r)/2;
build(node*2, l, mid);
build(node*2+1, mid+1, r);
}
void dfs(int node, int p) {
tin[node] = ++timer;
for(auto it : adj[node]) {
if(it == p) continue;
dfs(it, node);
}
tout[node] = timer;
}
void push(int node, int l, int r, int flag) {
if(l == r) return ;
if(flag == 0) {
lazy[node*2] += lazy[node];
lazy[node*2+1] += lazy[node];
st[node*2] += lazy[node];
st[node*2+1] += lazy[node];
lazy[node] = 0;
}
else {
lazy1[node*2] += lazy1[node];
lazy1[node*2+1] += lazy1[node];
st1[node*2] += lazy1[node];
st1[node*2+1] += lazy1[node];
lazy1[node] = 0;
}
}
int qry1(int node, int l, int r, int l1, int r1) {
push(node, l, r, 1);
if(l1 <= l && r <= r1) return st1[node];
if(l1 > r || r1 < l) return 0;
int mid = (l+r)/2;
return qry1(node*2, l, mid, l1, r1) + qry1(node*2+1, mid+1, r, l1, r1);
}
int qry(int node, int l, int r, int l1, int r1) {
push(node, l, r, 0);
if(l1 <= l && r <= r1) return st[node];
if(l1 > r || r1 < l) return 0;
int mid = (l+r)/2;
return qry(node*2, l, mid, l1, r1) + qry(node*2+1, mid+1, r, l1, r1);
}
void upd1(int node, int l, int r, int l1, int r1, int x) {
push(node, l, r, 1);
if(l1 <= l && r <= r1) {
st1[node] += x;
lazy1[node] += x;
return ;
}
if(l1 > r || r1 < l) return ;
int mid = (l+r)/2;
upd1(node*2, l, mid, l1, r1, x);
upd1(node*2+1, mid+1, r, l1, r1, x);
st1[node] = st1[node*2] + st1[node*2+1];
}
void upd(int node, int l, int r, int l1, int r1, int x) {
push(node, l, r, 0);
if(l1 <= l && r <= r1) {
st[node] += x;
lazy[node] += x;
return ;
}
if(l1 > r || r1 < l) return ;
int mid = (l+r)/2;
upd(node*2, l, mid, l1, r1, x);
upd(node*2+1, mid+1, r, l1, r1, x);
st[node] = st[node*2] + st[node*2+1];
}
void dfs1(int node, int p) {
if(adj[node].size() == 0) {
ans += w[node] * l;
upd(1, 0, timer+1, tin[node], tin[node], l);
return ;
}
mn[node].insert({w[node], node});
for(auto it : adj[node]) {
if(it == p) continue;
dfs1(it, node);
if(mn[it].size() > mn[node].size()) swap(mn[it], mn[node]);
for(auto it1 : mn[it]) {
mn[node].insert(it1);
}
mn[it].clear();
}
int cnt = qry(1, 0, timer+1, tin[node], tout[node]);
while(cnt > r) {
array<int, 2> now = *(mn[node].begin());
int del = qry1(1, 0, timer+1, tin[now[1]], tin[now[1]]);
if(del > 0) {
mn[node].erase(mn[node].begin());
continue;
}
int k = qry(1, 0, timer+1, tin[now[1]], tout[now[1]]);
int mx = k-l;
int needed = cnt-r;
if(mx >= needed) {
cnt = r;
ans += now[0] * needed;
upd(1, 0, timer+1, tin[now[1]], tin[now[1]], -needed);
}
else {
cnt -= mx;
ans += now[0] * mx;
upd(1, 0, timer+1, tin[now[1]], tin[now[1]], -mx);
upd1(1, 0, timer+1, tin[now[1]], tout[now[1]], 1);
mn[node].erase(mn[node].begin());
}
}
}
void init(vector<int> P, vector<int> W) {
n = P.size();
for(int i = 0; i < n; i++) w[i] = W[i];
for(int i = 1; i < n; i++) {
adj[P[i]].push_back(i);
}
dfs(0, -1);
}
ll query(int L, int R) {
ans = 0; l = L; r = R;
for(int i = 0; i < n; i++) {
mn[i].clear();
}
build(1, 0, timer+1);
dfs1(0, -1);
return ans;
}
/*int main()
{
//init({-1, 0, 0}, {1, 1, 1});
init({-1, 0, 0, 1, 1, 1, 2, 2, 2}, {2, 3, 1, 4, 4, 3, 3, 3, 1});
cout << query(1, 1) << ' ' << query(1, 2) << ' ' << query(3, 5);
cout << ' ' << query(5, 10);
}*/
