#include <bits/stdc++.h>
#include "factories.h"
#pragma GCC optimize("Ofast")
#pragma GCC optimize("unroll-loops")
#pragma GCC target("avx,avx2")
#define ll long long
#define all(x) (x).begin(), (x).end()
#define rall(x) (x).rbegin(), (x).rend()
#define watch(x) cout << (#x) << " : " << x << '\n'
#define boost ios_base::sync_with_stdio(0); cin.tie(0); cout.tie(0);
using namespace std;
const int N = 5e5 + 128;
const ll INF = 1e15 + 128;
const int LOG = 20;
vector < pair<int, int> > g[N];
int n, q;
bool was[N];
int h[N];
ll res[N];
void dfs(int v, int p = -1) {
h[v] = 1;
for (auto& [to, len] : g[v])
if (to != p && !was[to])
dfs(to, v), h[v] += h[to];
}
int p[N];
ll dist[N][LOG];
int depth[N];
void calc(int v, int dep, ll val, int pr = -1) {
dist[v][dep] = val;
for (auto& [to, len] : g[v])
if (to != pr && !was[to])
calc(to, dep, val+len, v);
}
int find_centroid(int v, int pr, int sz) {
for (auto& [to, len] : g[v])
if (to != pr && h[to] > sz / 2 && !was[to])
return find_centroid(to, v, sz);
return v;
}
void decompose(int v, int pr = -1) {
dfs(v);
int c = find_centroid(v, -1, h[v]);
p[c] = pr;
if (pr != -1)
depth[c] = depth[pr] + 1;
calc(c, depth[c], 0);
was[c] = true;
for (auto& [to, len] : g[c])
if (!was[to])
decompose(to, c);
}
void update(int v) {
int c = v;
while (c != -1)
res[c] = min(res[c], dist[v][depth[c]]), c = p[c];
}
void reset(int v) {
int c = v;
while (c != -1)
res[c] = INF, c = p[c];
}
ll get(int v) {
ll ans = INF;
int c = v;
while (c != -1)
ans = min(ans, dist[v][depth[c]] + res[c]), c = p[c];
return ans;
}
void Init(int N, int A[], int B[], int D[]) {
n = N;
for (int i = 0; i + 1 < n; i++) {
int u = A[i], v = B[i], w = D[i];
g[u].push_back(make_pair(v, w));
g[v].push_back(make_pair(u, w));
}
for (int i = 0; i <= n; i++)
res[i] = INF;
decompose(1);
}
long long Query(int S, int X[], int T, int Y[]) {
for (int i = 0; i < S; i++)
update(X[i]);
ll tot = INF;
for (int i = 0; i < T; i++)
tot = min(tot, get(Y[i]));
for (int i = 0; i < S; i++)
reset(X[i]);
return tot;
}
// main() {
// boost;
// int A[] = {0, 1, 2, 2, 4, 1};
// int B[] = {1, 2, 3, 4, 5, 6};
// int D[] = {4, 4, 5, 6, 5, 3};
// Init(7, A, B, D);
// int X[] = {0, 6};
// int Y[] = {3, 4};
// cout << Query(2, X, 2, Y) << '\n';
// return 0;
// }
