#include <bits/stdc++.h>
#include "swap.h"
using namespace std;
typedef long long ll;
typedef unsigned long long ull;
#define ALL(v) (v).begin(), (v).end()
#define MASK(i) (1LL << (i))
#define GETBIT(mask, i) (((mask) >> (i)) & 1)
// mt19937_64 rng(chrono::steady_clock::now().time_since_epoch().count());
mt19937_64 rng(1);
ll rngesus(ll l, ll r){return ((ull) rng()) % (r - l + 1) + l;}
ll max(ll a, ll b){return (a > b) ? a : b;}
ll min(ll a, ll b){return (a < b) ? a : b;}
ll LASTBIT(ll mask){return mask & (-mask);}
ll pop_cnt(ll mask){return __builtin_popcountll(mask);}
ll ctz(ll mask){return __builtin_ctzll(mask);}
ll clz(ll mask){return __builtin_clzll(mask);}
ll logOf(ll mask){return 63 - clz(mask);}
template <class T1, class T2>
bool minimize(T1 &a, T2 b){
if (a > b){a = b; return true;}
return false;
}
template <class T1, class T2>
bool maximize(T1 &a, T2 b){
if (a < b){a = b; return true;}
return false;
}
template <class T>
void printArr(T& a, string separator = " ", string finish = "\n", ostream& out = cout){
for(auto i: a) out << i << separator;
out << finish;
}
template <class T>
void remove_dup(vector<T> &a){
sort(ALL(a));
a.resize(unique(ALL(a)) - a.begin());
}
struct DSU{
int n;
vector<int> parent;
DSU(int _n){
n = _n;
parent.resize(n);
for(int i = 0; i<n; ++i) parent[i] = i;
}
int find_set(int u){return (u == parent[u]) ? u : (parent[u] = find_set(parent[u]));}
bool join_set(int u, int v){
u = find_set(u), v = find_set(v);
if (u != v){
parent[v] = u;
return true;
}
return false;
}
};
const int N = 1e5 + 69, M = N * 2, LOG_N = 17, INF = 1e9 + 69;
int n, m;
vector<pair<int, int>> graph[N];
int val[N];
int sz[N], h[N], parent[N][LOG_N], max_path[N][LOG_N], rizz[N][LOG_N];
int dp1[N], dp2[N];
int two_child(int u, int forbid){
vector<int> S;
for(pair<int, int> v: graph[u]) {
if (v.first != forbid) {
S.push_back(v.second);
}
if (S.size() == 2) break;
}
if (S.size() < 2) return INF;
return S.back();
}
void dfs(int u, int p){
h[u] = (u == p) ? 1 : (h[p] + 1);
sz[u] = 1;
for(int j = 1; MASK(j) < h[u]; ++j){
int prev = parent[u][j-1];
parent[u][j] = parent[prev][j-1];
max_path[u][j] = max(max_path[u][j-1], max_path[prev][j-1]);
rizz[u][j] = min(rizz[u][j-1], rizz[prev][j-1]);
}
int mi = INF, secondMi = INF;
for(pair<int, int> v: graph[u]) if (v.first != p){
if (mi > v.second){
secondMi = mi;
mi = v.second;
}
else minimize(secondMi, v.second);
}
dp1[u] = two_child(u, parent[u][0]);
for(pair<int, int> v: graph[u]) if (v.first != p && v.first >= 0){
parent[v.first][0] = u;
max_path[v.first][0] = v.second;
if (v.second == mi) rizz[v.first][0] = secondMi;
else rizz[v.first][0] = mi;
dfs(v.first, u);
sz[u] += sz[v.first];
minimize(dp1[u], max(dp1[v.first], v.second));
}
}
void dfs2(int u, int p){
if (h[u] > 1){
minimize(dp2[u], two_child(parent[u][0], u));
}
int mi = INF, secondMi = INF;
for(pair<int, int> v: graph[u]) if (v.first != p){
int val = max(v.second, dp1[v.first]);
if (mi > val){
secondMi = mi;
mi = val;
}
else minimize(secondMi, val);
}
for(pair<int, int> v: graph[u]) if (v.first != p && v.first >= 0){
int val = max(v.second, dp1[v.first]);
minimize(dp2[v.first], max(dp2[u], max_path[u][0]));
if (val == mi) minimize(dp2[v.first], secondMi);
else minimize(dp2[v.first], mi);
dfs2(v.first, u);
}
}
int LCA(int u, int v){
if (h[u] < h[v]) swap(u, v);
int diff = h[u] - h[v];
for(int j = 0; j < LOG_N; ++j) if (GETBIT(diff, j))
u = parent[u][j];
if (u == v) return u;
for(int j = LOG_N - 1; j>=0; --j) if (parent[u][j] != parent[v][j]){
u = parent[u][j];
v = parent[v][j];
}
return parent[u][0];
}
void init(int _n, int _m, vector<int> U, vector<int> V, vector<int> W) {
n = _n, m = _m;
vector<array<int, 3>> e;
for(int i = 0; i<m; ++i) e.push_back({{U[i], V[i], W[i]}});
sort(ALL(e), [](array<int, 3> x, array<int, 3> y){return x[2] < y[2];});
DSU mst(n);
vector<array<int, 3>> outlier;
for(auto i: e){
int u= i[0], v = i[1], w = i[2];
if (mst.join_set(i[0], i[1])) {
graph[u].push_back({v, w});
graph[v].push_back({u, w});
}
else {
outlier.push_back(i);
graph[u].push_back({-1, w});
graph[v].push_back({-1, w});
}
}
for(int i = 0; i<n; ++i){
sort(ALL(graph[i]), [](pair<int, int> x, pair<int, int> y){return x.second < y.second;});
}
for(int i = 0; i<n; ++i) dp1[i] = dp2[i] = INF;
dfs(0, 0);
dfs2(0, 0);
for(int i = 0; i<n; ++i) val[i] = INF;
DSU jump(n);
for(auto i: outlier){
int u = i[0], v = i[1], w = i[2];
int lck = LCA(u, v);
while(h[u] > h[lck]){
minimize(val[u], w);
jump.join_set(parent[u][0], u);
u = jump.find_set(u);
}
while(h[v] > h[lck]){
minimize(val[v], w);
jump.join_set(parent[v][0], v);
v = jump.find_set(v);
}
}
}
int get_weight(int u, int v, int lck = -1){
if (lck == -1) lck = LCA(u, v);
int ans= -1;
int diff = h[u] - h[lck];
for(int j = 0; j< LOG_N; ++j) if (GETBIT(diff, j)) {
maximize(ans, max_path[u][j]);
u = parent[u][j];
}
diff = h[v] - h[lck];
for(int j = 0; j<LOG_N; ++j) if (GETBIT(diff, j)){
maximize(ans, max_path[v][j]);
v = parent[v][j];
}
return ans;
}
int get_rizz(int u, int d){
int ans= INF;
for(int j = 0; j< LOG_N; ++j) if (GETBIT(d, j)) {
minimize(ans, rizz[u][j]);
u = parent[u][j];
}
return ans;
}
int binary_lift(int u, int d){
for(int j = 0; j < LOG_N; ++j) if (GETBIT(d, j))
u = parent[u][j];
return u;
}
int getMinimumFuelCapacity(int x, int y) {
if (h[x] > h[y]) swap(x, y);
int lck = LCA(x, y);
int lim = get_weight(x, y, lck);
int ans = INF;
if (lck == x){
int _x = binary_lift(y, h[y] - h[x] - 1);
int t1 = dp2[_x], t2 = dp1[y];
minimize(ans, min(t1, t2));
minimize(ans, val[y]);
minimize(ans, val[_x]);
minimize(ans, get_rizz(y, h[y] - h[lck] - 1));
}
else{
int t1 = dp1[x], t2 = dp1[y];
minimize(ans, min(t1, t2));
minimize(ans, val[x]);
minimize(ans, val[y]);
minimize(ans, get_rizz(x, h[x] - h[lck] - 1));
minimize(ans, get_rizz(y, h[y] - h[lck] - 1));
int _x = binary_lift(x, h[x] - h[lck] - 1);
int _y = binary_lift(y, h[y] - h[lck] - 1);
for(pair<int, int> v: graph[lck]) {
if (v.first == _x || v.first == _y) continue;
minimize(ans, v.second);
break;
}
}
if (ans == INF) return -1;
maximize(ans, lim);
return ans;
}
// int main(void){
// ios::sync_with_stdio(0); cin.tie(0); cout.tie(0);
// // freopen("input.inp", "r", stdin);
// int n, m; cin >> n >> m;
// vector<int> U, V, W;
// for(int i = 0; i<m; ++i){
// int u, v, w; cin >> u >> v >> w;
// U.push_back(u); V.push_back(v); W.push_back(w);
// }
// init(n, m, U, V, W);
// int q; cin >> q;
// while(q--){
// int x, y; cin >> x >> y;
// cout << getMinimumFuelCapacity(x, y) << "\n";
// }
// return 0;
// }
