#pragma GCC optimize("O3", "fast-math", "unroll-loops", "no-stack-protector")
#include <bits/stdc++.h>
using namespace std;
#if !defined(ONLINE_JUDGE) and !defined(EVAL)
#include "template/debug.h"
#else
#define d(x...)
#endif
#define fr first
#define er erase
#define in insert
#define sc second
#define ll long long
#define pb push_back
#define vll vector<ll>
#define pll pair<ll,ll>
#define len(x) (ll) x.size()
#define all(x) x.begin(),x.end()
const ll INF = 1e9, INFL = 1e18;
const ll MOD = 1e9 + 7;
// const ll MOD = 998244353;
const ll maxn = 2e5 + 5;
ll n, m, k = 0;
#include "split.h"
ll dsu[maxn], cap[maxn];
void build_dsu(ll _n){
for(ll i = 1; i <= _n; i ++) dsu[i] = i, cap[i] = 1;
}
ll find(ll x){
if(dsu[x] == x) return x;
return dsu[x] = find(dsu[x]);
}
ll merge(ll a, ll b){
ll par_a = find(a), par_b = find(b);
if(par_a == par_b) return 0;
dsu[par_b] = par_a;
cap[par_a] += cap[par_b];
return 1;
}
vll g[maxn], tg[maxn];
ll sz[maxn];
vector<pll>ot, edg;
bitset<maxn>vis;
void dfs(ll u, ll p = -1){
sz[u] ++;
for(auto v : tg[u]){
if(v == p) continue;
dfs(v, u);
sz[u] += sz[v];
}
}
void dsu_merge(ll u, ll p = -1){
for(auto v : tg[u]){
if(v == p) continue;
merge(u, v);
dsu_merge(v, u);
}
}
void fill1(ll u, vll &ve, ll le){
vis[u] = 1;
ve.pb(u);
if(len(ve) == le) return;
for(auto v : g[u]){
if(vis[v]) continue;
if(find(u) != find(v)) continue;
fill1(v, ve, le);
if(len(ve) == le) break;
}
}
void fill2(ll u, vll &ve, ll le){
vis[u] = 1;
ve.pb(u);
if(len(ve) == le) return;
for(auto v : g[u]){
if(vis[v]) continue;
fill2(v, ve, le);
if(len(ve) == le) break;
}
}
pair<vll, vll>f(ll a, ll b){
if(a > b) swap(a, b);
// 7 balliq subtask : cycle (AC)
// 11 balliq subtask : a = 1 (AC)
// 22 balliq subtask : tree (AC)
// demeli biz ele u - v cutu tapmaliyiq ki,
// 1) u ve v arasinda edge olsun;
// 2) bu edge-i silende v -nin subtree size-i >= a olsun ve u -nun subtree size-i >= b olsun;
// ** Esas Observation(+60 pts): tree olmayan qraf ucun ise, spanning tree mentiqi ile tree-ye cevire bilerik.
// n <= 2500
// 0 <= u <= n - 1 ucun dfs at, gor hansindasa alinirmi
vll ax, bx;
build_dsu(n);
// spanning tree duzelt
for(ll i = 0; i < len(edg); i ++){
auto [x, y] = edg[i];
if(merge(x, y)) tg[x].pb(y), tg[y].pb(x);
else ot.pb(edg[i]);
}
pll root = {-1, -1};
for(ll u = 0; u <= n - 1; u ++){
for(ll i = 0; i <= n - 1; i ++) sz[i] = 0;
dfs(u);
build_dsu(n);
for(auto v : tg[u]) dsu_merge(v, u);
for(auto v : tg[u]){
if(sz[v] >= a){
root = {v, u};
break;
}
}
if(root.fr != -1) break;
for(auto [x, y] : ot){
if(x == u or y == u) continue;
merge(x, y);
if(cap[find(x)] >= a){
root = {find(x), u};
break;
}
}
if(root.fr != -1) break;
}
if(root.fr == -1) return {{}, {}};
vis.reset();
vis[root.sc] = 1;
fill1(root.fr, ax, a);
vis[root.sc] = 0;
fill2(root.sc, bx, b);
return {ax, bx};
}
vector<int> find_split(int _n, int _a, int _b, int _c, vector<int> _p, vector<int> _q) {
n = _n;
for(ll i = 0; i < n; i ++) g[i].clear(), tg[i].clear(), sz[i] = 0;
ot.clear(); edg.clear();
for(ll i = 0; i < len(_p); i ++){
g[_p[i]].pb(_q[i]), g[_q[i]].pb(_p[i]);
edg.pb({_p[i], _q[i]});
}
vector<int>cv(n);
if(_a <= _c and _b <= _c){
auto [ax, bx] = f(_a, _b);
if(_a > _b) swap(ax, bx);
if(len(ax) != _a) return cv;
cv.assign(n, 3);
for(auto i : ax) cv[i] = 1;
for(auto i : bx) cv[i] = 2;
}
else if(_a <= _b and _c <= _b){
auto [ax, cx] = f(_a, _c);
if(_a > _c) swap(ax, cx);
if(len(ax) != _a) return cv;
cv.assign(n, 2);
for(auto i : ax) cv[i] = 1;
for(auto i : cx) cv[i] = 3;
}
else{
auto [bx, cx] = f(_b, _c);
if(_b > _c) swap(bx, cx);
if(len(bx) != _b) return cv;
cv.assign(n, 1);
for(auto i : bx) cv[i] = 2;
for(auto i : cx) cv[i] = 3;
}
return cv;
}
// void _() {
// }
// signed main() {
// ll tm = clock();
// cin.tie(0)->sync_with_stdio(0);
// ll t = 1;
// cin >> t;
// for(ll tt = 1; tt <= t; tt ++) _();
// cerr << "\n\033[1;31mTime: \033[1;30m" \
// << (double)(clock()-tm)/1000000 << "\033[1;32m seconds\n";
// }
