#include #include #include #include #include #include #include #include #include #include #include #include #include #include using namespace std; using ll = long long; class range {private: struct I{int x;int operator*(){return x;}bool operator!=(I& lhs){return x ostream& operator<<(ostream& os, const pair& p){ return os << "{" << p.first << ", " << p.second << "}"; } template ostream& operator<<(ostream& os, const vector& obj) { os << "{"; for (const auto& e : obj) os << e << ", "; return os << "}"; } template ostream& operator<<(ostream& os, const set& obj) { os << "set{"; for (const auto& e : obj) os << e << ", "; return os << "}"; } template ostream& operator<<(ostream& os, const map& obj) { os << "map{"; for (const auto& e : obj) os << e << ", "; return os << "}"; } template void take(vector& vec, int n) { vec.resize(n); for (int i = 0; i < n; ++i) cin >> vec[i]; } #ifdef ONLINE_JUDGE #define dump(expr) ; #else #define dump(expr) { cerr << "\033[33m#L" << __LINE__ << ": " << expr << "\033[39m" << endl; } #endif using EdgeCost = ll; struct E { int fr, to, eid; EdgeCost cost; E(int fr_, int to_, int eid_, EdgeCost cost_) : fr(fr_), to(to_), eid(eid_), cost(cost_) {} friend ostream &operator<<(ostream &os, const E &e) { os << "(" << e.fr << " -> " << e.to << ")"; return os; } }; using V = vector; struct G { int n, e_count; vector adj, rev; G(int n_) : n(n_), e_count(0), adj(n), rev(n) {} void add_directed_edge(int fr, int to, EdgeCost cost = (EdgeCost)1) { assert(0 <= fr && fr < n); assert(0 <= to && to < n); E e(fr, to, e_count++, cost); adj[fr].push_back(e); rev[to].push_back(e); } void add_undirected_edge(int fr, int to, EdgeCost cost = (EdgeCost)1) { assert(0 <= fr && fr < n); assert(0 <= to && to < n); E e1(fr, to, e_count, cost), e2(to, fr, e_count++, cost); adj[fr].push_back(e1); rev[to].push_back(e1); adj[to].push_back(e2); rev[to].push_back(e2); } }; namespace solver { template struct In2 { T1 a; T2 b; friend std::istream& operator>>(std::istream& is, In2& obj) { T1 t1; T2 t2; is >> t1 >> t2; obj = {t1, t2}; return is; } }; template struct In3 { T1 a; T2 b; T3 c; friend std::istream& operator>>(std::istream& is, In3& obj) { T1 t1; T2 t2; T3 t3; is >> t1 >> t2 >> t3; obj = {t1, t2, t3}; return is; } }; int n; vector> edges; void read() { cin >> n; take(edges, n - 1); } using I = pair; // [fir, sec) void split(I interval, vector& res) { auto [a, b] = interval; int N = 1 << 20; a += N; b += N; int len = 1; auto add = [&](int p) { int p2 = p * len; res.push_back({p2 - N, p2 + len - N}); }; while (a < b) { if (a & 1) { add(a); a++; } if (b & 1) { b--; add(b); } a >>= 1; b >>= 1; len <<= 1; } } vector masks; void take_xor(vector& intervals, int x, vector& res) { for (auto interval : intervals) { int s = interval.second - interval.first; int mask = s - 1; int na = (interval.first & ~mask) ^ (x & ~mask); res.push_back({na, na + s}); } } vector merge(vector& intervals) { vector res; int begin = -1, end = -1; ranges::sort(intervals); for (auto interval : intervals) { if (end < interval.first) { if (begin >= 0) res.push_back({begin, end}); begin = interval.first; end = interval.second; } else { end = max(end, interval.second); } } res.push_back({begin, end}); return res; } G g(0); vector vf, vg; vector> vGset; void dfs(int now, int par) { for (auto e : g.adj[now]) if (e.to != par) dfs(e.to, now); int f = 0; for (auto e : g.adj[now]) if (e.to != par) f ^= vg[e.to]; vf[now] = f; vector intervals{{f, f + 1}}; for (auto e : g.adj[now]) if (e.to != par) { take_xor(vGset[e.to], f ^ vg[e.to], intervals); if (now == 1) { dump(vGset[e.to] << " " << f << " " << vg[e.to]) dump(intervals) } } intervals = merge(intervals); vg[now] = intervals[0].second; for (auto interval : intervals) split(interval, vGset[now]); dump(now << " " << vGset[now]); } vector ans; void dfs2(int now, int par, int grundy) { if (grundy == 0) ans.push_back(now); for (auto e : g.adj[now]) if (e.to != par) { dfs2(e.to, now, grundy ^ vg[e.to] ^ vf[e.to]); } } using RetType = void; RetType run() { { vector res; split({2, 7}, res); ranges::sort(res); dump(res); } { vector iv{{12, 16}}, res; take_xor(iv, 128, res); dump(res); } g = G(n + 1); for (auto e : edges) g.add_undirected_edge(e.a, e.b); vf.assign(n + 1, -1); vg.assign(n + 1, -1); vGset.assign(n + 1, vector()); dfs(1, -1); dump(vg); dump(vf); ans.clear(); dfs2(1, -1, vf[1]); if (ans.size() == 0) { cout << "Bob" << endl; } else { cout << "Alice" << endl; cout << ans.size() << endl; ranges::sort(ans); for (auto a : ans) cout << a << " "; cout << endl; } } } // namespace template void run(F f) { if constexpr (std::is_same_v) f(); else cout << f() << endl; } int main(int argc, char** argv) { cerr << fixed << setprecision(12); cout << fixed << setprecision(12); int testcase = 1; if (argc > 1) testcase = atoi(argv[1]); while (testcase--) { solver::read(); } run(solver::run); }