#include "tree.h"
#include<bits/stdc++.h>
#define ll long long
#define fi first
#define se second
using namespace std;
const ll N = 2e5 + 52;
bool chk , oko;
ll n;
ll ans , sml;
vector<int> p , w;
vector<ll> g[N] , t(4 * N , 0);
priority_queue<pair<ll , ll>> st[N];
ll in[N] , out[N] , tim , kur , sz;
set<ll> stp;
void update (ll v, ll l, ll r, ll j , ll x) {
if(r - l == 1 and l == j) t[v] = x;
else {
ll m = (l + r) / 2;
if (j < m) update (v * 2 , l, m, j , x);
else update (v * 2 + 1 , m , r , j , x);
t[v] = t[v * 2] + t[v * 2 + 1];
}
}
void gett(ll v, ll l, ll r , ll l1 , ll r1) {
if(l <= l1 and r >= r1) kur += t[v];
else {
ll m = (l1 + r1) / 2;
if(!(l1 >= r || m <= l)) {
gett(v * 2 , l , r , l1 , m);
}
if(!(m >= r || r1 <= l)) {
gett(v * 2 + 1 , l , r , m , r1);
}
}
}
void upd(ll p , ll x){
update(1 , 0 , sz , p , x);
}
ll get(ll l , ll r){
kur = 0;
gett(1 , l , r + 1 , 0 , sz);
return kur;
}
ll l , r , sum[N];
void dfs(ll v){
for(auto to : g[v]){
dfs(to);
}
for(auto to : g[v]){
if(st[to].size() > st[v].size()){
swap(st[v] , st[to]);
}
while(st[to].size()){
st[v].push(st[to].top());
st[to].pop();
}
}
st[v].push({-w[v] , v});
upd(in[v] , 0);
if(g[v].size() == 0){
upd(in[v] , l);
stp.erase(in[v]);
return ;
}
while(get(in[v] , out[v]) > r){
auto u = st[v].top().se;
auto ww = st[v].top().fi;
st[v].pop();
if(stp.find(in[u]) == stp.end()){
continue ;
}
ll val = min(get(in[u] , out[u]) - l , get(in[v] , out[v]) - r);
ans += val * (-ww);
upd(in[u] , get(in[u] , in[u]) - val);
if(get(in[u] , out[u]) == l){
while(stp.lower_bound(in[u]) != stp.end() and (*stp.lower_bound(in[u])) <= out[u]){
stp.erase(stp.lower_bound(in[u]));
}
}
else st[v].push({ww , u});
}
}
void dsfs(int v){
for(auto to : g[v]){
dsfs(to);
sum[v] += sum[to];
}
sum[v] = max(sum[v] , l);
if(oko){
ans += max(0ll , sum[v] - r) * w[v];
sum[v] = min(sum[v] , r);
return ;
}
}
void dffs(ll v){
in[v] = (++ tim);
for(auto to : g[v]){
dffs(to);
}
out[v] = tim;
}
void init(std::vector<int> P, std::vector<int> W) {
p = P , w = W;
n = p.size();
chk = 1;
oko = 1;
for(ll i = 0;i < n; ++ i){
if(w[i] != 1) chk = false;
if(i) g[p[i]].push_back(i);
if(i) oko &= (w[p[i]] <= w[i]);
}
for(ll i = 0;i < n; ++ i){
if(g[i].size() == 0){
sml += w[i];
}
}
tim = -1;
dffs(0);
sz = n;
}
long long query(int L, int R) {
ans = 0;
l = L;
r = R;
if(! chk){
ans += L * sml;
if(oko){
for(int i = 0;i < n; ++ i) sum[i] = 0;
dsfs(0);
return ans;
}
while(st[0].size()) st[0].pop();
for(ll i = 0;i < n; ++ i) stp.insert(i);
dfs(0);
}
else{
//cout << sml << ' ';
ans = L * sml + max(0ll , L * sml - R);
}
return ans;
}
