#include "factories.h"
#include <bits/stdc++.h>
using namespace std;
#define ll long long
const int nx=5e5+5, kx=21;
ll ds[kx][nx], c[nx], sz[nx], dp[nx], lvl[nx];
vector<pair<ll, ll>> d[nx];
bool used[nx];
vector<ll> rem;
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 calcdist(int u, int p, ll dist, int dpt)
{
ds[dpt][u]=dist;
for (auto [v, w]:d[u]) if (v!=p&&!used[v]) calcdist(v, u, dist+w, dpt);
}
void decomposition(int u, int p, int dpt)
{
u=findcentroid(u, u, dfssz(u, u));
used[u]=1;
c[u]=p;
lvl[u]=dpt;
calcdist(u, u, 0, dpt);
for (auto [v, w]:d[u]) if (v!=p&&!used[v]) decomposition(v, u, dpt+1);
}
void update(int u)
{
int rt=u;
while (u!=-1) dp[u]=min(dp[u], ds[lvl[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, ds[lvl[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;
decomposition(0, -1, 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;
}
