// #include "swap.h"
#include <bits/stdc++.h>
using namespace std;
using tint = array <int, 3>;
const int mxN = 200005;
vector <int> info1[mxN], info2[mxN]; // time, group
int n, m, deg[mxN], ftime[mxN]; // time when deg3 or cycle
tint edge[mxN];
struct dsu {
int G[mxN];
vector <int> Gelm[mxN];
void init(){
for (int i = 0; i < n; i++){
G[i] = i;
Gelm[i].push_back(i);
info1[i].push_back(-1);
info2[i].push_back(i);
}
}
void uni(int time, int x, int y){
x = G[x], y = G[y];
if (x != y){
if (Gelm[x].size() < Gelm[y].size()) swap(x, y);
for (int elm : Gelm[y]) {
G[elm] = x;
Gelm[x].push_back(elm);
info1[elm].push_back(time);
info2[elm].push_back(x);
}
if (ftime[x] == -1 && ftime[y] != -1) ftime[x] = time;
Gelm[y].clear();
}
if (x == y && ftime[x] == -1) ftime[x] = time;
}
} dsu;
void init(int N, int M, vector<int> U, vector<int> V, vector<int> W) {
n = N, m = M;
for (int i = 0; i < n; i++) ftime[i] = -1;
for (int i = 0; i < m; i++) edge[i] = {W[i], U[i], V[i]};
sort(edge, edge + m);
dsu.init();
for (int i = 0; i < m; i++){
for (int j : {1, 2}){
int x = edge[i][j];
if (++deg[x] == 3){
x = dsu.G[x];
if (ftime[x] == -1) ftime[x] = i;
}
}
dsu.uni(i, edge[i][1], edge[i][2]);
}
}
int getMinimumFuelCapacity(int x, int y) {
int low = 0, high = m - 1, ans = -1;
while (low <= high){
int mid = (low + high) / 2;
int xi = upper_bound(info1[x].begin(), info1[x].end(), mid) - info1[x].begin() - 1;
int yi = upper_bound(info1[y].begin(), info1[y].end(), mid) - info1[y].begin() - 1;
x = info2[x][xi], y = info2[y][yi];
if (x == y && ftime[x] != -1 && ftime[x] <= mid){
ans = mid;
high = mid - 1;
}
else low = mid + 1;
}
return (ans != -1 ? edge[ans][0] : -1);
}
