#include "factories.h"
#include <bits/stdc++.h>
using namespace std;
template<typename T>
void out(T x) { cout << x << endl; exit(0); }
#define watch(x) cout << (#x) << " is " << (x) << endl
using ll = long long;
const ll inf = 1e18;
const ll mod = 1e9+7;
const int maxn = 1e6+10;
vector<pair<ll,int>> g[maxn];
const int LOG = 19;
int par[maxn][LOG+1];
int dep[maxn];
ll depw[maxn];
int n;
int cloc = 0;
int tin[maxn];
vector<pair<int,int>> ett;
struct sparse_table {
int LOG = 0;
int n;
vector<pair<int,int>> a[100];
vector<int> lg_floor;
pair<int,int> eval(pair<int,int> x, pair<int,int> y) {
return min(x, y);
}
void init(vector<pair<int,int>> v) {
n = v.size();
LOG = 0;
while ((1<<LOG) <= n) LOG++;
lg_floor.resize(n+10);
lg_floor[1] = 0;
for (int i=2; i<n+10; i++) lg_floor[i] = 1 + lg_floor[i/2];
for (int j=0; j<LOG; j++) a[j].resize(n);
for (int i=0; i<n; i++) a[0][i] = v[i];
for (int j=1; j<LOG; j++) {
for (int i=0; i<n; i++) {
a[j][i] = a[j-1][i];
if (i + (1<<(j-1)) < n) {
a[j][i] = eval(a[j][i], a[j-1][i + (1<<(j-1))]);
}
}
}
}
pair<int,int> get(int l, int r) {
assert(l<=r);
int lg = lg_floor[r - l + 1];
return eval(a[lg][l], a[lg][r-(1<<lg)+1]);
}
};
sparse_table tbl;
void dfs(int at, int p) {
tin[at] = cloc++;
ett.push_back({tin[at], at});
if (~p) {
for (int j=1; j<LOG; j++) {
par[at][j] = par[par[at][j-1]][j-1];
}
}
for (auto ed: g[at]) {
int to = ed.second;
if (to == p) continue;
par[to][0] = at;
dep[to] = 1+dep[at];
depw[to] = ed.first+depw[at];
dfs(to, at);
ett.push_back({tin[at], at});
cloc++;
}
ett.push_back({tin[at], at});
cloc++;
}
int lca(int u, int v) {
if (u==v) return u;
int lo = tin[u];
int hi = tin[v];
if (lo>hi) swap(lo, hi);
pair<int,int> res = tbl.get(lo, hi);
return res.second;
}
int lcaBrute(int u, int v) {
if (dep[u]<dep[v]) swap(u, v);
int dx = dep[u]-dep[v];
for (int j=0; j<LOG; j++) {
if (dx>>j&1) {
u=par[u][j];
}
}
if (u==v) return v;
for (int j=LOG-1; j>=0; j--) {
if (par[u][j] != par[v][j]) {
u=par[u][j];
v=par[v][j];
}
}
return par[v][0];
}
ll dist(int u, int v) {
if (u==v) return 0;
int mid = lca(u,v);
return depw[u]+depw[v]-2ll*depw[mid];
}
void Init(int N, int A[], int B[], int D[]) {
n = N;
for (int i=0; i<N-1; i++) {
g[A[i]].push_back({D[i],B[i]});
g[B[i]].push_back({D[i],A[i]});
}
dfs(0, -1);
tbl.init(ett);
}
ll QuerySmall(int S, int X[], int T, int Y[]) {
ll res = inf;
for (int i=0; i<S; i++) {
for (int j=0; j<T; j++) {
//cout<<X[i]<<","<<Y[j]<<endl;
res = min(res, dist(X[i],Y[j]));
}
}
return res;
}
ll dp[maxn];
bool dest[maxn];
long long Query(int S, int X[], int T, int Y[]) {
if (S<=10 && T<=10) {
return QuerySmall(S, X, T, Y);
}
for (int i=0; i<n; i++) {
dp[i] = inf;
dest[i] = false;
}
for (int i=0; i<S; i++) {
dp[X[i]] = 0;
}
for (int i=0; i<T; i++) {
dest[Y[i]] = true;
}
priority_queue<pair<ll,int>,vector<pair<ll,int>>,greater<pair<ll,int>>> pq;
for (int i=0; i<S; i++) {
pq.push({0, X[i]});
}
while (pq.size()) {
auto cur = pq.top();
pq.pop();
int at = cur.second;
ll len = cur.first;
if (len > dp[at]) {
continue;
}
if (dest[at]) {
return len;
}
for (auto ed: g[at]) {
int to = ed.second;
ll wei = ed.first;
if (len+wei < dp[to]) {
dp[to] = len+wei;
pq.push({dp[to], to});
}
}
}
ll res = inf;
for (int i=0; i<T; i++) {
res = min(res, dp[Y[i]]);
}
return res;
}
int q;
int a[maxn], b[maxn], d[maxn];
int x[maxn], y[maxn];
