#include "swap.h"
#include <bits/stdc++.h>
using namespace std;
const int MN = 1e5+5;
const int INF = 1e9+10;
int n, m;
int par[MN], sz[MN];
vector<tuple<int, int, int>> edges;
vector<vector<int>> g;
vector<bool> av, inPath, vis;
int ans1 = 0, ans2 = 0;
bool cyc = false;
int find(int u) {
if (par[u] == u) return u;
return par[u] = find(par[u]);
}
void merge(int e) {
int u = get<1>(edges[e]);
int v = get<2>(edges[e]);
u = find(u);
v = find(v);
if (u == v) return;
if (sz[u] > sz[v]) swap(u, v);
par[u] = v;
sz[v] += sz[u];
}
bool dfs1(int node, int targ) {
vis[node] = true;
if (node == targ) {
inPath[node] = true;
return true;
}
for (auto e: g[node]) {
if (!av[e]) continue;
int v = get<2>(edges[e]) ^ get<1>(edges[e]) ^ node;
if (!vis[v]) dfs1(v, targ);
inPath[node] = inPath[node] || inPath[v];
}
return inPath[node];
}
void init(int N, int M, vector<int> U, vector<int> V, vector<int> W) {
n = N;
m = M;
for (int i = 0; i < m; i++) {
edges.push_back({W[i], U[i], V[i]});
}
sort(edges.begin(), edges.end());
g.resize(n);
for (int i = 0; i < m; i++) {
int u = get<1>(edges[i]);
int v = get<2>(edges[i]);
g[u].push_back(i);
g[v].push_back(i);
}
}
int getMinimumFuelCapacity(int X, int Y) {
int a = X, b = Y;
ans1 = ans2 = INF;
for (int i = 0; i < n; i++) {
par[i] = i;
sz[i] = 1;
}
av.assign(m, false);
bool passedPath = false;
for (int i = 0; i < m; i++) {
av[i] = true;
merge(i);
if (!passedPath) {
ans1 = get<0>(edges[i]);
if (find(a) != find(b)) continue;
inPath.assign(n, false);
vis.assign(n, false);
dfs1(a, b);
vector<int> cand;
int other = INF;
for (int u = 0; u < n; u++) {
if (!inPath[u] || u == a || u == b) continue;
int tot = 0;
vector<int> alt;
for (auto e: g[u]) {
int w = get<0>(edges[e]);
int v = u ^ get<1>(edges[e]) ^ get<2>(edges[e]);
if (inPath[v]) {
alt.push_back(w);
tot++;
}
else cand.push_back(w);
}
if (tot < 3) continue;
sort(alt.begin(), alt.end());
other = min(other, alt[2]);
}
cand.push_back(other);
sort(cand.begin(), cand.end());
ans1 = max(ans1, cand[0]);
passedPath = true;
for (int i = 0; i < n; i++) {
par[i] = i;
sz[i] = 1;
}
for (int u = 0; u < n; u++) {
if (!inPath[u]) continue;
int tot = 0;
for (auto e: g[u]) {
int w = get<0>(edges[e]);
int v = u ^ get<1>(edges[e]) ^ get<2>(edges[e]);
if ((inPath[u] && inPath[v]) || (inPath[u] && u != a && u != b) || (inPath[v] && v != a && v != b)) {
av[e] = false;
}
}
}
for (int e = 0; e < m; e++) {
if (av[e]) merge(e);
}
}
else {
int u = get<1>(edges[i]);
int v = get<2>(edges[i]);
ans2 = get<0>(edges[i]);
if (find(a) != find(b)) continue;
break;
}
}
int ans = ans1;
if (find(a) == find(b)) ans = min(ans1, ans2);
if (ans == INF) return -1;
return ans;
}
