/* #region Head */ // #include #include #include #include #include // assert.h #include // math.h #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include using namespace std; using ll = long long; using ull = unsigned long long; using ld = long double; using pll = pair; template using vc = vector; template using vvc = vc>; using vll = vc; using vvll = vvc; using vld = vc; using vvld = vvc; using vs = vc; using vvs = vvc; template using um = unordered_map; template using pq = priority_queue; template using pqa = priority_queue, greater>; template using us = unordered_set; #define TREP(T, i, m, n) for (T i = (m), i##_len = (T)(n); i < i##_len; ++(i)) #define TREPM(T, i, m, n) for (T i = (m), i##_max = (T)(n); i <= i##_max; ++(i)) #define TREPR(T, i, m, n) for (T i = (m), i##_min = (T)(n); i >= i##_min; --(i)) #define TREPD(T, i, m, n, d) for (T i = (m), i##_len = (T)(n); i < i##_len; i += (d)) #define TREPMD(T, i, m, n, d) for (T i = (m), i##_max = (T)(n); i <= i##_max; i += (d)) #define REP(i, m, n) for (ll i = (m), i##_len = (ll)(n); i < i##_len; ++(i)) #define REPM(i, m, n) for (ll i = (m), i##_max = (ll)(n); i <= i##_max; ++(i)) #define REPR(i, m, n) for (ll i = (m), i##_min = (ll)(n); i >= i##_min; --(i)) #define REPD(i, m, n, d) for (ll i = (m), i##_len = (ll)(n); i < i##_len; i += (d)) #define REPMD(i, m, n, d) for (ll i = (m), i##_max = (ll)(n); i <= i##_max; i += (d)) #define REPI(itr, ds) for (auto itr = ds.begin(); itr != ds.end(); itr++) #define REPIR(itr, ds) for (auto itr = ds.rbegin(); itr != ds.rend(); itr++) #define ALL(x) begin(x), end(x) #define SIZE(x) ((ll)(x).size()) #define ISIZE(x) ((int)(x).size()) #define PERM(c) \ sort(ALL(c)); \ for (bool c##p = 1; c##p; c##p = next_permutation(ALL(c))) #define UNIQ(v) v.erase(unique(ALL(v)), v.end()); #define CEIL(a, b) (((a) + (b)-1) / (b)) #define endl '\n' constexpr ll INF = 1'010'000'000'000'000'017LL; constexpr int IINF = 1'000'000'007LL; constexpr ll MOD = 1'000'000'007LL; // 1e9 + 7 // constexpr ll MOD = 998244353; constexpr ld EPS = 1e-12; constexpr ld PI = 3.14159265358979323846; template istream &operator>>(istream &is, vc &vec) { // vector 入力 for (T &x : vec) is >> x; return is; } template ostream &operator<<(ostream &os, const vc &vec) { // vector 出力 (for dump) os << "{"; REP(i, 0, SIZE(vec)) os << vec[i] << (i == i_len - 1 ? "" : ", "); os << "}"; return os; } template ostream &operator>>(ostream &os, const vc &vec) { // vector 出力 (inline) REP(i, 0, SIZE(vec)) os << vec[i] << (i == i_len - 1 ? "\n" : " "); return os; } template istream &operator>>(istream &is, array &arr) { // array 入力 REP(i, 0, SIZE(arr)) is >> arr[i]; return is; } template ostream &operator<<(ostream &os, const array &arr) { // array 出力 (for dump) os << "{"; REP(i, 0, SIZE(arr)) os << arr[i] << (i == i_len - 1 ? "" : ", "); os << "}"; return os; } template istream &operator>>(istream &is, pair &pair_var) { // pair 入力 is >> pair_var.first >> pair_var.second; return is; } template ostream &operator<<(ostream &os, const pair &pair_var) { // pair 出力 os << "(" << pair_var.first << ", " << pair_var.second << ")"; return os; } // map, um, set, us 出力 template ostream &out_iter(ostream &os, const T &map_var) { os << "{"; REPI(itr, map_var) { os << *itr; auto itrcp = itr; if (++itrcp != map_var.end()) os << ", "; } return os << "}"; } template ostream &operator<<(ostream &os, const map &map_var) { return out_iter(os, map_var); } template ostream &operator<<(ostream &os, const um &map_var) { os << "{"; REPI(itr, map_var) { auto [key, value] = *itr; os << "(" << key << ", " << value << ")"; auto itrcp = itr; if (++itrcp != map_var.end()) os << ", "; } os << "}"; return os; } template ostream &operator<<(ostream &os, const set &set_var) { return out_iter(os, set_var); } template ostream &operator<<(ostream &os, const us &set_var) { return out_iter(os, set_var); } template ostream &operator<<(ostream &os, const pq &pq_var) { pq pq_cp(pq_var); os << "{"; if (!pq_cp.empty()) { os << pq_cp.top(), pq_cp.pop(); while (!pq_cp.empty()) os << ", " << pq_cp.top(), pq_cp.pop(); } return os << "}"; } // tuple 出力 template ostream &operator<<(ostream &os, tuple &a) { if constexpr (N < std::tuple_size_v>) { os << get(a); if constexpr (N + 1 < std::tuple_size_v>) { os << ' '; } else if constexpr (end_line) { os << '\n'; } return operator<< (os, a); } return os; } template void print_tuple(tuple &a) { operator<< <0, true>(cout, a); } void pprint() { cout << endl; } template void pprint(Head &&head, Tail &&...tail) { cout << head; if (sizeof...(Tail) > 0) cout << ' '; pprint(move(tail)...); } // dump #define DUMPOUT cerr void dump_func() { DUMPOUT << endl; } template void dump_func(Head &&head, Tail &&...tail) { DUMPOUT << head; if (sizeof...(Tail) > 0) DUMPOUT << ", "; dump_func(move(tail)...); } // chmax (更新「される」かもしれない値が前) template > bool chmax(T &xmax, const U &x, Comp comp = {}) { if (comp(xmax, x)) { xmax = x; return true; } return false; } // chmin (更新「される」かもしれない値が前) template > bool chmin(T &xmin, const U &x, Comp comp = {}) { if (comp(x, xmin)) { xmin = x; return true; } return false; } // ローカル用 #ifndef ONLINE_JUDGE #define DEBUG_ #endif #ifndef MYLOCAL #undef DEBUG_ #endif #ifdef DEBUG_ #define DEB #define dump(...) \ DUMPOUT << " " << string(#__VA_ARGS__) << ": " \ << "[" << to_string(__LINE__) << ":" << __FUNCTION__ << "]" << endl \ << " ", \ dump_func(__VA_ARGS__) #else #define DEB if (false) #define dump(...) #endif #define VAR(type, ...) \ type __VA_ARGS__; \ assert((cin >> __VA_ARGS__)); template istream &operator,(istream &is, T &rhs) { return is >> rhs; } template ostream &operator,(ostream &os, const T &rhs) { return os << ' ' << rhs; } struct AtCoderInitialize { static constexpr int IOS_PREC = 15; static constexpr bool AUTOFLUSH = false; AtCoderInitialize() { ios_base::sync_with_stdio(false), cin.tie(nullptr), cout.tie(nullptr); cout << fixed << setprecision(IOS_PREC); if (AUTOFLUSH) cout << unitbuf; } } ATCODER_INITIALIZE; void Yn(bool p) { cout << (p ? "Yes" : "No") << endl; } void YN(bool p) { cout << (p ? "YES" : "NO") << endl; } template constexpr void operator--(vc &v, int) noexcept { for (int i = 0; i < ISIZE(v); ++i) v[i]--; } template constexpr void operator++(vc &v, int) noexcept { for (int i = 0; i < ISIZE(v); ++i) v[i]++; } /* #endregion */ // #include // using namespace atcoder; /* #region Graph */ // エッジ(本来エッジは双方向だが,ここでは単方向で管理) template struct Edge { int src; // エッジ始点となる頂点 int dst; // エッジ終点となる頂点 weight_t weight; // 重み flow_t cap; Edge() : src(0), dst(0), weight(0) {} Edge(int src, int dst, weight_t weight) : src(src), dst(dst), weight(weight) {} Edge(int src, int dst, weight_t weight, flow_t cap) : src(src), dst(dst), weight(weight), cap(cap) {} // Edge 標準出力 friend ostream &operator<<(ostream &os, Edge &edge) { os << "(" << edge.src << " -> " << edge.dst << ", " << edge.weight << ")"; return os; } }; // 同じ頂点を始点とするエッジ集合 template class Node : public vc> { public: int idx; Node() : vc>() {} // void add(int a, int b, weight_t w, flow_t cap) { this->emplace_back(a, b, w, cap); }; }; // graph[i] := 頂点 i を始点とするエッジ集合 template class Graph : public vc> { public: Graph() : vc>() {} Graph(int n) : vc>(n) { REP(i, 0, n)(*this)[i].idx = i; } /** 単方向 */ void add_arc(int a, int b, weight_t w = 1, flow_t cap = 1) { (*this)[a].emplace_back(a, b, w, cap); } /** 双方向 */ void add_edge(int a, int b, weight_t w = 1, flow_t cap = 1) { add_arc(a, b, w, cap), add_arc(b, a, w, cap); } /** ノード追加 */ int add_node() { int idx = (int)this->size(); this->emplace_back(); Node &node = this->back(); node.idx = idx; return idx; } }; // using Array = vc; // using Matrix = vc; /* #endregion */ /* #region LCA */ template class LCA { public: const int n = 0; const int log2_n = 0; vc> parent; vc depth; vc weight_distances; using G = Graph; LCA() {} // コンストラクタ,前処理 O(N log N) LCA(const G &g, int root) : n(g.size()), log2_n(log2(n) + 1), parent(log2_n, vc(n)), depth(n), weight_distances(n) { dfs(g, root, -1, 0, (weight_t)0); REP(k, 0, log2_n - 1) REP(v, 0, SIZE(g)) parent[k + 1][v] = (parent[k][v] < 0) ? -1 : parent[k][parent[k][v]]; } // 根からの距離と1つ先の頂点を求める void dfs(const G &g, int v, int p, int d, weight_t w) { parent[0][v] = p, depth[v] = d; weight_distances[v] = w; for (const Edge &e : g[v]) if (e.dst != p) dfs(g, e.dst, v, d + 1, w + e.weight); } // 頂点 u, v の LCA を求めて返す,O(log N) int get(int u, int v) const { if (depth[u] > depth[v]) std::swap(u, v); // 深い方を浅い方と同じ浅さまで移動することで,LCA までの深さを同じにする REP(k, 0, log2_n) if ((depth[v] - depth[u]) >> k & 1) v = parent[k][v]; if (u == v) return u; // 二分探索で LCA を求める REPR(k, log2_n - 1, 0) if (parent[k][u] != parent[k][v]) u = parent[k][u], v = parent[k][v]; return parent[0][u]; } // 頂点 v から dist だけ根のほうに遡った頂点を返す. // dist が根までの距離よりも大きいときは -1 を返す. int get_par(int v, int dist) const { // dist 遡れない int v_init_depth = get_depth(v); if (v_init_depth < dist) return -1; int u_depth = v_init_depth - dist; // 深い方を浅い方と同じ浅さまで移動することで,LCA までの深さを同じにする REP(k, 0, log2_n) if ((depth[v] - u_depth) >> k & 1) v = parent[k][v]; return v; } // 根を深さ 0 として,頂点 v の深さを返す.O(1). int get_depth(int v) const { assert(0 <= v && v < n); return depth[v]; } // 頂点 u, v の間を最短距離で結ぶときの辺数を返す.O(log N). int get_distance(int u, int v) const { const int r = get(u, v); return depth[u] + depth[v] - 2 * depth[r]; } // 頂点 u, v の間を最短距離で結ぶときの距離を返す.O(log N). weight_t get_weight_distance(int u, int v) const { const int r = get(u, v); return weight_distances[u] + weight_distances[v] - weight_distances[r] * 2; } // {(src->lca), (lca->dst)} を返す array, 2> get_path2(const int src, const int dst) const { const int common = get(src, dst); vc path_from_src = {src}; { int v = src; while (v != common) { v = parent[0][v]; path_from_src.push_back(v); } } vc path_from_dst = {dst}; { int v = dst; while (v != common) { v = parent[0][v]; path_from_dst.push_back(v); } } reverse(ALL(path_from_dst)); vc &path_to_dst = path_from_dst; return {path_from_src, path_to_dst}; } // src -> dst のパスを返す vc get_path(const int src, const int dst) const { auto [path_from_src, path_to_dst] = get_path2(src, dst); path_from_src.reserve(ISIZE(path_from_src) + ISIZE(path_to_dst)); TREP(int, i, 1, ISIZE(path_to_dst)) { path_from_src.push_back(path_to_dst[i]); } return path_from_src; } }; /* #endregion */ // Problem void solve() { VAR(ll, n, q); vll a(n - 1), b(n - 1); REP(i, 0, n - 1) cin >> a[i], b[i]; a--, b--; vll s(q), t(q); REP(i, 0, q) cin >> s[i], t[i]; s--, t--; Graph<> graph(n); REP(i, 0, n - 1) graph.add_edge(a[i], b[i]); LCA<> lca(graph, 0); REP(i, 0, q) { ll d = lca.get_distance(s[i], t[i]); pprint(d % 2 == 0); } } // entry point int main() { solve(); return 0; }