//Never stop trying
/*#pragma GCC target ("avx2")
#pragma GCC optimize ("Ofast")
#pragma GCC optimization ("O3")
#pragma GCC optimization ("unroll-loops")*/
#include "bits/stdc++.h"
using namespace std;
#define boost ios_base::sync_with_stdio(false); cin.tie(0); cout.tie(0)
typedef long long ll;
typedef string str;
typedef double db;
typedef long double ld;
typedef pair<int, int> pi;
#define fi first
#define se second
typedef vector<int> vi;
typedef vector<pi> vpi;
typedef vector<str> vs;
typedef vector<ld> vd;
#define pb push_back
#define eb emplace_back
#define sz(x) (int)x.size()
#define all(x) begin(x), end(x)
#define rall(x) rbegin(x), rend(x)
#define endl "\n"
#define FOR(i,a,b) for (int i = (a); i < (b); ++i)
#define ROF(i,a,b) for (int i = (b)-1; i >= (a); --i)
const int MOD = 1e9 + 7; //998244353
const ll INF = 1e9;
const int MX = 2e5 + 10;
const int nx[4] = {0, 0, 1, -1}, ny[4] = {1, -1, 0, 0}; //right left down up
template<class T> using V = vector<T>;
template<class T> bool ckmin(T& a, const T& b) { return a > b ? a = b, 1 : 0; }
template<class T> bool ckmax(T& a, const T& b) { return a < b ? a = b, 1 : 0; }
ll cdiv(ll a, ll b) { return a / b + ((a ^ b) > 0 && a % b); } // divide a by b rounded up
//constexpr int log2(int x) { return 31 - __builtin_clz(x); } // floor(log2(x))
mt19937 rng(chrono::system_clock::now().time_since_epoch().count());
//mt19937_64 rng(chrono::system_clock::now().time_since_epoch().count());
ll random(ll a, ll b){
return a + rng() % (b - a + 1);
}
#ifndef LOCAL
#define cerr if(false) cerr
#endif
#define dbg(x) cerr << #x << " : " << x << endl;
#define dbgs(x,y) cerr << #x << " : " << x << " / " << #y << " : " << y << endl;
#define dbgv(v) cerr << #v << " : " << "[ "; for(auto it : v) cerr << it << ' '; cerr << ']' << endl;
#define here() cerr << "here" << endl;
void IO() {
#ifdef LOCAL
freopen("input.txt", "r", stdin);
freopen("output.txt", "w", stdout);
#endif
}
#ifndef LOCAL
#include "split.h"
#endif
int N,A,B,C;
vi adj[MX];
vi res;
bool sub1(){
FOR(i,0,N) if(sz(adj[i])>2) return false;
return true;
}
int nb,nb2;
void dfs(int u){
for(auto v: adj[u]) if(res[v]==-1 && nb<B){
res[v]=2;
nb++;
dfs(v);
}
}
vi v,vv;
bool cmp(int i, int j){
return v[i] < v[j];
}
int sub[MX],par[MX];
void dfs2(int u, int p){
sub[u]=1; par[u]=p;
for(auto v: adj[u]) if(v!=p){
dfs2(v,u);
sub[u]+=sub[v];
}
}
void dfs3(int u, int p, int node, int c){
res[u]=c;
if(c==vv[1]+1) nb2++;
else nb++;
for(auto nxt: adj[u]) if(nxt!=p && !((c==vv[1]+1 && nb2==v[vv[1]]) || (
c==vv[0]+1 && nb==v[vv[0]])) && nxt!=node){
dfs3(nxt,u,node,c);
}
}
vi find_split(int n, int a, int b, int c, vi p, vi q) {
N=n; A=a; B=b; C=c;
FOR(i,0,sz(p)){
int u=p[i],v=q[i];
adj[u].pb(v);
adj[v].pb(u);
}
if(sub1()){
int u=0,p=-1;
FOR(i,0,N) if(sz(adj[i])==1){u=i; break;}
vi vec;
while(sz(vec)<N){
vec.pb(u);
int nxt=-1;
for(auto v: adj[u]) if(v!=p) nxt=v;
p=u; u=nxt;
}
vi res(N,3);
FOR(i,0,a) res[vec[i]]=1;
FOR(i,a,a+b) res[vec[i]]=2;
return res;
}
else if(a==1){
res.assign(N,-1);
res[0]=2; nb=1;
dfs(0);
FOR(i,0,N) if(res[i]==-1){res[i]=1; break;}
FOR(i,0,N) if(res[i]==-1) res[i]=3;
return res;
}
else if(sz(p)==N-1){
v={a,b,c},vv={0,1,2};
sort(all(vv),cmp);
dfs2(0,0);
int u,mn=INF;
res.assign(N,0);
int stt;
FOR(i,0,N){
if(sub[i]>=v[vv[0]] && sub[i]<mn){
mn=sub[i];
u=i;
stt=0;
}
else if(N-sub[i]>=v[vv[0]] && N-sub[i]<mn){
mn=N-sub[i];
u=i;
stt=1;
}
}
if(N-mn<v[vv[1]]){
return res;
}
nb=0; nb2=0;
if(stt==0){
dfs3(0,0,u,vv[1]+1);
dfs3(u,par[u],u,vv[0]+1);
}
else{
dfs3(0,0,u,vv[0]+1);
dfs3(u,par[u],u,vv[1]+1);
}
FOR(i,0,N) if(res[i]==0) res[i]=vv[2]+1;
return res;
}
return{};
}
#ifdef LOCAL
int main() {
boost; IO();
int N,M,a,b,c; cin>>N>>M>>a>>b>>c;
vi p(M),q(M);
FOR(i,0,M) cin>>p[i]>>q[i];
vi v=find_split(N,a,b,c,p,q);
dbgv(v);
return 0;
}
#endif
/*
a=1
5 6 1 2 2
0 1
1 2
2 3
3 0
0 2
2 4
*/
/* Careful!!!
.Array bounds
.Infinite loops
.Uninitialized variables / empty containers
.Multisets are shit
Some insights:
.Binary search
.Graph representation
.Write brute force code
.Change your approach
*/
