#include <bits/stdc++.h>
#include <factories.h>
using namespace std;
#pragma GCC optimize ("O2,unroll-loops")
#pragma GCC optimize ("Ofast")
const int N = 5e5 + 55, L = 2e0 + 20, Q = 158;
const long long I = 1e18 + 118;
int n, q, h[N], par[N][L];
long long spt[N][L], dis[N];
vector<pair<int, int>> adj[N];
void dfs(int v, int p) {
for (auto [u, w]: adj[v])
if (u != p) {
par[u][0] = v;
spt[u][0] = w;
h[u] = h[v] + 1;
dfs(u, v);
}
}
void dfsu(int v, int p) {
for (auto [u, w]: adj[v])
if (u != p) {
dfsu(u, v);
dis[v] = min(dis[v], dis[u] + w);
}
}
void dfsd(int v, int p) {
for (auto [u, w]: adj[v])
if (u != p) {
dis[u] = min(dis[u], dis[v] + w);
dfsd(u, v);
}
}
long long distance(int v, int u) {
long long ans = 0;
if (h[v] < h[u]) swap(v, u);
for (int i = 0; i < L; i++)
if ((1 << i) & (h[v] - h[u])) {
ans += spt[v][i];
v = par[v][i];
}
if (v == u) return ans;
for (int i = L - 1; i >= 0; i--)
if (par[v][i] != par[u][i]) {
ans += spt[v][i] + spt[u][i];
v = par[v][i];
u = par[u][i];
}
return ans + spt[v][0] + spt[u][0];
}
void Init(int N, int A[], int B[], int D[]) {
n = N;
for (int i = 0; i < n - 1; i++) {
adj[A[i] + 1].push_back({B[i] + 1, D[i]});
adj[B[i] + 1].push_back({A[i] + 1, D[i]});
}
dfs(1, 0);
for (int i = 1; i < L; i++)
for (int j = 1; j <= n; j++) {
par[j][i] = par[par[j][i - 1]][i - 1];
spt[j][i] = spt[j][i - 1] + spt[par[j][i - 1]][i - 1];
}
for (int i = 0; i < N; dis[i++] = I);
}
long long Query(int S, int X[], int T, int Y[]) {
if (S < Q) {
long long ans = I;
for (int i = 0; i < T; i++)
for (int j = 0; j < S; j++)
ans = min(ans, distance(Y[i] + 1, X[j] + 1));
return ans;
}
for (int i = 0; i < S; i++)
dis[X[i] + 1] = 0;
dfsu(1, 0);
dfsd(1, 0);
long long ans = I;
for (int i = 0; i < T; i++) ans = min(ans, dis[Y[i] + 1]);
for (int i = 0; i < N; dis[i++] = I);
return ans;
}
