#ifndef hwe
#include "Joi.h"
#endif
#include <bits/stdc++.h>
using namespace std;
#define POPCOUNT(n) (__builtin_popcountll((n)))
#define CLZ(n) (__builtin_clzll((n)))
#define CTZ(n) (__builtin_ctzll((n)))
#define LOG(n) (63 - __builtin_clzll((n)))
#define BIT(n, i) (((n) >> (i)) & 1ll)
#define MASK(i) (1ll << (i))
#define FLIP(n, i) ((n) ^ (1ll << (i)))
#define ON(n, i) ((n) | MASK(i))
#define OFF(n, i) ((n) & ~MASK(i))
#define Int __int128
#define fi first
#define se second
typedef long long ll;
typedef unsigned long long ull;
typedef long double ld;
typedef pair<int, int> pii;
typedef pair<long long, long long> pll;
typedef pair<long long, int> pli;
typedef pair<int, long long> pil;
typedef vector<pair<int, int>> vii;
typedef vector<pair<long long, long long>> vll;
typedef vector<pair<long long, int>> vli;
typedef vector<pair<int, long long>> vil;
template <class T1, class T2> bool maximize(T1 &x, T2 y) {
if (x < y) {
x = y;
return true;
}
return false;
}
template <class T1, class T2> bool minimize(T1 &x, T2 y) {
if (x > y) {
x = y;
return true;
}
return false;
}
template <class T> void remove_duplicate(vector<T> &ve) {
sort (ve.begin(), ve.end());
ve.resize(unique(ve.begin(), ve.end()) - ve.begin());
}
mt19937_64 rng(chrono::high_resolution_clock::now().time_since_epoch().count());
long long random(long long l, long long r) {
return uniform_int_distribution<long long>(l, r)(rng);
}
unsigned long long random(unsigned long long l, unsigned long long r) {
return uniform_int_distribution<unsigned long long>(l, r)(rng);
}
template <class T> T random(T r) {
return rng() % r;
}
const int N = 1e6 + 5, LG = 60;
const int MOD = 1e9 + 7;
const int inf = 1e9;
const long long INF = 1e18;
#ifdef hwe
void MessageBoard(int u, int msg) {
cerr << "message " << u << ' ' << msg << endl;
}
#endif
int info[N], dep[N];
vector<int> adj[N], order;
void dfs(int u, int fa) {
order.emplace_back(u);
for (auto v : adj[u]) if (v != fa) {
dep[v] = dep[u] + 1;
dfs(v, u);
}
}
void Joi(int n, int m, int a[], int b[], ll X, int subtask) {
for (int i = 0; i < m; ++i) {
adj[a[i]].emplace_back(b[i]);
adj[b[i]].emplace_back(a[i]);
}
order.clear();
dfs(0, -1);
if (*max_element(dep, dep + n) + 1 >= LG) {
for (int i = 0; i < n; ++i)
MessageBoard(i, BIT(X, dep[i] % LG));
return;
}
vector<int> ve, state(n, 0);
// state[i]: 0: not visited, 1: activated, 2: deleted
for (int i = 0; i < LG; ++i) {
info[order[i]] = i;
state[order[i]] = 1, ve.emplace_back(order[i]);
}
for (int i = LG; i < n; ++i) {
state[order[i]] = 1, ve.emplace_back(order[i]);
for (int j = 0; j < ve.size(); ++j) {
int u = ve[j], cnt = 0;
for (auto v : adj[u]) cnt += (state[v] != 2);
if (cnt > 1) continue; // this is a leaf in the component
info[order[i]] = info[u], state[u] = 2;
ve.erase(ve.begin() + j);
break;
}
}
for (int i = 0; i < n; ++i)
cerr << info[i] << ' ';
cerr << '\n';
for (int i = 0; i < n; ++i)
MessageBoard(i, BIT(X, info[i]));
}
#ifdef hwe
int a[N], b[N];
signed main() {
int n, m; cin >> n >> m;
ll X; cin >> X;
for (int i = 0; i < m; ++i) cin >> a[i] >> b[i];
Joi(n, m, a, b, X, 0);
return 0;
}
#endif
#ifndef hwe
#include "Ioi.h"
#endif
#include <bits/stdc++.h>
using namespace std;
#define POPCOUNT(n) (__builtin_popcountll((n)))
#define CLZ(n) (__builtin_clzll((n)))
#define CTZ(n) (__builtin_ctzll((n)))
#define LOG(n) (63 - __builtin_clzll((n)))
#define BIT(n, i) (((n) >> (i)) & 1ll)
#define MASK(i) (1ll << (i))
#define FLIP(n, i) ((n) ^ (1ll << (i)))
#define ON(n, i) ((n) | MASK(i))
#define OFF(n, i) ((n) & ~MASK(i))
#define Int __int128
#define fi first
#define se second
typedef long long ll;
typedef unsigned long long ull;
typedef long double ld;
typedef pair<int, int> pii;
typedef pair<long long, long long> pll;
typedef pair<long long, int> pli;
typedef pair<int, long long> pil;
typedef vector<pair<int, int>> vii;
typedef vector<pair<long long, long long>> vll;
typedef vector<pair<long long, int>> vli;
typedef vector<pair<int, long long>> vil;
template <class T1, class T2> bool maximize(T1 &x, T2 y) {
if (x < y) {
x = y;
return true;
}
return false;
}
template <class T1, class T2> bool minimize(T1 &x, T2 y) {
if (x > y) {
x = y;
return true;
}
return false;
}
template <class T> void remove_duplicate(vector<T> &ve) {
sort (ve.begin(), ve.end());
ve.resize(unique(ve.begin(), ve.end()) - ve.begin());
}
mt19937_64 rng(chrono::high_resolution_clock::now().time_since_epoch().count());
long long random(long long l, long long r) {
return uniform_int_distribution<long long>(l, r)(rng);
}
unsigned long long random(unsigned long long l, unsigned long long r) {
return uniform_int_distribution<unsigned long long>(l, r)(rng);
}
template <class T> T random(T r) {
return rng() % r;
}
const int N = 1e6 + 5, LG = 60;
const int MOD = 1e9 + 7;
const int inf = 1e9;
const long long INF = 1e18;
#ifdef hwe
int Move(int u) {
return 1;
}
#endif
ll X = 0;
int info[N], dep[N], par[N];
vector<int> adj[N], order;
void dfs(int u, int fa) {
order.emplace_back(u);
for (auto v : adj[u]) if (v != fa) {
par[v] = u, dep[v] = dep[u] + 1;
dfs(v, u);
}
}
void getAns(vector<int> &state, int u) {
assert(state[u] == 1); state[u] = 0;
for (auto v : adj[u]) if (state[v] == 1) {
X |= (ll)Move(v) << info[v];
getAns(state, v);
Move(u);
}
}
ll Ioi(int n, int m, int a[], int b[], int P, int V, int subtask) {
for (int i = 0; i < m; ++i) {
adj[a[i]].emplace_back(b[i]);
adj[b[i]].emplace_back(a[i]);
}
order.clear();
dfs(0, -1);
if (*max_element(dep, dep + n) + 1 >= LG) {
for (int i = 0; i < n; ++i) info[i] = dep[i] % LG;
while (info[P] != 0) X = Move(P = par[P]);
for (int _ = 1; _ < LG; ++_) {
for (auto v : adj[P]) if (dep[v] == dep[P] + 1) {
X |= (ll)Move(v) << info[v];
P = v; break;
}
}
return X;
}
vector<int> ve, state(n, 0);
// state[i]: 0: not visited, 1: activated, 2: deleted
for (int i = 0; i < LG; ++i) {
info[order[i]] = i;
state[order[i]] = 1, ve.emplace_back(order[i]);
}
for (int i = LG; state[P] == 0; ++i) {
state[order[i]] = 1, ve.emplace_back(order[i]);
for (int j = 0; j < ve.size(); ++j) {
int u = ve[j], cnt = 0;
for (auto v : adj[u]) cnt += (state[v] != 2);
if (cnt > 1) continue; // this is a leaf in the component
info[order[i]] = info[u], state[u] = 2;
ve.erase(ve.begin() + j);
break;
}
}
X = (ll)V << info[P];
getAns(state, P);
return X;
}
#ifdef hwe
int a[N], b[N];
signed main() {
int n, m; cin >> n >> m;
ll X; cin >> X;
for (int i = 0; i < m; ++i) cin >> a[i] >> b[i];
return 0;
}
#endif
