#include "factories.h"
#include <bits/stdc++.h>
using namespace std;
const int N = 5e5 + 5;
vector<array<int, 2>>G[N];
vector<array<long long, 2>>C[N];
bool del[N];
int tsz[N];
long long f[N];
void findsz(int node, int par){
tsz[node] = 1;
for(auto &[v, w] : G[node]){
if(v == par || del[v])continue;
findsz(v, node);
tsz[node] += tsz[v];
}
}
int findcent(int node, int par, int T){
int mx = -1;
for(auto &[v, w] : G[node]){
if(v == par || del[v])continue;
if(mx == -1 || tsz[mx] < tsz[v]){
mx = v;
}
}
if(mx == -1 || tsz[mx] <= T / 2)return node;
return findcent(mx, node, T);
}
void populC(int node, int par, int cent, long long d){
C[node].push_back({cent, d});
for(auto &[v, w] : G[node]){
if(v == par || del[v])continue;
populC(v, node, cent, d + w);
}
}
void decompose(int node){
findsz(node, node);
int cent = findcent(node, node, tsz[node]);
populC(cent, cent, cent, 0);
del[cent] = 1;
for(auto &[v, w] : G[cent]){
if(del[v])continue;
decompose(v);
}
}
void Init(int N, int A[], int B[], int D[]){
for(int i = 0;i < N - 1;++i){
G[A[i]].push_back({B[i], D[i]});
G[B[i]].push_back({A[i], D[i]});
}
decompose(0);
for(int i = 0;i < N;++i){
f[i] = 1e18;
}
}
long long Query(int S, int X[], int T, int Y[]){
for(int i = 0;i < S;++i){
for(auto &[node, dist] : C[X[i]]){
f[node] = min(f[node], dist);
}
}
long long mn = 1e18;
for(int i = 0;i < T;++i){
for(auto &[node, dist] : C[Y[i]]){
mn = min(mn, dist + f[node]);
}
}
for(int i = 0;i < S;++i){
for(auto &[node, dist] : C[X[i]]){
f[node] = 1e18;
}
}
return mn;
}
// int main(){
// ios_base::sync_with_stdio(0);
// cin.tie(0);
// int n, q;
// cin >> n >> q;
// int a[n - 1], b[n - 1], d[n - 1];
// for(int i = 0;i < n - 1;++i){
// cin >> a[i] >> b[i] >> d[i];
// }
// Init(n, a, b, d);
// while(q--){
// int s, t;
// cin >> s >> t;
// int x[s], y[t];
// for(int i = 0;i < s;++i){
// cin >> x[i];
// }
// for(int i = 0;i < t;++i){
// cin >> y[i];
// }
// cout << Query(s, x, t, y) << '\n';
// }
// }
