#include <bits/stdc++.h>
#include "factories.h"
using namespace std;
const int N = 5e5 + 10;
const long long INF = 1e18 + 7;
vector <pair <int, int>> adj[N];
// Centroid Decomposition
int sz[N], ancestor[N], level[N];
long long dist[N][20];
long long min_dist[N];
bool processed[N];
int find_size(int u, int p) {
sz[u] = 1;
for(auto [v, w] : adj[u]) {
if(v == p or processed[v] == true) {
continue;
}
sz[u] += find_size(v, u);
}
return sz[u];
}
int find_centroid(int u, int p, int n) {
for(auto [v, w] : adj[u]) {
if(v == p or processed[v] == true) {
continue;
}
if(sz[v] > n/2) {
return find_centroid(v, u, n);
}
}
return u;
}
void get_distance(int u, int p, int l) {
for(auto [v, w] : adj[u]) {
if(v == p or processed[v] == true) {
continue;
}
dist[v][l] = dist[u][l] + w;
get_distance(v, u, l);
}
}
void build_centroid(int u, int p) {
int c = find_centroid(u, -1, find_size(u, -1));
ancestor[c] = p;
processed[c] = true;
level[c] = level[p] + 1;
get_distance(c, -1, level[c]);
for(auto [v, w] : adj[c]) {
if(processed[v] == true) {
continue;
}
build_centroid(v, c);
}
}
void Init(int N, int A[], int B[], int D[]) {
for(int i = 0; i < N - 1; i++) {
A[i]++, B[i]++;
adj[A[i]].emplace_back(B[i], D[i]);
adj[B[i]].emplace_back(A[i], D[i]);
}
build_centroid(1, 0);
for(int i = 1; i <= N; i++) {
min_dist[i] = INF;
}
}
void reset(int u) {
int a = u;
while(a != 0) {
min_dist[a] = INF;
a = ancestor[a];
}
}
void update(int u) {
int a = u;
while(a != 0) {
min_dist[a] = min(min_dist[a], dist[u][level[a]]);
a = ancestor[a];
}
}
long long query(int u) {
int a = u;
long long res = INF;
while(a != 0) {
res = min(res, min_dist[a] + dist[u][level[a]]);
a = ancestor[a];
}
return res;
}
long long Query(int S, int X[], int T, int Y[]) {
for(int i = 0; i < S; i++) {
update(X[i] + 1);
}
long long ans = INF;
for(int i = 0; i < T; i++) {
ans = min(ans, query(Y[i] + 1));
}
for(int i = 0; i < S; i++) {
reset(X[i] + 1);
}
return ans;
}
