#include "bits/stdc++.h"
#include "factories.h"
using namespace std;
#define task ""
#define ll long long
#define endl '\n'
#define fi first
#define se second
#define vall(a) (a).begin(), (a).end()
#define sze(a) (int)a.size()
#define pii pair<int, int>
#define pll pair<ll, ll>
#define ep emplace_back
#define pb push_back
#define pf push_front
const ll mod = 1e9 + 7;
const int N = 5e5 + 5;
const ll oo = 1e18;
bool START;
int n, q, par[N], sz[N];
vector<pii> adj[N];
multiset<ll> s[N];
bool del[N];
vector<pair<int, ll>> d[N];
int get_sz(int u, int p = -1) {
sz[u] = 1;
for (auto[v, w] : adj[u]) {
if (v == p || del[v]) continue;
sz[u] += get_sz(v, u);
}
return sz[u];
}
int get_cen(int sigma, int u, int p = -1) {
for (auto[v, w] : adj[u]) {
if (v != p && !del[v] && sz[v] * 2 > sigma) return get_cen(sigma, v, u);
}
return u;
}
void make_dist(int u, int p, int root, ll depth) {
d[root].pb(make_pair(u, depth));
for (auto[v, w] : adj[u]) {
if (v == p || del[v]) continue;
make_dist(v, u, root, depth + w);
}
}
int centroid(int u) {
u = get_cen(get_sz(u), u);
del[u] = true;
d[u].pb(make_pair(u, 0));
for (auto[v, w] : adj[u]) {
if (del[v]) continue;
make_dist(v, u, u, w);
}
sort(vall(d[u]));
for (auto[v, w] : adj[u]) {
if (del[v]) continue;
int x = centroid(v);
par[x] = u;
}
return u;
}
void Init(int N, int A[], int B[], int D[]){
for (int i = 0; i < N; ++i) par[i] = -1;
for (int i = 0; i < N - 1; ++i) {
adj[A[i]].pb(make_pair(B[i], D[i]));
adj[B[i]].pb(make_pair(A[i], D[i]));
}
centroid(0);
return;
}
ll getdist(int u, int v) {
auto[node, dist] = *lower_bound(vall(d[u]), make_pair(v, 0ll));
return dist;
}
long long Query(int S, int X[], int T, int Y[]){
for (int i = 0; i < S; ++i) {
int u = X[i];
int p = u;
while(p != -1) {
s[p].insert(getdist(p, u));
p = par[p];
}
}
ll ans = oo;
for (int i = 0; i < T; ++i) {
int u = Y[i];
int p = u;
while(p != -1) {
if (!s[p].empty()) ans = min(ans, *s[p].begin() + getdist(p, u));
p = par[p];
}
}
for (int i = 0; i < S; ++i) {
int u = X[i];
int p = u;
while(p != -1) {
s[p].erase(s[p].find(getdist(p, u)));
p = par[p];
}
}
return ans;
}
