#include <bits/stdc++.h>
using namespace std;
struct UnionFind{
vector<vector<pair<int, int>>> data;
vector<int> flag_time, degree;
UnionFind(int n = 0): data(n, {{-1, -1}}), flag_time(n, INT_MAX), degree(n){}
int merged_time(int x) const {
const auto [time, root] = data[x].back();
if(root < 0) return INT_MAX;
return time;
}
int root(int t, int x) const { // after t
if(t < merged_time(x)) return x;
return root(t, data[x].back().second);
}
bool unite(int t, int x, int y){
bool flag = ++degree[x] >= 3 || ++degree[y] >= 3;
x = root(t, x);
y = root(t, y);
if(x == y){
if(flag_time[x] == INT_MAX) flag_time[x] = t;
return 0;
}
const int size_x = data[x].back().second, size_y = data[y].back().second;
if(size_x > size_y) swap(x, y);
if(flag_time[x] == INT_MAX && (flag || flag_time[y] != INT_MAX)) flag_time[x] = t;
data[x].emplace_back(t, size_x + size_y);
data[y].emplace_back(t, x);
return 1;
}
} uf;
vector<array<int, 3>> edge;
void init(int N, int M, vector<int> U, vector<int> V, vector<int> W){
uf = UnionFind(N);
edge.resize(M);
for(int i = 0; i < M; i++) edge[i] = {U[i], V[i], W[i]};
sort(edge.begin(), edge.end(), [&](const auto& a, const auto& b){ return a[2] < b[2]; });
for(int i = 0; i < M; i++){
const auto& [U, V, W] = edge[i];
uf.unite(i + 1, U, V);
}
}
int getMinimumFuelCapacity(int X, int Y){
auto check = [&](int t){
const int x = uf.root(t, X), y = uf.root(t, Y);
return x == y && uf.flag_time[x] <= t;
};
int ng = 0, ok = edge.size();
if(!check(ok)) return -1;
while(ok - ng > 1){
const int cen = (ok + ng) / 2;
(check(cen) ? ok : ng) = cen;
}
return edge[ok - 1][2];
}
