#include "tree.h"
#include <bits/stdc++.h>
using namespace std;
using ll = long long;
constexpr int SZ = 1001000;
int n;
vector<int> adj[200200], buf[SZ];
ll a[200200], sum;
struct Seg{
ll tree[SZ*2];
int sz;
void init(int n){sz = n;}
void update(ll p, ll x){
if (p >= sz) return;
for (p+=sz;p;p>>=1) tree[p] += x;
}
ll query(int l, int r){
++r;
ll ret = 0;
for (l+=sz,r+=sz;l<r;l>>=1,r>>=1){
if (l&1) ret += tree[l++];
if (r&1) ret += tree[--r];
}
return ret;
}
}tree1, tree2;
struct DSU{
int path[200200], rt[200200];
ll sum[200200];
void init(int n){
for (int i=1;i<=n;i++) path[i] = i;
}
int find(int s){
if (s==path[s]) return s;
return path[s] = find(path[s]);
}
void toggle(int x, int t, ll v){
assert(!rt[x]);
rt[x] = t;
sum[x] = v;
}
void push(int x, int t){
x = find(x);
tree1.update(sum[x], sum[x] * (rt[x] - t));
tree2.update(sum[x], rt[x] - t);
rt[x] = t;
}
void merge(int x, int y, int t){
x = find(x);
y = find(y);
if (!rt[x] || !rt[y]) return;
push(x, t);
push(y, t);
if (x==y) return;
path[x] = y;
sum[y] += sum[x];
}
}dsu;
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];
for (int i=1;i<=n;i++) if (adj[i].empty()) sum += a[i];
dsu.init(n);
tree1.init(SZ);
tree2.init(SZ);
for (int i=1;i<=n;i++) if (!adj[i].empty()) buf[a[i]].push_back(i);
for (int t=SZ-1;t>=1;t--){
for (auto &x:buf[t]){
dsu.toggle(x, t, max((int)adj[x].size() - 1, 0));
dsu.merge(x, P[x-1]+1, t);
for (auto &y:adj[x]) dsu.merge(x, y, t);
}
}
dsu.push(1, 0);
}
long long query(int L, int R) {
return sum * L + tree1.query((R-L) / L + 1, SZ-1) * L - tree2.query((R-L) / L + 1, SZ-1) * (R-L);
}
