#include "factories.h"
#include <bits/stdc++.h>
#define Loop(x,l,r) for (ll x = (l); x < (r); ++x)
#define LoopR(x,l,r) for (ll x = (r)-1; x >= (l); --x)
typedef long long ll;
typedef std::pair<int, int> pii;
typedef std::pair<ll , ll > pll;
using namespace std;
const int N = 510'010;
const int lg = 19;
vector<pll> A[N];
int anc[N][lg];
int h[N];
ll dis[N][lg];
int n;
void dfs(int v, int p, ll w, int h)
{
::h[v] = h;
anc[v][0] = p;
dis[v][0] = w;
Loop (i,0,lg-1) {
anc[v][i+1] = anc[anc[v][i]][i];
dis[v][i+1] = dis[v][i] + dis[anc[v][i]][i];
}
for (auto [u, w] : A[v]) {
if (u != p)
dfs(u, v, w, h+1);
}
}
ll get_dis(int v, int u)
{
if (h[v] < h[u])
swap(v, u);
ll ans = 0;
int diff = h[v] - h[u];
Loop (i,0,lg) {
if (diff & (1<<i)) {
ans += dis[v][i];
v = anc[v][i];
}
}
if (v == u)
return ans;
LoopR (i,0,lg) {
if (anc[v][i] != anc[u][i]) {
ans += dis[v][i];
ans += dis[u][i];
v = anc[v][i];
u = anc[u][i];
}
}
return ans + dis[v][0] + dis[u][0];
}
void Init(int N, int X[], int Y[], int D[])
{
n = N;
Loop (i,0,n) {
A[X[i]].push_back({Y[i],D[i]});
A[Y[i]].push_back({X[i],D[i]});
}
dfs(0, 0, 0, 0);
}
ll dij(int s, int x[], int t, int y[])
{
static ll dis[N];
fill(dis, dis+N, (ll)1e18);
set<pair<ll,int>> q;
Loop (i,0,s) {
dis[x[i]] = 0;
q.insert({0,x[i]});
}
while (q.size()) {
auto [d, v] = *q.begin();
q.erase(q.begin());
for (auto [u, w] : A[v]) {
if (d + w < dis[u]) {
q.erase({dis[u], u});
dis[u] = d + w;
q.insert({dis[u], u});
}
}
}
ll ans = 1e18;
Loop (i,0,t)
ans = min(ans, dis[y[i]]);
return ans;
}
long long Query(int S, int X[], int T, int Y[])
{
if ((ll)S * T <= n) {
ll ans = 1e18;
Loop (i,0,S) Loop (j,0,T)
ans = min(ans, get_dis(X[i], Y[j]));
return ans;
} else {
return dij(S, X, T, Y);
}
}
