#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
const int N = 2e5+5;
long long L, R, w[N];
vector<int> adj[N];
int n, pr[N], x[N], in[N], sz[N], idx;
int srtx[N], rv[N];
bool f;
pair<int, ll> srtox[N];
ll srtx2[N];
struct node {
pair<int, int> mn;
ll sm;
} t[(1 << 19)];
void build(int l, int r, int x) {
if (l == r) {
t[x].sm = 0;
t[x].mn = {w[rv[l]], l};
if (adj[rv[l]].empty())t[x].mn = {int(1e9), int(1e9)};
return;
}
int m = (l + r) >> 1;
build(l, m, x*2+1);
build(m+1, r, x*2+2);
t[x].sm = 0;
t[x].mn = min(t[x*2+1].mn, t[x*2+2].mn);
}
void upd(int l, int r, int x, int i, ll v) {
t[x].sm -= v;
if (l == r)return;
int m = (l + r) >> 1;
if (i <= m) {
upd(l, m, x*2+1, i, v);
} else {
upd(m+1, r, x*2+2, i, v);
}
}
ll getsm(int li, int ri, int x, int l, int r) {
if (li >= l && ri <= r)return t[x].sm;
if (li > r || ri < l)return 0;
int m = (li + ri) >> 1;
return getsm(li, m, x*2+1, l, r) + getsm(m+1, ri, x*2+2, l, r);
}
pair<int, int> geti(int li, int ri, int x, int l, int r) {
if (li >= l && ri <= r)return t[x].mn;
if (li > r || ri < l)return {int(1e9), int(1e9)};
int m = (li + ri) >> 1;
return min(geti(li, m, x*2+1, l, r), geti(m+1, ri, x*2+2, l, r));
}
void rem(int li, int ri, int x, int l, int r) {
if (t[x].mn.first == 1e9)return;
if (li > r || ri < l)return;
if (li == ri) {
t[x].mn = {int(1e9), int(1e9)};
return;
}
int m = (li + ri) >> 1;
rem(li, m, x*2+1, l, r);
rem(m+1, ri, x*2+2, l, r);
t[x].mn = min(t[x*2+1].mn, t[x*2+2].mn);
}
ll bit[int(1e6+1)];
void init(int u) {
x[u] = (adj[u].empty());
rv[idx] = u;
in[u] = idx++;
sz[u] = 1;
for (auto &v : adj[u]) {
init(v);
x[u] += x[v];
sz[u] += sz[v];
}
if (w[u] == 0) {
x[u] = 1;
}
}
ll lf;
ll getb(int i) {
ll ret = 0;
while (i) {
ret += bit[i];
i -= (i & -i);
}
return ret;
}
void updop(int i, ll v) {
while (i <= 1e6) {
bit[i] += v;
i += (i & -i);
}
}
void updb(int lo, int ro, ll v) {
if (lo > ro)return;
updop(lo, v);
updop(ro+1, -v);
}
int id[N];
bool cmp(int i, int j) {
return (x[i] < x[j]);
}
void init(vector<int> P, vector<int> W) {
n = P.size();
f = true;
idx = 0;
lf = 0;
for (int i = 0; i < n; i++) {
adj[i].clear();
w[i] = W[i];
pr[i] = P[i];
f &= (w[i] <= 1);
}
for (int i = 1; i < n; i++) {
adj[P[i]].push_back(i);
}
init(0);
for (int i = 0; i < n; i++) {
srtx[i] = x[i];
if (adj[i].empty())lf += w[i];
srtox[i] = {x[i], w[i]};
}
sort(srtox, srtox+n);
sort(srtx, srtx+n);
ll smr = 0, smr2 = 0;
for (int i = 0; i < n; i++) {
id[i] = i;
}
sort(id, id+n, cmp);
for (int i = n-1; i >= 0; i--) {
smr += srtox[i].second;
srtox[i].second = smr;
if (id[i] == 0) {
smr2 += 0;
} else {
smr2 += w[pr[id[i]]];
}
srtx2[i] = smr2;
}
srtx2[n] = srtox[n].second = 0;
for (int i = 0; i <= 1e6; i++) {
bit[i] = 0;
}
for (int i = 1; i < n; i++) {
if (x[pr[i]] > x[i])updb(x[i], x[pr[i]]-1, w[pr[i]] * x[i]);
}
}
ll ans;
void dfs(int u) {
if (adj[u].empty()) {
ans += L * w[u];
upd(0, n-1, 0, in[u], -L);
return;
}
for (auto &v : adj[u]) {
dfs(v);
}
ll xx = getsm(0, n-1, 0, in[u], in[u] + sz[u] - 1);
while (xx > R) {
ll nedi = xx - R;
pair<int, int> mno = geti(0, n-1, 0, in[u], in[u] + sz[u] - 1);
ll xo = getsm(0, n-1, 0, mno.second, mno.second + sz[rv[mno.second]] - 1);
if (xo == L) {
rem(0, n-1, 0, mno.second, mno.second + sz[rv[mno.second]] - 1);
continue;
}
if (xo - L >= nedi) {
ans += nedi * w[rv[mno.second]];
upd(0, n-1, 0, mno.second, nedi);
rem(0, n-1, 0, mno.second + 1, mno.second + sz[rv[mno.second]] - 1);
break;
}
xx -= (xo - L);
ans += (xo - L) * w[rv[mno.second]];
upd(0, n-1, 0, mno.second, xo - L);
rem(0, n-1, 0, mno.second, mno.second + sz[rv[mno.second]] - 1);
}
}
long long query(int lo, int ro) {
L = lo, R = ro;
if (f) {
ans = L * lf;
ll sb = max(1ll, (R / L) - 1ll);
while ((sb + 1ll) * L <= R)sb++;
int id = upper_bound(srtx, srtx+n, sb) - srtx;
ans -= R * srtox[id].second;
ans += R * srtx2[id];
ans += L * getb(sb);
return ans;
}
build(0, n-1, 0);
ans = 0;
dfs(0);
return ans;
}
