#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];
map<int, ll> d[N];
int get_sz(int u, int p = 0) {
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 = 0) {
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][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][u] = 0;
for (auto[v, w] : adj[u]) {
if (del[v]) continue;
make_dist(v, u, u, w);
}
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;
}
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(d[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() + d[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(d[p][u]));
p = par[p];
}
}
return ans;
}
// int main(){
// int N, Q;
// assert(scanf("%i %i", &N, &Q) == 2);
// int *A = (int*)malloc(sizeof(int) * (N - 1));
// int *B = (int*)malloc(sizeof(int) * (N - 1));
// int *D = (int*)malloc(sizeof(int) * (N - 1));
// for(int a = 0; a < N - 1; a++){
// assert(scanf("%i %i %i", A + a, B + a, D + a) == 3);
// }
// Init(N, A, B, D);
// for(int a = 0; a < Q; a++){
// int S, T;
// assert(scanf("%i %i", &S, &T) == 2);
// int *X = (int*)malloc(sizeof(int) * S);
// int *Y = (int*)malloc(sizeof(int) * T);
// for(int b = 0; b < S; b++){
// assert(scanf("%i", X + b) == 1);
// }
// for(int b = 0; b < T; b++){
// assert(scanf("%i", Y + b) == 1);
// }
// printf("%lld\n", Query(S, X, T, Y));
// free(X);
// free(Y);
// }
// free(A);
// free(B);
// free(D);
// }
