#include <bits/stdc++.h>
#include "factories.h"
using namespace std;
const int MAXN = 500005;
const long long INF = 1e18;
const int LOG = 20;
int n;
vector<pair<int, long long>> adj[MAXN];
long long dist[MAXN];
int up[MAXN][LOG];
int depth[MAXN];
long long dist1[MAXN];
bool visited[MAXN];
void dfs(int u, int par)
{
visited[u] = true;
up[u][0] = par;
if (par == -1) depth[u] = 0;
else depth[u] = depth[par] + 1;
for (int i = 1; i < LOG; i++)
{
if (up[u][i-1] != -1)
up[u][i] = up[up[u][i-1]][i-1];
else
up[u][i] = -1;
}
for (auto [v, w] : adj[u])
{
if (v != par)
{
dist1[v] = dist1[u] + w;
dfs(v, u);
}
}
}
int lca(int u, int v)
{
if (depth[u] < depth[v])
{
swap(u, v);
}
int diff = depth[u] - depth[v];
for (int j = 0; j < LOG; j++)
{
if (diff & (1 << j))
{
u = up[u][j];
}
}
if (u == v)
{
return u;
}
for (int i = LOG - 1; i >= 0; i--)
{
if (up[u][i] != up[v][i])
{
u = up[u][i];
v = up[v][i];
}
}
return up[u][0];
}
long long peal(int u, int v)
{
int k = lca(u, v);
return dist1[u] + dist1[v] - 2 * dist1[k];
}
void dijkstra(int S, int X[])
{
priority_queue<pair<long long, int>, vector<pair<long long, int>>, greater<pair<long long, int>>> pq;
for (int i = 0; i < n; i++)
{
dist[i] = INF;
}
for (int i = 0; i < S; i++)
{
dist[X[i]] = 0;
pq.push({0, X[i]});
}
while (!pq.empty())
{
auto [d, u] = pq.top();
pq.pop();
if (d > dist[u]) continue;
for (auto [v, w] : adj[u])
{
if (dist[v] > dist[u] + w)
{
dist[v] = dist[u] + w;
pq.push({dist[v], v});
}
}
}
}
void Init(int N, int A[], int B[], int D[])
{
n = N;
for (int i = 0; i < n; i++)
{
adj[i].clear();
}
for (int i = 0; i < n - 1; i++)
{
adj[A[i]].push_back({B[i], D[i]});
adj[B[i]].push_back({A[i], D[i]});
}
memset(visited, 0, sizeof(visited));
for (int i = 0; i < n; i++)
{
if (!visited[i])
{
dist1[i] = 0;
dfs(i, -1);
}
}
}
long long Query(int S, int X[], int T, int Y[])
{
if (S <= 20 || T <= 20)
{
long long res = INF;
for (int i = 0; i < S; i++)
{
for (int j = 0; j < T; j++)
{
res = min(res, peal(X[i], Y[j]));
}
}
return res;
}
else
{
dijkstra(S, X);
long long res = INF;
for (int i = 0; i < T; i++)
{
if (dist[Y[i]] < res)
{
res = dist[Y[i]];
}
}
return res;
}
}
