#include <bits/stdc++.h>
using namespace std;
const int N = 5e5;
vector<pair<int, long long>> adj[N];
int n, m;
vector<int> euler, depth;
int first[N], last[N], l2[N * 2];
long long dep[N], p2[N * 2];
int sparse[N * 2][22];
int c = 0;
int sub[N], par[N];
long long ans[N];
bool isCen[N];
int size = 0;
// LCA begins
void pre(int v, int p = -1, long long d = 0, int de = 0) {
first[v] = c++;
dep[v] = d;
euler.push_back(v);
depth.push_back(de);
for (auto i : adj[v]) {
if (i.first != p) {
pre(i.first, v, d + i.second, de + 1);
euler.push_back(v);
depth.push_back(de);
c++;
}
}
last[v] = c - 1;
}
int merge(int a, int b) {
return depth[a] < depth[b] ? a : b;
}
void build_sparse() {
for (int i = 0; i < euler.size(); i++)
sparse[i][0] = i;
for (int i = 1; i <= l2[euler.size()]; i++) {
for (int j = 0; j < euler.size() && j - 1 + p2[i] < euler.size(); j++)
sparse[j][i] = merge(sparse[j][i - 1], sparse[j + (p2[i - 1])][i - 1]);
}
}
int lca(int u, int v) {
if (u == v) return u;
int f1 = min(first[u], first[v]), f2 = max(first[v], first[u]), diff = f2 - f1;
int dx = l2[diff];
return euler[merge(sparse[f1][dx], sparse[f2 - (p2[dx])][dx])];
}
long long dist(int u, int v) {
return dep[u] + dep[v] - 2 * dep[lca(u, v)];
}
// LCA ends
// Centroid decomposition begins
void calc(int v, int p = -1) { // Pre calculate subtree sizes
sub[v] = 1;
size++;
for (auto i : adj[v]) {
if (i.first != p && !isCen[v])
calc(i.first, v), sub[v] += sub[i.first];
}
}
int find(int v, int p = -1) { // Find the centroid in current subtree
for (auto i : adj[v]) {
if (i.first != p && !isCen[i.first] && sub[i.first] > size / 2)
return find(i.first, v);
}
return v;
}
void decompose(int v, int p = -1) {
size = 0; // Stores size of current subtree
calc(v);
int centroid = find(v);
par[centroid] = p;
isCen[centroid] = true;
for (auto i : adj[centroid]) {
if (i.first != p && !isCen[i.first])
decompose(i.first, centroid);
}
}
// Centroid decomposition ends
void update(int v) {
int p = v;
while (p != -1) {
ans[p] = min(ans[p], dist(p, v));
p = par[p];
}
}
long long query(int v) {
int p = v;
long long val = 1e18;
while (p != -1) {
val = min(val, ans[p] + dist(p, v));
p = par[p];
}
return val;
}
void revert(int v) {
int p = v;
while (p != -1) {
ans[p] = 1e18;
p = par[p];
}
}
long long Query(int S, int X[], int T, int Y[]) {
for (int i = 0; i < S; i++)
update(X[i]);
long long ans = 1e18;
for (int i = 0; i < T; i++)
ans = min(ans, query(Y[i]));
for (int i = 0; i < S; i++)
revert(X[i]);
return ans;
}
void Init(int N, int A[], int B[], int D[]) {
n = N;
for (int i = 0; i < n - 1; i++) {
adj[A[i]].emplace_back(B[i], D[i]);
adj[B[i]].emplace_back(A[i], D[i]);
}
pre(0);
build_sparse();
decompose(0);
fill(ans, ans + N, 1e18);
for (int i = 2, j = 1; i < N * 2; i *= 2, j++) {
for (int k = i; k < i * 2 && k < N * 2; k++)
l2[k] = j;
}
p2[0] = 1;
for (int i = 1; i < N * 2; i++)
p2[i] = p2[i - 1] * 2;
}
