graph/ds/mo_on_tree.hpp

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• Last update: 2026-09-01 10:19:35+09:00
• Include: #include "graph/ds/mo_on_tree.hpp"
• Link: https://codeforces.com/contest/852/problem/I

Depends on

• ds/hashmap.hpp
• ds/offline_query/mo.hpp
• graph/base.hpp
• graph/tree.hpp

Verified with

• test/1_mytest/mo_on_tree.test.cpp

Code

#include "graph/tree.hpp"
#include "ds/offline_query/mo.hpp"

// https://codeforces.com/contest/852/problem/I
template <typename TREE, bool ORIENTED = false>
struct Mo_on_Tree {
  TREE& tree;
  vc<pair<int, int>> LR;

  Mo mo;
  Mo_on_Tree(TREE& tree) : tree(tree) {}
  void add(int u, int v) {
    if constexpr (!ORIENTED) {
      if (tree.LID[u] > tree.LID[v]) swap(u, v);
    }
    LR.eb(tree.ELID(u) + 1, tree.ELID(v) + 1);
  }

  // init(): root だけからなる path
  // add_l(v), add_r(v)：パスの先頭 / 末尾に v を追加
  // rm_l(v), rm_r(v)：パスの先頭 / 末尾から v を削除
  // query(qid)
  template <typename F1, typename F2, typename F3, typename F4, typename F5,
            typename F6>
  void calc_vertex(F1 init, F2 add_l, F3 add_r, F4 rm_l, F5 rm_r, F6 query) {
    const int N = tree.G.N;
    auto I = Mo::get_mo_order(LR);

    vc<int> FRM(2 * N), TO(2 * N), idx(2 * N);
    vc<int> cnt(N);
    deque<int> path = {0};
    FOR(v, N) {
      int a = tree.ELID(v), b = tree.ERID(v);
      FRM[a] = tree.parent[v], TO[a] = v;
      FRM[b] = v, TO[b] = tree.parent[v];
      idx[a] = idx[b] = v;
    }

    auto flip_left = [&](int i) -> void {
      const int a = FRM[i], b = TO[i], c = idx[i];
      if (cnt[c] == 0) {
        int v = path.front() ^ a ^ b;
        path.emplace_front(v), add_l(v);
      } else {
        int v = path.front();
        path.pop_front(), rm_l(v);
      }
      cnt[c] ^= 1;
    };
    auto flip_right = [&](int i) -> void {
      const int a = FRM[i], b = TO[i], c = idx[i];
      if (cnt[c] == 0) {
        int v = path.back() ^ a ^ b;
        path.emplace_back(v), add_r(v);
      } else {
        int v = path.back();
        path.pop_back(), rm_r(v);
      }
      cnt[c] ^= 1;
    };

    init();

    int l = 1, r = 1;
    for (auto idx: I) {
      int L = LR[idx].fi, R = LR[idx].se;
      while (l > L) { flip_left(--l); }
      while (r < R) { flip_right(r++); }
      while (l < L) { flip_left(l++); }
      while (r > R) { flip_right(--r); }
      query(idx);
    }
  }

  // init(): root だけからなる path
  // add_l(frm, to), add_r(frm, to)：パスの先頭 / 末尾に (frm,to) を追加
  // rm_l(frm, to), rm_r(frm, to)：パスの先頭 / 末尾に (frm,to) を追加
  // query(qid)
  template <typename F1, typename F2, typename F3, typename F4, typename F5,
            typename F6>
  void calc_edge(F1 init, F2 add_l, F3 add_r, F4 rm_l, F5 rm_r, F6 query) {
    const int N = tree.G.N;
    auto I = Mo::get_mo_order(LR);

    vc<int> FRM(2 * N), TO(2 * N), idx(2 * N);
    vc<int> cnt(N);
    deque<int> path = {0};
    FOR(v, N) {
      int a = tree.ELID(v), b = tree.ERID(v);
      FRM[a] = tree.parent[v], TO[a] = v;
      FRM[b] = v, TO[b] = tree.parent[v];
      idx[a] = idx[b] = v;
    }

    auto flip_left = [&](int i) -> void {
      const int a = FRM[i], b = TO[i], c = idx[i];
      if (cnt[c] == 0) {
        int v = path.front() ^ a ^ b;
        path.emplace_front(v), add_l(v, v ^ a ^ b);
      } else {
        int v = path.front();
        path.pop_front(), rm_l(v, v ^ a ^ b);
      }
      cnt[c] ^= 1;
    };
    auto flip_right = [&](int i) -> void {
      const int a = FRM[i], b = TO[i], c = idx[i];
      if (cnt[c] == 0) {
        int v = path.back() ^ a ^ b;
        path.emplace_back(v), add_r(v ^ a ^ b, v);
      } else {
        int v = path.back();
        path.pop_back(), rm_r(v ^ a ^ b, v);
      }
      cnt[c] ^= 1;
    };

    init();

    int l = 1, r = 1;
    for (auto idx: I) {
      int L = LR[idx].fi, R = LR[idx].se;
      while (l > L) { flip_left(--l); }
      while (r < R) { flip_right(r++); }
      while (l < L) { flip_left(l++); }
      while (r > R) { flip_right(--r); }
      query(idx);
    }
  }
};

#line 1 "graph/tree.hpp"

#line 1 "ds/hashmap.hpp"

// u64 -> Val
template <typename Val>
struct HashMap {
  // n は入れたいものの個数で ok
  HashMap(u32 n = 0) { build(n); }
  void build(u32 n) {
    u32 k = 8;
    while (k < n * 2) k *= 2;
    cap = k / 2, mask = k - 1;
    key.resize(k), val.resize(k), used.assign(k, 0);
  }

  // size を保ったまま. size=0 にするときは build すること.
  void clear() {
    used.assign(len(used), 0);
    cap = (mask + 1) / 2;
  }
  int size() { return len(used) / 2 - cap; }

  int index(const u64& k) {
    int i = 0;
    for (i = hash(k); used[i] && key[i] != k; i = (i + 1) & mask) {
    }
    return i;
  }

  Val& operator[](const u64& k) {
    int i = index(k);
    if (used[i]) return val[i];
    if (cap == 0) extend(), i = index(k);
    used[i] = 1, key[i] = k, val[i] = Val{}, --cap;
    return val[i];
  }

  Val get(const u64& k, Val default_value) {
    int i = index(k);
    return (used[i] ? val[i] : default_value);
  }

  bool count(const u64& k) {
    int i = index(k);
    return used[i] && key[i] == k;
  }

  // f(key, val)
  template <typename F>
  void enumerate_all(F f) {
    FOR(i, len(used)) if (used[i]) f(key[i], val[i]);
  }

 private:
  u32 cap, mask;
  vc<u64> key;
  vc<Val> val;
  vc<bool> used;

  u64 hash(u64 x) {
    static const u64 FIXED_RANDOM =
        std::chrono::steady_clock::now().time_since_epoch().count();
    x += FIXED_RANDOM;
    x = (x ^ (x >> 30)) * 0xbf58476d1ce4e5b9;
    x = (x ^ (x >> 27)) * 0x94d049bb133111eb;
    return (x ^ (x >> 31)) & mask;
  }

  void extend() {
    vc<pair<u64, Val>> dat;
    dat.reserve(len(used) / 2 - cap);
    FOR(i, len(used)) {
      if (used[i]) dat.eb(key[i], val[i]);
    }
    build(2 * len(dat));
    for (auto& [a, b] : dat) (*this)[a] = b;
  }
};
#line 2 "graph/base.hpp"

template <typename T>
struct Edge {
  int frm, to;
  T cost;
  int id;
};

template <typename T = int, bool directed = false>
struct Graph {
  static constexpr bool is_directed = directed;
  int N, M;
  using cost_type = T;
  using edge_type = Edge<T>;
  vector<edge_type> edges;
  vector<int> indptr;
  vector<edge_type> csr_edges;
  vc<int> vc_deg, vc_indeg, vc_outdeg;
  HashMap<int> MP_FOR_EID;
  bool prepared;

  class OutgoingEdges {
   public:
    OutgoingEdges(const Graph* G, int l, int r) : G(G), l(l), r(r) {}

    const edge_type* begin() const {
      if (l == r) {
        return 0;
      }
      return &G->csr_edges[l];
    }

    const edge_type* end() const {
      if (l == r) {
        return 0;
      }
      return &G->csr_edges[r];
    }

   private:
    const Graph* G;
    int l, r;
  };

  bool is_prepared() { return prepared; }

  Graph() : N(0), M(0), prepared(0) {}
  Graph(int N) : N(N), M(0), prepared(0) {}

  void build(int n) {
    N = n, M = 0;
    prepared = 0;
    edges.clear();
    indptr.clear();
    csr_edges.clear();
    vc_deg.clear();
    vc_indeg.clear();
    vc_outdeg.clear();
    MP_FOR_EID.clear();
  }

  void add(int frm, int to, T cost = 1, int i = -1) {
    assert(!prepared);
    assert(0 <= frm && frm < N && 0 <= to && to < N);
    if (i == -1) i = M;
    auto e = edge_type({frm, to, cost, i});
    edges.eb(e);
    ++M;
  }

#ifdef FASTIO
  // wt, off
  void read_tree(bool wt = false, int off = 1) { read_graph(N - 1, wt, off); }

  void read_graph(int M, bool wt = false, int off = 1) {
    for (int m = 0; m < M; ++m) {
      INT(a, b);
      a -= off, b -= off;
      if (!wt) {
        add(a, b);
      } else {
        T c;
        read(c);
        add(a, b, c);
      }
    }
    build();
  }
#endif

  void build() {
    assert(!prepared);
    prepared = true;
    indptr.assign(N + 1, 0);
    for (auto&& e : edges) {
      indptr[e.frm + 1]++;
      if (!directed) indptr[e.to + 1]++;
    }
    for (int v = 0; v < N; ++v) {
      indptr[v + 1] += indptr[v];
    }
    auto counter = indptr;
    csr_edges.resize(indptr.back() + 1);
    for (auto&& e : edges) {
      csr_edges[counter[e.frm]++] = e;
      if (!directed)
        csr_edges[counter[e.to]++] = edge_type({e.to, e.frm, e.cost, e.id});
    }
  }

  OutgoingEdges operator[](int v) const {
    assert(prepared);
    return {this, indptr[v], indptr[v + 1]};
  }

  vc<int> deg_array() {
    if (vc_deg.empty()) calc_deg();
    return vc_deg;
  }

  pair<vc<int>, vc<int>> deg_array_inout() {
    if (vc_indeg.empty()) calc_deg_inout();
    return {vc_indeg, vc_outdeg};
  }

  int deg(int v) {
    if (vc_deg.empty()) calc_deg();
    return vc_deg[v];
  }

  int in_deg(int v) {
    if (vc_indeg.empty()) calc_deg_inout();
    return vc_indeg[v];
  }

  int out_deg(int v) {
    if (vc_outdeg.empty()) calc_deg_inout();
    return vc_outdeg[v];
  }

#ifdef FASTIO
  void debug() {
#ifdef LOCAL
    print("Graph");
    if (!prepared) {
      print("frm to cost id");
      for (auto&& e : edges) print(e.frm, e.to, e.cost, e.id);
    } else {
      print("indptr", indptr);
      print("frm to cost id");
      FOR(v, N) for (auto&& e : (*this)[v]) print(e.frm, e.to, e.cost, e.id);
    }
    flush();
#endif
  }
#endif

  vc<int> new_idx;
  vc<bool> used_e;

  // G における頂点 V[i] が、新しいグラフで i になるようにする
  // {G, es}
  // sum(deg(v)) の計算量になっていて、
  // 新しいグラフの n+m より大きい可能性があるので注意
  Graph<T, directed> rearrange(vc<int> V, bool keep_eid = 0) {
    if (len(new_idx) != N) new_idx.assign(N, -1);
    int n = len(V);
    FOR(i, n) new_idx[V[i]] = i;
    Graph<T, directed> G(n);
    vc<int> history;
    FOR(i, n) {
      for (auto&& e : (*this)[V[i]]) {
        if (len(used_e) <= e.id) used_e.resize(e.id + 1);
        if (used_e[e.id]) continue;
        int a = e.frm, b = e.to;
        if (new_idx[a] != -1 && new_idx[b] != -1) {
          history.eb(e.id);
          used_e[e.id] = 1;
          int eid = (keep_eid ? e.id : -1);
          G.add(new_idx[a], new_idx[b], e.cost, eid);
        }
      }
    }
    FOR(i, n) new_idx[V[i]] = -1;
    for (auto&& eid : history) used_e[eid] = 0;
    G.build();
    return G;
  }

  Graph<T, true> to_directed_tree(int root = -1) {
    if (root == -1) root = 0;
    assert(!is_directed && prepared && M == N - 1);
    Graph<T, true> G1(N);
    vc<int> par(N, -1);
    auto dfs = [&](auto& dfs, int v) -> void {
      for (auto& e : (*this)[v]) {
        if (e.to == par[v]) continue;
        par[e.to] = v, dfs(dfs, e.to);
      }
    };
    dfs(dfs, root);
    for (auto& e : edges) {
      int a = e.frm, b = e.to;
      if (par[a] == b) swap(a, b);
      assert(par[b] == a);
      G1.add(a, b, e.cost);
    }
    G1.build();
    return G1;
  }

  int get_eid(u64 a, u64 b) {
    if (len(MP_FOR_EID) == 0) {
      MP_FOR_EID.build(N - 1);
      for (auto& e : edges) {
        u64 a = e.frm, b = e.to;
        u64 k = to_eid_key(a, b);
        MP_FOR_EID[k] = e.id;
      }
    }
    return MP_FOR_EID.get(to_eid_key(a, b), -1);
  }

  u64 to_eid_key(u64 a, u64 b) {
    if (!directed && a > b) swap(a, b);
    return N * a + b;
  }

 private:
  void calc_deg() {
    assert(vc_deg.empty());
    vc_deg.resize(N);
    for (auto&& e : edges) vc_deg[e.frm]++, vc_deg[e.to]++;
  }

  void calc_deg_inout() {
    assert(vc_indeg.empty());
    vc_indeg.resize(N);
    vc_outdeg.resize(N);
    for (auto&& e : edges) {
      vc_indeg[e.to]++, vc_outdeg[e.frm]++;
    }
  }
};
#line 3 "graph/tree.hpp"

// HLD euler tour をとっていろいろ
// HLD=false: 入力辺順で preorder
template <typename GT, bool HLD = true>
struct Tree {
  using Graph_type = GT;
  GT &G;
  using WT = typename GT::cost_type;
  int N;
  vector<int> LID, RID, head, V, parent, VtoE;
  vc<int> depth;
  vc<WT> depth_weighted;
  vc<int> memo_tail;

  Tree(GT &G, int r = 0) : G(G) { build(r); }

  void build(int r = 0) {
    if (r == -1) return;  // build を遅延したいとき
    if constexpr (!HLD)
      build_simple(r);
    else
      build_HLD(r);
  }

  vc<int> heavy_path_at(int v) const {
    static_assert(HLD);
    assert(head[v] == v);
    int k = LID[v];
    vc<int> P;
    while (k < N && head[V[k]] == v) P.eb(V[k++]);
    return P;
  }

  int heavy_child(int v) const {
    static_assert(HLD);
    if (RID[v] == LID[v] + 1) return -1;
    return V[LID[v] + 1];
  }

  int tail(int v) {
    static_assert(HLD);
    if (memo_tail.empty()) {
      memo_tail.assign(N, -1);
      FOR_R(i, N) {
        int v = V[i];
        int w = heavy_child(v);
        memo_tail[v] = (w == -1 ? v : memo_tail[w]);
      }
    }
    return memo_tail[v];
  }

  int e_to_v(int eid) const {
    auto e = G.edges[eid];
    return (parent[e.frm] == e.to ? e.frm : e.to);
  }
  int v_to_e(int v) const { return VtoE[v]; }
  int get_eid(int u, int v) const {
    if (parent[u] != v) swap(u, v);
    assert(parent[u] == v);
    return VtoE[u];
  }

  int ELID(int v) const { return 2 * LID[v] - depth[v]; }
  int ERID(int v) const { return 2 * RID[v] - depth[v] - 1; }

  // 目標地点へ進む個数が k
  int LA(int v, int k) const {
    static_assert(HLD);
    assert(k <= depth[v]);
    while (1) {
      int u = head[v];
      if (LID[v] - k >= LID[u]) return V[LID[v] - k];
      k -= LID[v] - LID[u] + 1;
      v = parent[u];
    }
  }

  int LCA(int u, int v) const {
    static_assert(HLD);
    for (;; v = parent[head[v]]) {
      if (LID[u] > LID[v]) swap(u, v);
      if (head[u] == head[v]) return u;
    }
  }

  int meet(int a, int b, int c) const {
    static_assert(HLD);
    return LCA(a, b) ^ LCA(a, c) ^ LCA(b, c);
  }

  int subtree_size(int v) const { return RID[v] - LID[v]; }

  int subtree_size(int v, int root) const {
    static_assert(HLD);
    if (v == root) return N;
    int x = jump(v, root, 1);
    if (in_subtree(v, x)) return RID[v] - LID[v];
    return N - RID[x] + LID[x];
  }

  int dist(int a, int b) const {
    static_assert(HLD);
    int c = LCA(a, b);
    return depth[a] + depth[b] - 2 * depth[c];
  }

  WT dist_weighted(int a, int b) const {
    static_assert(HLD);
    int c = LCA(a, b);
    return depth_weighted[a] + depth_weighted[b] - WT(2) * depth_weighted[c];
  }

  // a is in b
  bool in_subtree(int a, int b) const {
    return LID[b] <= LID[a] && LID[a] < RID[b];
  }

  int jump(int a, int b, ll k) const {
    static_assert(HLD);
    if (k == 1) {
      if (a == b) return -1;
      return (in_subtree(b, a) ? LA(b, depth[b] - depth[a] - 1) : parent[a]);
    }
    int c = LCA(a, b);
    int d_ac = depth[a] - depth[c];
    int d_bc = depth[b] - depth[c];
    if (k > d_ac + d_bc) return -1;
    if (k <= d_ac) return LA(a, k);
    return LA(b, d_ac + d_bc - k);
  }

  vc<int> collect_child(int v) const {
    vc<int> res;
    for (auto &&e : G[v])
      if (e.to != parent[v]) res.eb(e.to);
    return res;
  }

  vc<int> collect_subtree(int v) const {
    return {V.begin() + LID[v], V.begin() + RID[v]};
  }

  vc<int> collect_light(int v) const {
    static_assert(HLD);
    vc<int> res;
    for (auto &&e : G[v]) {
      if (e.to != parent[v] && head[e.to] == e.to) res.eb(e.to);
    }
    return res;
  }

  vc<pair<int, int>> get_path_decomposition(int u, int v, bool edge) const {
    static_assert(HLD);
    // [始点, 終点] の"閉"区間列。
    vc<pair<int, int>> up, down;
    while (1) {
      if (head[u] == head[v]) break;
      if (LID[u] < LID[v]) {
        down.eb(LID[head[v]], LID[v]);
        v = parent[head[v]];
      } else {
        up.eb(LID[u], LID[head[u]]);
        u = parent[head[u]];
      }
    }
    if (LID[u] < LID[v]) down.eb(LID[u] + edge, LID[v]);
    elif (LID[v] + edge <= LID[u]) up.eb(LID[u], LID[v] + edge);
    reverse(all(down));
    up.insert(up.end(), all(down));
    return up;
  }

  // 辺の列の情報 (frm,to,str)
  // str = "heavy_up", "heavy_down", "light_up", "light_down"
  vc<tuple<int, int, string>> get_path_decomposition_detail(
      int u, int v) const {
    static_assert(HLD);
    vc<tuple<int, int, string>> up, down;
    while (1) {
      if (head[u] == head[v]) break;
      if (LID[u] < LID[v]) {
        if (v != head[v]) down.eb(head[v], v, "heavy_down"), v = head[v];
        down.eb(parent[v], v, "light_down"), v = parent[v];
      } else {
        if (u != head[u]) up.eb(u, head[u], "heavy_up"), u = head[u];
        up.eb(u, parent[u], "light_up"), u = parent[u];
      }
    }
    if (LID[u] < LID[v]) down.eb(u, v, "heavy_down");
    elif (LID[v] < LID[u]) up.eb(u, v, "heavy_up");
    reverse(all(down));
    concat(up, down);
    return up;
  }

  vc<int> restore_path(int u, int v) const {
    vc<int> L, R;
    while (depth[u] > depth[v]) L.eb(u), u = parent[u];
    while (depth[u] < depth[v]) R.eb(v), v = parent[v];
    while (u != v) L.eb(u), R.eb(v), u = parent[u], v = parent[v];
    L.eb(u);
    while (len(R)) L.eb(POP(R));
    return L;
  }

  // path [a,b] と [c,d] の交わり. 空ならば {-1,-1}.
  // https://codeforces.com/problemset/problem/500/G
  pair<int, int> path_intersection(int a, int b, int c, int d) const {
    static_assert(HLD);
    int ab = LCA(a, b), ac = LCA(a, c), ad = LCA(a, d);
    int bc = LCA(b, c), bd = LCA(b, d), cd = LCA(c, d);
    int x = ab ^ ac ^ bc, y = ab ^ ad ^ bd;  // meet(a,b,c), meet(a,b,d)
    if (x != y) return {x, y};
    int z = ac ^ ad ^ cd;
    if (x != z) x = -1;
    return {x, x};
  }

  // uv path 上で check(v) を満たす最後の v
  // なければ （つまり check(v) が ng ）-1
  template <class F>
  int max_path(F check, int u, int v) const {
    static_assert(HLD);
    if (!check(u)) return -1;
    auto pd = get_path_decomposition(u, v, false);
    for (auto [a, b] : pd) {
      if (!check(V[a])) return u;
      if (check(V[b])) {
        u = V[b];
        continue;
      }
      int c =
          binary_search([&](int c) -> bool { return check(V[c]); }, a, b, 0);
      return V[c];
    }
    return u;
  }

 private:
  void build_simple(int r = 0) {
    N = G.N;
    LID.assign(N, 0), RID.assign(N, 0);
    V.assign(N, -1), parent.assign(N, -1), VtoE.assign(N, -1);
    depth.assign(N, 0), depth_weighted.assign(N, 0);
    assert(G.is_prepared());

    // 1st dfs.
    int k = 0;
    vc<int> st;
    st.reserve(N);
    st.eb(r);
    while (len(st)) {
      int v = POP(st);
      LID[v] = k, V[k] = v;
      ++k;
      for (int i = G.indptr[v + 1] - 1; i >= G.indptr[v]; --i) {
        auto &e = G.csr_edges[i];
        if (e.to == parent[v]) continue;
        parent[e.to] = v;
        depth[e.to] = depth[v] + 1;
        depth_weighted[e.to] = depth_weighted[v] + e.cost;
        VtoE[e.to] = e.id;
        st.eb(e.to);
      }
    }

    FOR_R(i, N) {
      int v = V[i];
      chmax(RID[v], LID[v] + 1);
      if (parent[v] != -1) chmax(RID[parent[v]], RID[v]);
    }
  }

  void build_HLD(int r = 0) {
    N = G.N;
    LID.assign(N, 0), RID.assign(N, 0), head.assign(N, r);
    V.assign(N, -1), parent.assign(N, -1), VtoE.assign(N, -1);
    depth.assign(N, 0), depth_weighted.assign(N, 0);
    memo_tail.clear();
    assert(G.is_prepared());

    // 1st dfs.
    {
      int k = 0;
      vc<int> st;
      st.reserve(N);
      st.eb(r);
      while (len(st)) {
        int v = POP(st);
        V[k++] = v;
        for (auto &e : G[v]) {
          if (e.to == parent[v]) continue;
          parent[e.to] = v, st.eb(e.to), depth[e.to] = depth[v] + 1;
          depth_weighted[e.to] = depth_weighted[v] + e.cost;
          VtoE[e.to] = e.id;
        }
      }
      // 一時的に RID[v] := sz[v]
      FOR_R(i, N) {
        int v = V[i];
        RID[v] += 1;
        if (parent[v] != -1) RID[parent[v]] += RID[v];
      }
    }
    // 2nd dfs.
    {
      int k = 0;
      vc<int> st;
      st.reserve(N);
      st.eb(r);
      while (len(st)) {
        int v = POP(st);
        V[k] = v, LID[v] = k;
        RID[v] = k + RID[v];
        ++k;
        int max_sz = 0, max_ch = -1;
        for (auto &e : G[v]) {
          if (e.to == parent[v]) continue;
          if (chmax(max_sz, RID[e.to])) max_ch = e.to;
        }
        for (int i = G.indptr[v + 1] - 1; i >= G.indptr[v]; --i) {
          auto &e = G.csr_edges[i];
          if (e.to == parent[v] || e.to == max_ch) continue;
          st.eb(e.to), head[e.to] = e.to;
        }
        if (max_ch != -1) st.eb(max_ch), head[max_ch] = head[v];
      }
    }
  }
};
#line 1 "ds/offline_query/mo.hpp"
// Nsqrt(Q)

struct Mo {
  vc<pair<int, int>> LR;
  void add(int L, int R) { LR.emplace_back(L, R); }

  static vc<int> get_mo_order(vc<pair<int, int>> LR) {
    int N = 1;
    for (auto &&[l, r]: LR) chmax(N, l), chmax(N, r);
    int Q = len(LR);
    if (Q == 0) return {};
    int bs = sqrt(3) * N / sqrt(2 * Q);
    chmax(bs, 1);
    vc<int> I(Q);
    iota(all(I), 0);
    sort(all(I), [&](int a, int b) {
      int aa = LR[a].fi / bs, bb = LR[b].fi / bs;
      if (aa != bb) return aa < bb;
      return (aa & 1) ? LR[a].se > LR[b].se : LR[a].se < LR[b].se;
    });

    auto cost = [&](int a, int b) -> int {
      return abs(LR[I[a]].fi - LR[I[b]].fi) + abs(LR[I[a]].se - LR[I[b]].se);
    };

    // ランダムケースで数パーセント

    FOR(k, Q - 5) {
      if (cost(k, k + 2) + cost(k + 1, k + 3)
          < cost(k, k + 1) + cost(k + 2, k + 3)) {
        swap(I[k + 1], I[k + 2]);
      }
      if (cost(k, k + 3) + cost(k + 1, k + 4)
          < cost(k, k + 1) + cost(k + 3, k + 4)) {
        swap(I[k + 1], I[k + 3]);
      }
    }
    return I;
  }

  template <typename F1, typename F2, typename F3, typename F4, typename F5>
  void calc(F1 add_l, F2 add_r, F3 rm_l, F4 rm_r, F5 query) {
    auto I = get_mo_order(LR);
    int l = 0, r = 0;
    for (auto idx: I) {
      while (l > LR[idx].fi) add_l(--l);
      while (r < LR[idx].se) add_r(r++);
      while (l < LR[idx].fi) rm_l(l++);
      while (r > LR[idx].se) rm_r(--r);
      query(idx);
    }
  }
};
#line 3 "graph/ds/mo_on_tree.hpp"

// https://codeforces.com/contest/852/problem/I
template <typename TREE, bool ORIENTED = false>
struct Mo_on_Tree {
  TREE& tree;
  vc<pair<int, int>> LR;

  Mo mo;
  Mo_on_Tree(TREE& tree) : tree(tree) {}
  void add(int u, int v) {
    if constexpr (!ORIENTED) {
      if (tree.LID[u] > tree.LID[v]) swap(u, v);
    }
    LR.eb(tree.ELID(u) + 1, tree.ELID(v) + 1);
  }

  // init(): root だけからなる path
  // add_l(v), add_r(v)：パスの先頭 / 末尾に v を追加
  // rm_l(v), rm_r(v)：パスの先頭 / 末尾から v を削除
  // query(qid)
  template <typename F1, typename F2, typename F3, typename F4, typename F5,
            typename F6>
  void calc_vertex(F1 init, F2 add_l, F3 add_r, F4 rm_l, F5 rm_r, F6 query) {
    const int N = tree.G.N;
    auto I = Mo::get_mo_order(LR);

    vc<int> FRM(2 * N), TO(2 * N), idx(2 * N);
    vc<int> cnt(N);
    deque<int> path = {0};
    FOR(v, N) {
      int a = tree.ELID(v), b = tree.ERID(v);
      FRM[a] = tree.parent[v], TO[a] = v;
      FRM[b] = v, TO[b] = tree.parent[v];
      idx[a] = idx[b] = v;
    }

    auto flip_left = [&](int i) -> void {
      const int a = FRM[i], b = TO[i], c = idx[i];
      if (cnt[c] == 0) {
        int v = path.front() ^ a ^ b;
        path.emplace_front(v), add_l(v);
      } else {
        int v = path.front();
        path.pop_front(), rm_l(v);
      }
      cnt[c] ^= 1;
    };
    auto flip_right = [&](int i) -> void {
      const int a = FRM[i], b = TO[i], c = idx[i];
      if (cnt[c] == 0) {
        int v = path.back() ^ a ^ b;
        path.emplace_back(v), add_r(v);
      } else {
        int v = path.back();
        path.pop_back(), rm_r(v);
      }
      cnt[c] ^= 1;
    };

    init();

    int l = 1, r = 1;
    for (auto idx: I) {
      int L = LR[idx].fi, R = LR[idx].se;
      while (l > L) { flip_left(--l); }
      while (r < R) { flip_right(r++); }
      while (l < L) { flip_left(l++); }
      while (r > R) { flip_right(--r); }
      query(idx);
    }
  }

  // init(): root だけからなる path
  // add_l(frm, to), add_r(frm, to)：パスの先頭 / 末尾に (frm,to) を追加
  // rm_l(frm, to), rm_r(frm, to)：パスの先頭 / 末尾に (frm,to) を追加
  // query(qid)
  template <typename F1, typename F2, typename F3, typename F4, typename F5,
            typename F6>
  void calc_edge(F1 init, F2 add_l, F3 add_r, F4 rm_l, F5 rm_r, F6 query) {
    const int N = tree.G.N;
    auto I = Mo::get_mo_order(LR);

    vc<int> FRM(2 * N), TO(2 * N), idx(2 * N);
    vc<int> cnt(N);
    deque<int> path = {0};
    FOR(v, N) {
      int a = tree.ELID(v), b = tree.ERID(v);
      FRM[a] = tree.parent[v], TO[a] = v;
      FRM[b] = v, TO[b] = tree.parent[v];
      idx[a] = idx[b] = v;
    }

    auto flip_left = [&](int i) -> void {
      const int a = FRM[i], b = TO[i], c = idx[i];
      if (cnt[c] == 0) {
        int v = path.front() ^ a ^ b;
        path.emplace_front(v), add_l(v, v ^ a ^ b);
      } else {
        int v = path.front();
        path.pop_front(), rm_l(v, v ^ a ^ b);
      }
      cnt[c] ^= 1;
    };
    auto flip_right = [&](int i) -> void {
      const int a = FRM[i], b = TO[i], c = idx[i];
      if (cnt[c] == 0) {
        int v = path.back() ^ a ^ b;
        path.emplace_back(v), add_r(v ^ a ^ b, v);
      } else {
        int v = path.back();
        path.pop_back(), rm_r(v ^ a ^ b, v);
      }
      cnt[c] ^= 1;
    };

    init();

    int l = 1, r = 1;
    for (auto idx: I) {
      int L = LR[idx].fi, R = LR[idx].se;
      while (l > L) { flip_left(--l); }
      while (r < R) { flip_right(r++); }
      while (l < L) { flip_left(l++); }
      while (r > R) { flip_right(--r); }
      query(idx);
    }
  }
};

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