#include "tree.h"
#include <bits/stdc++.h>
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>
#define ll long long
#define ld long double
#define ull unsigned long long
#define ff first
#define ss second
#define pii pair<int,int>
#define pll pair<long long, long long>
#define vi vector<int>
#define vl vector<long long>
#define pb push_back
#define rep(i, b) for(int i = 0; i < (b); ++i)
#define rep2(i,a,b) for(int i = a; i <= (b); ++i)
#define rep3(i,a,b,c) for(int i = a; i <= (b); i+=c)
#define count_bits(x) __builtin_popcountll((x))
#define all(x) (x).begin(),(x).end()
#define siz(x) (int)(x).size()
#define forall(it,x) for(auto& it:(x))
using namespace __gnu_pbds;
using namespace std;
typedef tree<int, null_type, less<int>, rb_tree_tag,tree_order_statistics_node_update> ordered_set;
//mt19937 mt;void random_start(){mt.seed(chrono::time_point_cast<chrono::milliseconds>(chrono::high_resolution_clock::now()).time_since_epoch().count());}
//ll los(ll a, ll b) {return a + (mt() % (b-a+1));}
vi sons[200001];
int P[200001];
ll W[200001];
vl K[200001];
ll Z[200001];
bool is_leaf[200001];
bool used[200001];
int rep_[200001];
int leafs[200001];
int n;
ll leafs_cnt;
ll Ld[1000001];
ll Rd[1000001];
int cur_k[200001];
vector<pll> events[1000001];
int fint(int v)
{
if(rep_[v] == v) return v;
rep_[v] = fint(rep_[v]);
return rep_[v];
}
void onion(int a, int b)
{
a = fint(a);
b = fint(b);
rep_[b] = a;
leafs[a] += leafs[b]-1;
}
void init(vi P2, vi W2)
{
n = siz(P2);
rep(i,n)
{
P[i] = P2[i];
W[i] = W2[i];
sons[P[i]].pb(i);
rep_[i] = i;
is_leaf[i] = 1;
}
rep(i,n) is_leaf[P[i]] = 0;
rep(i,n) leafs[P[i]]++;
rep(i,n) if(is_leaf[i]) leafs_cnt += W[i];
vector<pll> v_sort;
rep(i,n) if(!is_leaf[i]) v_sort.pb({W[i],i});
sort(all(v_sort));
reverse(all(v_sort));
forall(it,v_sort)
{
int v = it.ss;
used[v] = 1;
forall(it,sons[v])
{
if(used[it]) K[v].pb(leafs[fint(it)]);
else K[v].pb(1);
}
Z[v] = (P[v] != -1 ? (used[P[v]] ? leafs[fint(P[v])]-1 : 0):0);
forall(it,sons[v])
{
if(used[it])
{
onion(v,it);
}
}
if(P[v] != -1 && used[P[v]])
{
onion(P[v],v);
}
}
ll cur_L = 0;
ll cur_R = 0;
rep(i,n)
{
if(is_leaf[i]) continue;
cur_R += W[i] * siz(K[i]);
cur_L -= W[i];
ll sk = 0;
forall(it,K[i])
{
sk += it;
events[it].pb({it*W[i],-W[i]});
}
events[Z[i]+1].pb({(1+Z[i])*W[i],-W[i]});
events[max(K[i].back(),Z[i]+sk)].pb({-(Z[i]+sk) * W[i],W[i]});
}
rep2(d,1,1000000)
{
forall(it,events[d])
{
cur_L += it.ff;
cur_R += it.ss;
}
Ld[d] = cur_L;
Rd[d] = cur_R;
}
}
ll query(int L, int R)
{
int d = R/L;
return leafs_cnt*L + Ld[d] * L + Rd[d] * R;
}
