#include "simurgh.h"
#include<bits/stdc++.h>
using namespace std;
#define pb push_back
#define ff first
#define ss second
#define all(x) (x).begin(), (x).end()
typedef pair<int, int> pii;
typedef long long lld;
typedef long double ld;
template<typename Iter>
ostream& outIt(ostream& out, Iter b, Iter e){
for(Iter i = b; i != e; ++i)
out << (i == b?"":" ") << *i;
return out;
}
template<typename T1, typename T2>
ostream& operator<<(ostream& out, pair<T1, T2> p){
return out << '(' << p.ff << ", " << p.ss << ')';
}
template<typename T>
ostream& operator<<(ostream& out, vector<T> v){
return outIt(out << '[', all(v)) << ']';
}
vector<vector<pii>> G;
vector<bool> asked, ans;
vector<int> te, es, dep, par, pe;
vector<pii> Edges;
//int c = 0;
int dfs(int i, int d = 1){
//cout << i << " " << d << " " << par[i] << endl;
//if(c++>100)exit(-1);
dep[i] = d;
int minup = d;
for(auto x : G[i]){
if(x.ss == pe[i])continue;
if(dep[x.ff]){
//cout << "counter" << x << endl;
minup = min(minup, dep[x.ff]);
continue;
}
es.pb(x.ss);
te[x.ss] = es.size();
pe[x.ff] = x.ss; par[x.ff] = i;
minup = min(minup, dfs(x.ff, d + 1));
}
if(!i)return 0;
//cout << i << minup << endl;
if(minup == d){
ans[pe[i]] = true;
asked[pe[i]] = true;
}
return minup;
}
int asking(int tree, int nontree){
//cout << "ask " << tree << " " << nontree << endl;
swap(es[te[tree]-1], nontree);
int ansx = count_common_roads(es);
swap(es[te[tree]-1], nontree);
//cout << ansx << endl;
return ansx;
}
vector<int> dsu;
int root(int i){ return i == dsu[i] ? i : (dsu[i] = root(dsu[i])); }
inline bool join(int i, int j){ i = root(i), j = root(j); if(i == j)return false; dsu[i] = j; return true; }
int ask2(vector<int>& v){
//cout << v << es << endl;
iota(all(dsu), 0);
int mm = v.size(), cnt = 0;
for(auto i: v)assert(join(Edges[i].ff, Edges[i].ss));
//cout << "gh" << endl;
for(auto i: es)
if(join(Edges[i].ff, Edges[i].ss))
cnt += ans[i], v.pb(i);
int ret = count_common_roads(v);
v.resize(mm);
return ret - cnt;
}
void process(int k){
vector<int> gt, a;
for(auto x: G[k])
if(!asked[x.ss])gt.pb(x.ss);
if(gt.size() == 0)return;
int deg = ask2(gt);
//cout << "process" << k << endl;
//for(auto i: gt)cout << Edges[i]; cout << endl;
//cout << deg << endl;
for(int i = 0; i < deg; i++){
int l = 0, r = gt.size();
while(r-l > 1){
a.resize(0);
for(int j = 0; j < (l+r>>1); j++)a.pb(gt[j]);
(ask2(a) <= i?l:r) = l+r>>1;
}
ans[gt[l]] = true;
}
for(auto i: gt)asked[i] = true;
//cout << asked << endl << ans << endl << endl;
}
vector<int> find_roads(int n, vector<int> u, vector<int> v) {
int m = u.size();
te.resize(m); asked.resize(m); ans.resize(m); pe.resize(n); par.resize(n); dep.resize(n); pe[0] = -1; dsu.resize(n);
G.resize(n);
for(int i = 0; i < m; i++)Edges.pb({u[i], v[i]});
for(int i = 0; i < m; i++)G[u[i]].pb({v[i], i}), G[v[i]].pb({u[i], i});
dfs(0);
int tans = count_common_roads(es);
//cout << tans << endl;
//cout << asked << endl;
//cout << te << es << dep << par << endl;
for(int i = 0; i < m; i++) if(dep[u[i]] < dep[v[i]])swap(u[i], v[i]);
for(int i = 0; i < m; i++)
if(!te[i]){
//cout << i << endl;
int tt = -1, go = false;
for(int c = u[i]; c != v[i]; c = par[c]){
if(asked[pe[c]])tt = pe[c];
else go = true;
}
if(!go)continue;
if(tt != -1){
{
int cans = asking(tt, i);
if(cans == tans)ans[i] = ans[tt];
else if(cans < tans)ans[i] = false, assert(ans[tt] == true);
else if(cans > tans)ans[i] = true, assert(ans[tt] == false);
asked[i] = true;
}
for(int c = u[i]; c != v[i]; c = par[c])
if(!asked[pe[c]]){
int cans = asking(pe[c], i);
if(cans == tans)ans[pe[c]] = ans[i];
else if(cans < tans)ans[pe[c]] = true;
else if(cans > tans)ans[i] = true;
asked[pe[c]] = true;
}
}else{
for(int c = u[i]; c != v[i]; c = par[c])
if(!asked[pe[c]]){
int cans = asking(pe[c], i);
if(cans < tans)ans[pe[c]] = true;
else if(cans > tans)ans[i] = true;
if(cans != tans)asked[pe[c]] = asked[i] = true;
}
asked[i] = true;
for(int c = u[i]; c != v[i]; c = par[c])
if(!asked[pe[c]]) ans[pe[c]] = ans[i], asked[pe[c]] = true;
}
}
//cout << asked << endl << ans << endl;
for(int i = 0; i < n; i++)process(i);
//cout << asked << endl << ans << endl;
vector<int> ret;
for(int i = 0; i < m; i++){
assert(asked[i]);
if(ans[i])ret.pb(i);
}
//assert(ret.size() == n-1);
return ret;
}
