#include "tree.h"
#include <bits/stdc++.h>
using namespace std;
#define all(x) x.begin(), x.end()
#define sp << " " <<
#define inf 1000000000000000000LL
int N;
vector<int> parent;
vector<vector<int>> childs;
vector<long long> weights;
vector<int> leafsize;
vector<array<long long, 3>> searchspace;
vector<int> eulerstart, eulerend;
int timer = -1;
class Mintre{
private:
vector<array<long long, 2>> tre;
vector<long long> lazy;
int size;
void _update(int ind, long long a, long long b, int l, int r, int s){
a -= lazy[s];
if (r < ind || l > ind)
return;
if (l == r){
tre[s][0] = a;
tre[s][1] = b;
return;
}
int m = (l + r) >> 1;
_update(ind, a, b, l, m, s << 1);
_update(ind, a, b, m + 1, r, (s << 1) | 1);
tre[s] = min(tre[s << 1], tre[(s << 1) | 1]);
tre[s][0] += lazy[s];
}
void _add(int tl, int tr, int a, int l, int r, int s){
if (r < tl || l > tr)
return;
if (tl <= l && r <= tr){
lazy[s] = a;
tre[s] = min(tre[s << 1], tre[(s << 1) | 1]);
tre[s][0] += lazy[s];
return;
}
int m = (l + r) >> 1;
_add(tl, tr, a, l, m, s << 1);
_add(tl, tr, a, m + 1, r, (s << 1) | 1);
tre[s] = min(tre[s << 1], tre[(s << 1) | 1]);
tre[s][0] += lazy[s];
}
array<long long, 2> _query(int tl, int tr, int l, int r, int s){
if (r < tl || l > tr)
return { inf, -1 };
if (tl <= l && r <= tr){
return tre[s];
}
int m = (l + r) >> 1;
auto f = min(_query(tl, tr, l, m, s << 1), _query(tl, tr, m + 1, r, (s << 1) | 1));
f[0] += lazy[s];
return f;
}
public:
void init(int sz){
size = sz;
tre.resize(sz * 4);
lazy.resize(sz * 4);
}
void update(int x, long long a, long long b){
_update(x, a, b, 0, size, 1);
}
void add(int l, int r, int a){
_add(l, r, a, 0, size, 1);
}
array<long long, 2> query(int l, int r){
return _query(l, r, 0, size, 1);
}
};
class Addtre{
private:
vector<int> tre;
int size;
void _update(int ind, int a, int l, int r, int s){
if (r < ind || l > ind)
return;
if (l == r){
tre[s] += a;
return;
}
int m = (l + r) >> 1;
_update(ind, a, l, m, s << 1);
_update(ind, a, m + 1, r, (s << 1) | 1);
tre[s] = tre[s << 1] + tre[(s << 1) | 1];
}
int _query(int tl, int tr, int l, int r, int s){
if (r < tl || l > tr)
return 0;
if (tl <= l && r <= tr){
return tre[s];
}
int m = (l + r) >> 1;
return _query(tl, tr, l, m, s << 1) + _query(tl, tr, m + 1, r, (s << 1) | 1);
}
public:
void init(int sz){
size = sz;
tre.resize(sz * 4);
}
void update(int x, int a){
_update(x, a, 0, size, 1);
}
int query(int l, int r){
return _query(l, r, 0, size, 1);
}
};
Addtre Sleafs;
Mintre Sweights;
void dfs(int a){
timer++;
eulerstart[a] = timer;
Sweights.update(eulerstart[a], weights[a], a);
if (!childs[a].size()){
eulerend[a] = timer;
Sleafs.update(eulerstart[a], 1);
return;
}
leafsize[a] = 0;
for (auto u : childs[a]){
dfs(u);
leafsize[a] += leafsize[u];
}
eulerend[a] = timer;
}
void solve(int a, int d){
Sweights.update(eulerstart[a], inf, -1);
if (childs[a].size() == 0){
searchspace[N - 1][0] += 1;
return;
}
if (a == 0){
while (Sweights.query(eulerstart[a] + 1, eulerend[a])[0] < 1e9){
solve(Sweights.query(eulerstart[a] + 1, eulerend[a])[1], Sleafs.query(eulerstart[a], eulerend[a]));
}
int l = Sleafs.query(eulerstart[a], eulerend[a]);
searchspace[l][0] += l * weights[a];
searchspace[l][1] -= weights[a];
}else{
int l = Sleafs.query(eulerstart[a], eulerend[a]);
Sleafs.update(eulerstart[a], -l + 1);
Sweights.add(eulerstart[a] + 1, eulerend[a], -weights[a]);
searchspace[d][0] += d * weights[a];
searchspace[d][1] += -weights[a];
searchspace[l - 1][0] -= d * weights[a];
searchspace[l - 1][1] -= -weights[a];
searchspace[l - 1][0] += (l - 1) * weights[a];
}
while (Sweights.query(eulerstart[a] + 1, eulerend[a])[0] < 1e9){
solve(Sweights.query(eulerstart[a] + 1, eulerend[a])[1], Sleafs.query(eulerstart[a], eulerend[a]));
}
}
void init(vector<int> P, vector<int> W) {
N = P.size();
parent.resize(N);
childs.resize(N);
weights.resize(N);
leafsize.resize(N);
searchspace.resize(N + 1);
Sleafs.init(N);
Sweights.init(N);
eulerstart.resize(N);
eulerend.resize(N);
for (int i = 0; i < N; i++){
weights[i] = W[i];
parent[i] = P[i];
if (i)
childs[P[i]].push_back(i);
}
dfs(0);
solve(0, 0);
for (int i = N - 1; i >= 0; i--){
searchspace[i][0] += searchspace[i + 1][0];
searchspace[i][1] += searchspace[i + 1][1];
searchspace[i][2] += searchspace[i + 1][2];
}
}
long long query(int L, int R) {
return searchspace[R / L][0] * L + searchspace[R / L][1] * R + searchspace[R / L][2];
}
