#include <bits/stdc++.h>
#include "factories.h"
using namespace std;
using ll = long long;
#define MAXN (1000005)
vector<pair<ll,ll> > v[MAXN];
ll sub[MAXN];
ll par[MAXN];
ll lvl[MAXN];
ll dist[MAXN][20];
ll m[MAXN];
ll dfs1(ll x,ll p,ll l){
sub[x] = 1;
for(auto u : v[x]){
if(u.first != p && lvl[u.first] == -1){ //unvisited
sub[x] += dfs1(u.first,x,l);
}
}
return sub[x];
}
ll dfs2(ll x,ll p,ll siz){ //siz is total size of this centroid tree
for(auto u : v[x]){
if(u.first != p && lvl[u.first] == -1 && sub[u.first] > siz / 2){
return dfs2(u.first,x,siz); //remember that siz remains constant
}
}
return x;
}
void dfsdist(ll x,ll p,ll curlvl,ll curdist){
dist[x][curlvl] = curdist;
for(auto u : v[x]){
if(u.first != p && lvl[u.first] == -1){ //unvisited
dfsdist(u.first,x,curlvl,curdist + u.second);
//Note: curlvl is unchanged since we are moving down so
//the relative lvl has already changed
}
}
}
void build(ll x,ll p,ll l){
ll siz = dfs1(x,p,l);
ll cent = dfs2(x,p,siz);
if(p == -1) p = cent;
par[cent] = p;
lvl[cent] = l;
dfsdist(cent,-1,l,0);
for(auto u : v[cent]){
if(lvl[u.first] == -1){ //unvisited
build(u.first,cent,l + 1);
}
}
}
void Init(int N, int A[], int B[], int D[]) {
for(ll i = 0;i < N - 1;i++){
v[A[i]].push_back(make_pair(B[i],D[i]));
v[B[i]].push_back(make_pair(A[i],D[i]));
}
for(ll i = 0;i < MAXN;i++){
for(ll j = 0;j < 20;j++){
dist[i][j] = 1e18;
}
}
memset(lvl,-1,sizeof(lvl)); //need lvl to find dist[i][lvl]
build(0,-1,0);
for(ll i = 0;i < MAXN;i++){
m[i] = 1e18;
}
}
long long Query(int S, int X[], int T, int Y[]) {
for(ll i = 0;i < S;i++){
ll curlevel = lvl[X[i]];
ll x = X[i];
while(curlevel >= 0){
m[x] = min(m[x],dist[X[i]][curlevel]);
x = par[x];
curlevel--;
}
}
ll ans = 1e18;
for(ll i = 0;i < T;i++){
ll curlevel = lvl[Y[i]];
ll y = Y[i];
while(curlevel >= 0){
ans = min(ans,m[y] + dist[Y[i]][curlevel]);
y = par[y];
curlevel--;
}
}
for(ll i = 0;i < S;i++){ //undo, prepare for next query
ll curlevel = lvl[X[i]];
ll x = X[i];
while(curlevel >= 0){
m[x] = 1e18;
x = par[x];
curlevel--;
}
}
return ans;
}
