#include "factories.h"
#include <bits/stdc++.h>
using namespace std;
#define ll long long
const int nx=5e5+5, kx=19;
ll lvl[nx], pa[nx][kx], ds[nx], c[nx], sz[nx], dp[nx];
vector<pair<ll, ll>> d[nx];
bool used[nx];
vector<ll> rem;
void dfs(int u, int p)
{
lvl[u]=lvl[p]+1;
pa[u][0]=p;
for (int i=1; i<kx; i++) pa[u][i]=pa[pa[u][i-1]][i-1];
for (auto [v, w]:d[u]) if (v!=p) ds[v]=ds[u]+w, dfs(v, u);
}
int lca(int u, int v)
{
if (lvl[u]>lvl[v]) swap(u, v);
for (int i=kx-1; i>=0; i--) if (lvl[pa[v][i]]>=lvl[u]) v=pa[v][i];
if (u==v) return v;
for (int i=kx-1; i>=0; i--) if (pa[u][i]!=pa[v][i]) u=pa[u][i], v=pa[v][i];
return pa[u][0];
}
ll distance(int u, int v)
{
return ds[u]+ds[v]-2*ds[lca(u, v)];
}
int dfssz(int u, int p)
{
sz[u]=1;
for (auto [v, w]:d[u]) if (v!=p&&!used[v]) sz[u]+=dfssz(v, u);
return sz[u];
}
int findcentroid(int u, int p, int rtsz)
{
for (auto [v, w]:d[u]) if (v!=p&&!used[v]&&2*sz[v]>rtsz) return findcentroid(v, u, rtsz);
return u;
}
void decomposition(int u, int p)
{
u=findcentroid(u, u, dfssz(u, u));
used[u]=1;
c[u]=p;
for (auto [v, w]:d[u]) if (v!=p&&!used[v]) decomposition(v, u);
}
void update(int u)
{
int rt=u;
while (u!=-1) dp[u]=min(dp[u], distance(u, rt)), rem.push_back(u), u=c[u];
}
ll query(int u)
{
ll tmp=LLONG_MAX, rt=u;
while (u!=-1) tmp=(dp[u]!=LLONG_MAX)?min(tmp, distance(u, rt)+dp[u]):tmp, u=c[u];
return tmp;
}
void Init(int N, int A[], int B[], int D[]) {
for (int i=0; i<N-1; i++) d[A[i]].push_back({B[i], D[i]}), d[B[i]].push_back({A[i], D[i]});
for (int i=0; i<N; i++) dp[i]=LLONG_MAX;
dfs(0, 0);
decomposition(0, -1);
}
long long Query(int S, int X[], int T, int Y[]) {
ll res=LLONG_MAX;
for (int i=0; i<S; i++) update(X[i]);
for (int i=0; i<T; i++) res=min(res, query(Y[i]));
for (auto x:rem) dp[x]=LLONG_MAX;
rem.clear();
return res;
}
