#include <bits/stdc++.h>
#include "factories.h"
using namespace std;
const int N = 5e5 + 5;
vector <pair <int, int> > g[N];
int h[N], child[N], par[N];
bool visited[N];
long long dist[20][N], ans[N];
void dfs (int u, int p) {
child[u] = 1;
for (auto v: g[u]) {
if (v.first != p && !visited[v.first]) {
dfs(v.first, u);
child[u] += child[v.first];
}
}
}
int findcen (int u, int p, int sz) {
for (auto v: g[u]) {
if (v.first != p && !visited[v.first] && child[v.first] >= sz / 2) return findcen(v.first, u, sz);
}
return u;
}
void redfs (int level, int u, int p, int cost) {
if (p != -1) dist[level][u] = dist[level][p] + cost;
for (auto v: g[u]) {
if (v.first != p && !visited[v.first]) {
redfs(level, v.first, u, v.second);
}
}
}
void centroid (int root, int p) {
dfs(root, -1);
int cen = findcen(root, -1, child[root]);
visited[cen] = true; par[cen] = p;
if (p != -1) h[cen] = h[p] + 1;
redfs(h[cen], cen, -1, 0);
for (auto v: g[cen]) if (v.first != p && !visited[v.first]) centroid(v.first, cen);
}
void update (int u) {
for (int v = u; v != -1; v = par[v])
ans[v] = min(ans[v], dist[h[v]][u]);
}
long long query (int u) {
long long res = 1e18;
for (int v = u; v != -1; v = par[v])
res = min(res, ans[v] + dist[h[v]][u]);
return res;
}
void Init (int N, int A[], int B[], int D[]) {
for (int i = 0; i < N - 1; i++) {
g[A[i]].push_back(make_pair(B[i], D[i]));
g[B[i]].push_back(make_pair(A[i], D[i]));
}
for (int i = 0; i < N; i++) ans[i] = 1e18;
centroid(0, -1);
}
long long Query (int S, int X[], int T, int Y[]) {
if (S < T) {
for (int i = 0; i < S; i++) update(X[i]);
long long res = 1e18;
for (int i = 0; i < T; i++) res = min(res, query(Y[i]));
for (int i = 0; i < S; i++)
for (int v = X[i]; v != -1; v = par[v])
ans[v] = 1e18;
return res;
}
else {
for (int i = 0; i < T; i++) update(Y[i]);
long long res = 1e18;
for (int i = 0; i < S; i++) res = min(res, query(X[i]));
for (int i = 0; i < T; i++)
for (int v = Y[i]; v != -1; v = par[v])
ans[v] = 1e18;
return res;
}
}
