test/yukicoder/1600.Seg2D.test.cpp

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• Last update: 2024-10-01 17:03:34+09:00
• Problem: https://yukicoder.me/problems/no/1600

Depends on

• Segment-Tree(2次元) (src/DataStructure/SegmentTree_2D.hpp)
• Union-Find (src/DataStructure/UnionFind.hpp)
• グラフ (src/Graph/Graph.hpp)
• 重軽分解 (src/Graph/HeavyLightDecomposition.hpp)
• CSR 表現を用いた二次元配列 他 (src/Internal/ListRange.hpp)
• modintを扱うテンプレート (src/Internal/modint_traits.hpp)
• 剰余の高速化 (src/Internal/Remainder.hpp)
• tupleやarrayに関するテンプレート 他 (src/Internal/tuple_traits.hpp)
• 逆元 ($\mathbb{Z}/m\mathbb{Z}$) (src/Math/mod_inv.hpp)
• ModInt (src/Math/ModInt.hpp)

Code

// competitive-verifier: PROBLEM https://yukicoder.me/problems/no/1600
// competitive-verifier: TLE 0.5
// competitive-verifier: MLE 64
#include <iostream>
#include <vector>
#include <array>
#include <tuple>

#include "src/Math/ModInt.hpp"
#include "src/DataStructure/UnionFind.hpp"
#include "src/Graph/Graph.hpp"
#include "src/Graph/HeavyLightDecomposition.hpp"
#include "src/DataStructure/SegmentTree_2D.hpp"
using namespace std;
struct RMQ {
 using T= int;
 static T ti() { return 0x7fffffff; }
 static T op(T a, T b) { return min(a, b); }
};
signed main() {
 cin.tie(0);
 ios::sync_with_stdio(0);
 using Mint= ModInt<1000000007>;
 int N, M;
 cin >> N >> M;
 vector<Edge> es(M);
 for (int i= 0; i < M; ++i) cin >> es[i], --es[i];
 Graph g(N);
 vector<Mint> C;
 Mint w= 1;
 UnionFind uf(N);
 vector<char> used(M);
 for (int i= 0; i < M; ++i) {
  auto [A, B]= es[i];
  w+= w;
  if (uf.unite(A, B)) {
   used[i]= true;
   g.add_edge(A, B), C.push_back(w);
  }
 }
 HeavyLightDecomposition tree(g);
 auto adj= g.adjacency_edge(0);
 vector<Mint> dep(N);
 for (int i= 0, v; i < N; ++i)
  for (int e: adj[v= tree.to_vertex(i)])
   if (int u= g[e].to(v); u != tree.parent(v)) dep[u]= dep[v] + C[e];
 auto dist= [&](int u, int v) { return dep[u] + dep[v] - dep[tree.lca(u, v)] * 2; };
 vector<array<int, 3>> xyw;
 for (int i= 0; i < M; ++i) {
  if (used[i]) continue;
  auto [A, B]= es[i];
  int a= tree.to_seq(A), b= tree.to_seq(B);
  if (a > b) swap(a, b);
  xyw.push_back({a, b, i});
 }
 SegmentTree_2D<int, RMQ> seg(xyw);
 int Q;
 cin >> Q;
 while (Q--) {
  int u, v, e;
  cin >> u >> v >> e, --u, --v, --e;
  auto [x, y]= es[e];
  if (tree.parent(y) == x) swap(x, y);
  bool u_in= tree.in_subtree(u, x);
  if (!used[e] || u_in == tree.in_subtree(v, x)) {
   cout << dist(u, v) << '\n';
   continue;
  }
  auto [l, r]= tree.subtree(x);
  int i= min(seg.prod(0, l, l, r), seg.prod(l, r, r, N));
  if (i > M) {
   cout << -1 << '\n';
   continue;
  }
  auto [p, q]= es[i];
  if (!u_in) swap(u, v);
  if (tree.in_subtree(q, x)) swap(p, q);
  cout << dist(u, p) + dist(v, q) + Mint(2).pow(i + 1) << '\n';
 }
 return 0;
}

#line 1 "test/yukicoder/1600.Seg2D.test.cpp"
// competitive-verifier: PROBLEM https://yukicoder.me/problems/no/1600
// competitive-verifier: TLE 0.5
// competitive-verifier: MLE 64
#include <iostream>
#include <vector>
#include <array>
#include <tuple>

#line 2 "src/Math/mod_inv.hpp"
#include <utility>
#include <type_traits>
#include <cassert>
template <class Uint> constexpr inline Uint mod_inv(Uint a, Uint mod) {
 std::make_signed_t<Uint> x= 1, y= 0, z= 0;
 for (Uint q= 0, b= mod, c= 0; b;) z= x, x= y, y= z - y * (q= a / b), c= a, a= b, b= c - b * q;
 return assert(a == 1), x < 0 ? mod - (-x) % mod : x % mod;
}
#line 2 "src/Internal/Remainder.hpp"
namespace math_internal {
using namespace std;
using u8= unsigned char;
using u32= unsigned;
using i64= long long;
using u64= unsigned long long;
using u128= __uint128_t;
struct MP_Na {  // mod < 2^32
 u32 mod;
 constexpr MP_Na(): mod(0) {}
 constexpr MP_Na(u32 m): mod(m) {}
 constexpr inline u32 mul(u32 l, u32 r) const { return u64(l) * r % mod; }
 constexpr inline u32 set(u32 n) const { return n; }
 constexpr inline u32 get(u32 n) const { return n; }
 constexpr inline u32 norm(u32 n) const { return n; }
 constexpr inline u32 plus(u64 l, u32 r) const { return l+= r, l < mod ? l : l - mod; }
 constexpr inline u32 diff(u64 l, u32 r) const { return l-= r, l >> 63 ? l + mod : l; }
};
template <class u_t, class du_t, u8 B> struct MP_Mo {  // mod < 2^32, mod < 2^62
 u_t mod;
 constexpr MP_Mo(): mod(0), iv(0), r2(0) {}
 constexpr MP_Mo(u_t m): mod(m), iv(inv(m)), r2(-du_t(mod) % mod) {}
 constexpr inline u_t mul(u_t l, u_t r) const { return reduce(du_t(l) * r); }
 constexpr inline u_t set(u_t n) const { return mul(n, r2); }
 constexpr inline u_t get(u_t n) const { return n= reduce(n), n >= mod ? n - mod : n; }
 constexpr inline u_t norm(u_t n) const { return n >= mod ? n - mod : n; }
 constexpr inline u_t plus(u_t l, u_t r) const { return l+= r, l < (mod << 1) ? l : l - (mod << 1); }
 constexpr inline u_t diff(u_t l, u_t r) const { return l-= r, l >> (B - 1) ? l + (mod << 1) : l; }
private:
 u_t iv, r2;
 static constexpr u_t inv(u_t n, int e= 6, u_t x= 1) { return e ? inv(n, e - 1, x * (2 - x * n)) : x; }
 constexpr inline u_t reduce(const du_t &w) const { return u_t(w >> B) + mod - ((du_t(u_t(w) * iv) * mod) >> B); }
};
using MP_Mo32= MP_Mo<u32, u64, 32>;
using MP_Mo64= MP_Mo<u64, u128, 64>;
struct MP_Br {  // 2^20 < mod <= 2^41
 u64 mod;
 constexpr MP_Br(): mod(0), x(0) {}
 constexpr MP_Br(u64 m): mod(m), x((u128(1) << 84) / m) {}
 constexpr inline u64 mul(u64 l, u64 r) const { return rem(u128(l) * r); }
 static constexpr inline u64 set(u64 n) { return n; }
 constexpr inline u64 get(u64 n) const { return n >= mod ? n - mod : n; }
 constexpr inline u64 norm(u64 n) const { return n >= mod ? n - mod : n; }
 constexpr inline u64 plus(u64 l, u64 r) const { return l+= r, l < (mod << 1) ? l : l - (mod << 1); }
 constexpr inline u64 diff(u64 l, u64 r) const { return l-= r, l >> 63 ? l + (mod << 1) : l; }
private:
 u64 x;
 constexpr inline u128 quo(const u128 &n) const { return (n * x) >> 84; }
 constexpr inline u64 rem(const u128 &n) const { return n - quo(n) * mod; }
};
template <class du_t, u8 B> struct MP_D2B1 {  // mod < 2^63, mod < 2^64
 u64 mod;
 constexpr MP_D2B1(): mod(0), s(0), d(0), v(0) {}
 constexpr MP_D2B1(u64 m): mod(m), s(__builtin_clzll(m)), d(m << s), v(u128(-1) / d) {}
 constexpr inline u64 mul(u64 l, u64 r) const { return rem((u128(l) * r) << s) >> s; }
 constexpr inline u64 set(u64 n) const { return n; }
 constexpr inline u64 get(u64 n) const { return n; }
 constexpr inline u64 norm(u64 n) const { return n; }
 constexpr inline u64 plus(du_t l, u64 r) const { return l+= r, l < mod ? l : l - mod; }
 constexpr inline u64 diff(du_t l, u64 r) const { return l-= r, l >> B ? l + mod : l; }
private:
 u8 s;
 u64 d, v;
 constexpr inline u64 rem(const u128 &u) const {
  u128 q= (u >> 64) * v + u;
  u64 r= u64(u) - (q >> 64) * d - d;
  if (r > u64(q)) r+= d;
  if (r >= d) r-= d;
  return r;
 }
};
using MP_D2B1_1= MP_D2B1<u64, 63>;
using MP_D2B1_2= MP_D2B1<u128, 127>;
template <class u_t, class MP> constexpr u_t pow(u_t x, u64 k, const MP &md) {
 for (u_t ret= md.set(1);; x= md.mul(x, x))
  if (k & 1 ? ret= md.mul(ret, x) : 0; !(k>>= 1)) return ret;
}
}
#line 3 "src/Internal/modint_traits.hpp"
namespace math_internal {
struct m_b {};
struct s_b: m_b {};
}
template <class mod_t> constexpr bool is_modint_v= std::is_base_of_v<math_internal::m_b, mod_t>;
template <class mod_t> constexpr bool is_staticmodint_v= std::is_base_of_v<math_internal::s_b, mod_t>;
#line 6 "src/Math/ModInt.hpp"
namespace math_internal {
template <class MP, u64 MOD> struct SB: s_b {
protected:
 static constexpr MP md= MP(MOD);
};
template <class U, class B> struct MInt: public B {
 using Uint= U;
 static constexpr inline auto mod() { return B::md.mod; }
 constexpr MInt(): x(0) {}
 template <class T, typename= enable_if_t<is_modint_v<T> && !is_same_v<T, MInt>>> constexpr MInt(T v): x(B::md.set(v.val() % B::md.mod)) {}
 constexpr MInt(__int128_t n): x(B::md.set((n < 0 ? ((n= (-n) % B::md.mod) ? B::md.mod - n : n) : n % B::md.mod))) {}
 constexpr MInt operator-() const { return MInt() - *this; }
#define FUNC(name, op) \
 constexpr MInt name const { \
  MInt ret; \
  return ret.x= op, ret; \
 }
 FUNC(operator+(const MInt & r), B::md.plus(x, r.x))
 FUNC(operator-(const MInt & r), B::md.diff(x, r.x))
 FUNC(operator*(const MInt & r), B::md.mul(x, r.x))
 FUNC(pow(u64 k), math_internal::pow(x, k, B::md))
#undef FUNC
 constexpr MInt operator/(const MInt &r) const { return *this * r.inv(); }
 constexpr MInt &operator+=(const MInt &r) { return *this= *this + r; }
 constexpr MInt &operator-=(const MInt &r) { return *this= *this - r; }
 constexpr MInt &operator*=(const MInt &r) { return *this= *this * r; }
 constexpr MInt &operator/=(const MInt &r) { return *this= *this / r; }
 constexpr bool operator==(const MInt &r) const { return B::md.norm(x) == B::md.norm(r.x); }
 constexpr bool operator!=(const MInt &r) const { return !(*this == r); }
 constexpr bool operator<(const MInt &r) const { return B::md.norm(x) < B::md.norm(r.x); }
 constexpr inline MInt inv() const { return mod_inv<U>(val(), B::md.mod); }
 constexpr inline Uint val() const { return B::md.get(x); }
 friend ostream &operator<<(ostream &os, const MInt &r) { return os << r.val(); }
 friend istream &operator>>(istream &is, MInt &r) {
  i64 v;
  return is >> v, r= MInt(v), is;
 }
private:
 Uint x;
};
template <u64 MOD> using MP_B= conditional_t < (MOD < (1 << 30)) & MOD, MP_Mo32, conditional_t < MOD < (1ull << 32), MP_Na, conditional_t<(MOD < (1ull << 62)) & MOD, MP_Mo64, conditional_t<MOD<(1ull << 41), MP_Br, conditional_t<MOD<(1ull << 63), MP_D2B1_1, MP_D2B1_2>>>>>;
template <u64 MOD> using ModInt= MInt < conditional_t<MOD<(1 << 30), u32, u64>, SB<MP_B<MOD>, MOD>>;
}
using math_internal::ModInt;
#line 3 "src/DataStructure/UnionFind.hpp"
#include <algorithm>
class UnionFind {
 std::vector<int> par;
public:
 UnionFind(int n): par(n, -1) {}
 int leader(int u) { return par[u] < 0 ? u : par[u]= leader(par[u]); }
 bool unite(int u, int v) {
  if ((u= leader(u)) == (v= leader(v))) return false;
  if (par[u] > par[v]) std::swap(u, v);
  return par[u]+= par[v], par[v]= u, true;
 }
 bool connected(int u, int v) { return leader(u) == leader(v); }
 int size(int u) { return -par[leader(u)]; }
};
#line 4 "src/Internal/ListRange.hpp"
#include <iterator>
#line 6 "src/Internal/ListRange.hpp"
#define _LR(name, IT, CT) \
 template <class T> struct name { \
  using Iterator= typename std::vector<T>::IT; \
  Iterator bg, ed; \
  Iterator begin() const { return bg; } \
  Iterator end() const { return ed; } \
  size_t size() const { return std::distance(bg, ed); } \
  CT &operator[](int i) const { return bg[i]; } \
 }
_LR(ListRange, iterator, T);
_LR(ConstListRange, const_iterator, const T);
#undef _LR
template <class T> struct CSRArray {
 std::vector<T> dat;
 std::vector<int> p;
 size_t size() const { return p.size() - 1; }
 ListRange<T> operator[](int i) { return {dat.begin() + p[i], dat.begin() + p[i + 1]}; }
 ConstListRange<T> operator[](int i) const { return {dat.cbegin() + p[i], dat.cbegin() + p[i + 1]}; }
};
template <template <class> class F, class T> std::enable_if_t<std::disjunction_v<std::is_same<F<T>, ListRange<T>>, std::is_same<F<T>, ConstListRange<T>>, std::is_same<F<T>, CSRArray<T>>>, std::ostream &> operator<<(std::ostream &os, const F<T> &r) {
 os << '[';
 for (int _= 0, __= r.size(); _ < __; ++_) os << (_ ? ", " : "") << r[_];
 return os << ']';
}
#line 3 "src/Graph/Graph.hpp"
struct Edge: std::pair<int, int> {
 using std::pair<int, int>::pair;
 Edge &operator--() { return --first, --second, *this; }
 int to(int v) const { return first ^ second ^ v; }
 friend std::istream &operator>>(std::istream &is, Edge &e) { return is >> e.first >> e.second, is; }
};
struct Graph: std::vector<Edge> {
 size_t n;
 Graph(size_t n= 0, size_t m= 0): vector(m), n(n) {}
 size_t vertex_size() const { return n; }
 size_t edge_size() const { return size(); }
 size_t add_vertex() { return n++; }
 size_t add_edge(int s, int d) { return emplace_back(s, d), size() - 1; }
 size_t add_edge(Edge e) { return emplace_back(e), size() - 1; }
#define _ADJ_FOR(a, b) \
 for (auto [u, v]: *this) a; \
 for (size_t i= 0; i < n; ++i) p[i + 1]+= p[i]; \
 for (int i= size(); i--;) { \
  auto [u, v]= (*this)[i]; \
  b; \
 }
#define _ADJ(a, b) \
 vector<int> p(n + 1), c(size() << !dir); \
 if (!dir) { \
  _ADJ_FOR((++p[u], ++p[v]), (c[--p[u]]= a, c[--p[v]]= b)) \
 } else if (dir > 0) { \
  _ADJ_FOR(++p[u], c[--p[u]]= a) \
 } else { \
  _ADJ_FOR(++p[v], c[--p[v]]= b) \
 } \
 return {c, p}
 CSRArray<int> adjacency_vertex(int dir) const { _ADJ(v, u); }
 CSRArray<int> adjacency_edge(int dir) const { _ADJ(i, i); }
#undef _ADJ
#undef _ADJ_FOR
};
#line 5 "src/Graph/HeavyLightDecomposition.hpp"
class HeavyLightDecomposition {
 std::vector<int> P, PP, D, I, L, R;
public:
 HeavyLightDecomposition()= default;
 HeavyLightDecomposition(const Graph &g, int root= 0): HeavyLightDecomposition(g.adjacency_vertex(0), root) {}
 HeavyLightDecomposition(const CSRArray<int> &adj, int root= 0) {
  const int n= adj.size();
  P.assign(n, -2), PP.resize(n), D.resize(n), I.resize(n), L.resize(n), R.resize(n);
  auto f= [&, i= 0, v= 0, t= 0](int r) mutable {
   for (P[r]= -1, I[t++]= r; i < t; ++i)
    for (int u: adj[v= I[i]])
     if (P[v] != u) P[I[t++]= u]= v;
  };
  f(root);
  for (int r= 0; r < n; ++r)
   if (P[r] == -2) f(r);
  std::vector<int> Z(n, 1), nx(n, -1);
  for (int i= n, v; i--;) {
   if (P[v= I[i]] == -1) continue;
   if (Z[P[v]]+= Z[v]; nx[P[v]] == -1) nx[P[v]]= v;
   if (Z[nx[P[v]]] < Z[v]) nx[P[v]]= v;
  }
  for (int v= n; v--;) PP[v]= v;
  for (int v: I)
   if (nx[v] != -1) PP[nx[v]]= v;
  for (int v: I)
   if (P[v] != -1) PP[v]= PP[PP[v]], D[v]= D[P[v]] + 1;
  for (int i= n; i--;) L[I[i]]= i;
  for (int v: I) {
   int ir= R[v]= L[v] + Z[v];
   for (int u: adj[v])
    if (u != P[v] && u != nx[v]) L[u]= (ir-= Z[u]);
   if (nx[v] != -1) L[nx[v]]= L[v] + 1;
  }
  for (int i= n; i--;) I[L[i]]= i;
 }
 int to_seq(int v) const { return L[v]; }
 int to_vertex(int i) const { return I[i]; }
 size_t size() const { return P.size(); }
 int parent(int v) const { return P[v]; }
 int head(int v) const { return PP[v]; }
 int root(int v) const {
  for (v= PP[v];; v= PP[P[v]])
   if (P[v] == -1) return v;
 }
 bool connected(int u, int v) const { return root(u) == root(v); }
 // u is in v
 bool in_subtree(int u, int v) const { return L[v] <= L[u] && L[u] < R[v]; }
 int subtree_size(int v) const { return R[v] - L[v]; }
 int lca(int u, int v) const {
  for (;; v= P[PP[v]]) {
   if (L[u] > L[v]) std::swap(u, v);
   if (PP[u] == PP[v]) return u;
  }
 }
 int la(int v, int k) const {
  assert(k <= D[v]);
  for (int u;; k-= L[v] - L[u] + 1, v= P[u])
   if (L[v] - k >= L[u= PP[v]]) return I[L[v] - k];
 }
 int jump(int u, int v, int k) const {
  if (!k) return u;
  if (u == v) return -1;
  if (k == 1) return in_subtree(v, u) ? la(v, D[v] - D[u] - 1) : P[u];
  int w= lca(u, v), d_uw= D[u] - D[w], d_vw= D[v] - D[w];
  return k > d_uw + d_vw ? -1 : k <= d_uw ? la(u, k) : la(v, d_uw + d_vw - k);
 }
 int depth(int v) const { return D[v]; }
 int dist(int u, int v) const { return D[u] + D[v] - D[lca(u, v)] * 2; }
 // half-open interval [l,r)
 std::pair<int, int> subtree(int v) const { return {L[v], R[v]}; }
 // sequence of closed intervals [l,r]
 std::vector<std::pair<int, int>> path(int u, int v, bool edge= 0) const {
  std::vector<std::pair<int, int>> up, down;
  while (PP[u] != PP[v]) {
   if (L[u] < L[v]) down.emplace_back(L[PP[v]], L[v]), v= P[PP[v]];
   else up.emplace_back(L[u], L[PP[u]]), u= P[PP[u]];
  }
  if (L[u] < L[v]) down.emplace_back(L[u] + edge, L[v]);
  else if (L[v] + edge <= L[u]) up.emplace_back(L[u], L[v] + edge);
  return up.insert(up.end(), down.rbegin(), down.rend()), up;
 }
};
#line 4 "src/DataStructure/SegmentTree_2D.hpp"
#include <numeric>
#include <map>
#include <set>
#line 5 "src/Internal/tuple_traits.hpp"
#include <cstddef>
template <class T> static constexpr bool tuple_like_v= false;
template <class... Args> static constexpr bool tuple_like_v<std::tuple<Args...>> = true;
template <class T, class U> static constexpr bool tuple_like_v<std::pair<T, U>> = true;
template <class T, size_t K> static constexpr bool tuple_like_v<std::array<T, K>> = true;
template <class T> auto to_tuple(const T &t) {
 if constexpr (tuple_like_v<T>) return std::apply([](auto &&...x) { return std::make_tuple(x...); }, t);
}
template <class T> auto forward_tuple(const T &t) {
 if constexpr (tuple_like_v<T>) return std::apply([](auto &&...x) { return std::forward_as_tuple(x...); }, t);
}
template <class T> static constexpr bool array_like_v= false;
template <class T, size_t K> static constexpr bool array_like_v<std::array<T, K>> = true;
template <class T, class U> static constexpr bool array_like_v<std::pair<T, U>> = std::is_convertible_v<T, U>;
template <class T> static constexpr bool array_like_v<std::tuple<T>> = true;
template <class T, class U, class... Args> static constexpr bool array_like_v<std::tuple<T, U, Args...>> = array_like_v<std::tuple<T, Args...>> && std::is_convertible_v<U, T>;
template <class T> auto to_array(const T &t) {
 if constexpr (array_like_v<T>) return std::apply([](auto &&...x) { return std::array{x...}; }, t);
}
template <class T> using to_tuple_t= decltype(to_tuple(T()));
template <class T> using to_array_t= decltype(to_array(T()));
#line 9 "src/DataStructure/SegmentTree_2D.hpp"
template <class pos_t, class M> class SegmentTree_2D {
 using T= typename M::T;
 using Pos= std::array<pos_t, 2>;
 std::vector<pos_t> xs;
 std::vector<Pos> yxs;
 std::vector<int> id, tol;
 std::vector<T> val;
 template <class P> using canbe_Pos= std::is_convertible<to_tuple_t<P>, std::tuple<pos_t, pos_t>>;
 template <class P> using canbe_PosV= std::is_convertible<to_tuple_t<P>, std::tuple<pos_t, pos_t, T>>;
 template <class P, class U> static constexpr bool canbe_Pos_and_T_v= std::conjunction_v<canbe_Pos<P>, std::is_convertible<U, T>>;
 int sz;
 inline int x2i(pos_t x) const { return std::lower_bound(xs.begin(), xs.end(), x) - xs.begin(); }
 inline int y2i(pos_t y) const {
  return std::lower_bound(yxs.begin(), yxs.end(), Pos{y, 0}, [](const Pos &a, const Pos &b) { return a[0] < b[0]; }) - yxs.begin();
 }
 inline int xy2i(pos_t x, pos_t y) const {
  Pos p{y, x};
  auto it= std::lower_bound(yxs.begin(), yxs.end(), p);
  return assert(p == *it), it - yxs.begin();
 }
 template <bool z, size_t k, class P> inline auto get_(const P &p) {
  if constexpr (z) return std::get<k>(p);
  else return std::get<k>(p.first);
 }
 template <bool z, class XYW> inline void build(const XYW *xyw, int n, const T &v= M::ti()) {
  xs.resize(n);
  for (int i= n; i--;) xs[i]= get_<z, 0>(xyw[i]);
  std::sort(xs.begin(), xs.end()), xs.erase(std::unique(xs.begin(), xs.end()), xs.end()), id.resize((sz= 1 << (32 - __builtin_clz(xs.size()))) + xs.size() + 1);
  std::vector<int> ord(n);
  for (int j= n; j--;)
   for (int i= x2i(get_<z, 0>(xyw[j])) + sz; i; i>>= 1) ++id[i + 1];
  for (int i= 1, e= sz + xs.size(); i < e; ++i) id[i + 1]+= id[i];
  val.assign(id.back() * 2, M::ti()), tol.resize(id[sz] + 1), std::iota(ord.begin(), ord.end(), 0), std::sort(ord.begin(), ord.end(), [&](int i, int j) { return get_<z, 1>(xyw[i]) == get_<z, 1>(xyw[j]) ? get_<z, 0>(xyw[i]) < get_<z, 0>(xyw[j]) : get_<z, 1>(xyw[i]) < get_<z, 1>(xyw[j]); });
  {
   std::vector<int> ptr= id;
   for (int r: ord)
    for (int i= x2i(get_<z, 0>(xyw[r])) + sz, j= -1; i; j= i, i>>= 1) {
     int p= ptr[i]++;
     if constexpr (z) {
      if constexpr (std::tuple_size_v<XYW> == 3) val[id[i + 1] + p]= std::get<2>(xyw[r]);
      else val[id[i + 1] + p]= v;
     } else val[id[i + 1] + p]= xyw[r].second;
     if (j != -1) tol[p + 1]= !(j & 1);
    }
   for (int i= 1, e= id[sz]; i < e; ++i) tol[i + 1]+= tol[i];
   for (int i= 0, e= sz + xs.size(); i < e; ++i) {
    auto dat= val.begin() + id[i] * 2;
    for (int j= id[i + 1] - id[i]; --j > 0;) dat[j]= M::op(dat[j * 2], dat[j * 2 + 1]);
   }
  }
  yxs.resize(n);
  for (int i= n; i--;) yxs[i]= {get_<z, 1>(xyw[ord[i]]), get_<z, 0>(xyw[ord[i]])};
 }
 inline T prdi(int i, int a, int b) const {
  int n= id[i + 1] - id[i];
  T ret= M::ti();
  auto dat= val.begin() + id[i] * 2;
  for (a+= n, b+= n; a < b; a>>= 1, b>>= 1) {
   if (a & 1) ret= M::op(ret, dat[a++]);
   if (b & 1) ret= M::op(dat[--b], ret);
  }
  return ret;
 }
 template <bool z> inline void seti(int i, int j, T v) {
  auto dat= val.begin() + id[i] * 2;
  j+= id[i + 1] - id[i];
  if constexpr (z) dat[j]= v;
  else dat[j]= M::op(dat[j], v);
  for (; j;) j>>= 1, dat[j]= M::op(dat[2 * j], dat[2 * j + 1]);
 }
 template <bool z> inline void set_(pos_t x, pos_t y, T v) {
  for (int i= 1, p= xy2i(x, y);;) {
   if (seti<z>(i, p - id[i], v); i >= sz) break;
   if (int lc= tol[p] - tol[id[i]], rc= (p - id[i]) - lc; tol[p + 1] - tol[p]) p= id[2 * i] + lc, i= 2 * i;
   else p= id[2 * i + 1] + rc, i= 2 * i + 1;
  }
 }
public:
 template <class P, typename= std::enable_if_t<std::disjunction_v<canbe_Pos<P>, canbe_PosV<P>>>> SegmentTree_2D(const P *p, size_t n) { build<1>(p, n); }
 template <class P, typename= std::enable_if_t<std::disjunction_v<canbe_Pos<P>, canbe_PosV<P>>>> SegmentTree_2D(const std::vector<P> &p): SegmentTree_2D(p.data(), p.size()) {}
 template <class P, typename= std::enable_if_t<canbe_Pos<P>::value>> SegmentTree_2D(const std::set<P> &p): SegmentTree_2D(std::vector(p.begin(), p.end())) {}
 template <class P, class U, typename= std::enable_if_t<canbe_Pos_and_T_v<P, U>>> SegmentTree_2D(const P *p, size_t n, const U &v) { build<1>(p, n, v); }
 template <class P, class U, typename= std::enable_if_t<canbe_Pos_and_T_v<P, U>>> SegmentTree_2D(const std::vector<P> &p, const U &v): SegmentTree_2D(p.data(), p.size(), v) {}
 template <class P, class U, typename= std::enable_if_t<canbe_Pos_and_T_v<P, U>>> SegmentTree_2D(const std::set<P> &p, const U &v): SegmentTree_2D(std::vector(p.begin(), p.end()), v) {}
 template <class P, class U, typename= std::enable_if_t<canbe_Pos_and_T_v<P, U>>> SegmentTree_2D(const std::pair<P, U> *p, size_t n) { build<0>(p, n); }
 template <class P, class U, typename= std::enable_if_t<canbe_Pos_and_T_v<P, U>>> SegmentTree_2D(const std::vector<std::pair<P, U>> &p): SegmentTree_2D(p.data(), p.size()) {}
 template <class P, class U, typename= std::enable_if_t<canbe_Pos_and_T_v<P, U>>> SegmentTree_2D(const std::map<P, U> &p): SegmentTree_2D(std::vector(p.begin(), p.end())) {}
 // [l,r) x [u,d)
 T prod(pos_t l, pos_t r, pos_t u, pos_t d) const {
  T ret= M::ti();
  int L= x2i(l), R= x2i(r);
  auto dfs= [&](auto &dfs, int i, int a, int b, int c, int d) -> void {
   if (c == d || R <= a || b <= L) return;
   if (L <= a && b <= R) return ret= M::op(ret, prdi(i, c, d)), void();
   int m= (a + b) / 2, ac= tol[id[i] + c] - tol[id[i]], bc= c - ac, ad= tol[id[i] + d] - tol[id[i]], bd= d - ad;
   dfs(dfs, i * 2, a, m, ac, ad), dfs(dfs, i * 2 + 1, m, b, bc, bd);
  };
  return dfs(dfs, 1, 0, sz, y2i(u), y2i(d)), ret;
 }
 void set(pos_t x, pos_t y, T v) { set_<1>(x, y, v); }
 void mul(pos_t x, pos_t y, T v) { set_<0>(x, y, v); }
 T get(pos_t x, pos_t y) const { return val[xy2i(x, y) + id[2]]; }
};
#line 14 "test/yukicoder/1600.Seg2D.test.cpp"
using namespace std;
struct RMQ {
 using T= int;
 static T ti() { return 0x7fffffff; }
 static T op(T a, T b) { return min(a, b); }
};
signed main() {
 cin.tie(0);
 ios::sync_with_stdio(0);
 using Mint= ModInt<1000000007>;
 int N, M;
 cin >> N >> M;
 vector<Edge> es(M);
 for (int i= 0; i < M; ++i) cin >> es[i], --es[i];
 Graph g(N);
 vector<Mint> C;
 Mint w= 1;
 UnionFind uf(N);
 vector<char> used(M);
 for (int i= 0; i < M; ++i) {
  auto [A, B]= es[i];
  w+= w;
  if (uf.unite(A, B)) {
   used[i]= true;
   g.add_edge(A, B), C.push_back(w);
  }
 }
 HeavyLightDecomposition tree(g);
 auto adj= g.adjacency_edge(0);
 vector<Mint> dep(N);
 for (int i= 0, v; i < N; ++i)
  for (int e: adj[v= tree.to_vertex(i)])
   if (int u= g[e].to(v); u != tree.parent(v)) dep[u]= dep[v] + C[e];
 auto dist= [&](int u, int v) { return dep[u] + dep[v] - dep[tree.lca(u, v)] * 2; };
 vector<array<int, 3>> xyw;
 for (int i= 0; i < M; ++i) {
  if (used[i]) continue;
  auto [A, B]= es[i];
  int a= tree.to_seq(A), b= tree.to_seq(B);
  if (a > b) swap(a, b);
  xyw.push_back({a, b, i});
 }
 SegmentTree_2D<int, RMQ> seg(xyw);
 int Q;
 cin >> Q;
 while (Q--) {
  int u, v, e;
  cin >> u >> v >> e, --u, --v, --e;
  auto [x, y]= es[e];
  if (tree.parent(y) == x) swap(x, y);
  bool u_in= tree.in_subtree(u, x);
  if (!used[e] || u_in == tree.in_subtree(v, x)) {
   cout << dist(u, v) << '\n';
   continue;
  }
  auto [l, r]= tree.subtree(x);
  int i= min(seg.prod(0, l, l, r), seg.prod(l, r, r, N));
  if (i > M) {
   cout << -1 << '\n';
   continue;
  }
  auto [p, q]= es[i];
  if (!u_in) swap(u, v);
  if (tree.in_subtree(q, x)) swap(p, q);
  cout << dist(u, p) + dist(v, q) + Mint(2).pow(i + 1) << '\n';
 }
 return 0;
}

Test cases

Env	Name	Status	Elapsed	Memory
g++-13	in01.txt	AC	5 ms	4 MB
g++-13	in02.txt	AC	4 ms	4 MB
g++-13	in03.txt	AC	4 ms	4 MB
g++-13	in04.txt	AC	4 ms	4 MB
g++-13	in05.txt	AC	135 ms	18 MB
g++-13	in06.txt	AC	137 ms	18 MB
g++-13	in07.txt	AC	6 ms	4 MB
g++-13	in08.txt	AC	5 ms	4 MB
g++-13	in09.txt	AC	5 ms	4 MB
g++-13	in10.txt	AC	5 ms	4 MB
g++-13	in11.txt	AC	132 ms	36 MB
g++-13	in12.txt	AC	165 ms	44 MB
g++-13	in13.txt	AC	175 ms	40 MB
g++-13	in14.txt	AC	151 ms	27 MB
g++-13	in15.txt	AC	132 ms	18 MB
g++-13	in16.txt	AC	5 ms	3 MB
g++-13	in17.txt	AC	5 ms	4 MB
g++-13	in18.txt	AC	158 ms	34 MB
g++-13	in19.txt	AC	131 ms	18 MB
g++-13	in20.txt	AC	5 ms	4 MB
g++-13	in21.txt	AC	4 ms	4 MB
g++-13	in22.txt	AC	156 ms	34 MB
g++-13	in23.txt	AC	5 ms	3 MB
g++-13	in24.txt	AC	5 ms	4 MB
g++-13	in25.txt	AC	131 ms	18 MB
g++-13	in26.txt	AC	5 ms	4 MB
g++-13	in27.txt	AC	5 ms	4 MB
g++-13	in28.txt	AC	4 ms	4 MB
g++-13	in29.txt	AC	4 ms	4 MB
g++-13	in30.txt	AC	176 ms	34 MB
g++-13	in31.txt	AC	210 ms	34 MB
g++-13	in32.txt	AC	150 ms	34 MB
g++-13	in33.txt	AC	153 ms	34 MB
g++-13	in34.txt	AC	5 ms	4 MB
g++-13	in35.txt	AC	5 ms	3 MB
g++-13	in36.txt	AC	114 ms	18 MB
g++-13	in37.txt	AC	84 ms	18 MB
g++-13	in38.txt	AC	5 ms	4 MB
g++-13	in39.txt	AC	110 ms	17 MB
g++-13	in40.txt	AC	5 ms	4 MB
g++-13	in41.txt	AC	207 ms	34 MB
g++-13	in42.txt	AC	137 ms	34 MB
g++-13	in43.txt	AC	144 ms	34 MB
g++-13	in44.txt	AC	145 ms	34 MB
g++-13	in45.txt	AC	156 ms	34 MB
g++-13	in46.txt	AC	157 ms	34 MB
g++-13	in47.txt	AC	129 ms	34 MB
g++-13	in48.txt	AC	189 ms	34 MB
g++-13	in49.txt	AC	133 ms	34 MB
g++-13	in50.txt	AC	5 ms	4 MB
g++-13	in51.txt	AC	5 ms	4 MB
g++-13	sample_01.txt	AC	5 ms	4 MB
g++-13	sample_02.txt	AC	5 ms	4 MB
g++-13	sample_03.txt	AC	5 ms	3 MB
clang++-18	in01.txt	AC	5 ms	4 MB
clang++-18	in02.txt	AC	5 ms	4 MB
clang++-18	in03.txt	AC	4 ms	4 MB
clang++-18	in04.txt	AC	4 ms	4 MB
clang++-18	in05.txt	AC	158 ms	18 MB
clang++-18	in06.txt	AC	163 ms	18 MB
clang++-18	in07.txt	AC	5 ms	4 MB
clang++-18	in08.txt	AC	5 ms	4 MB
clang++-18	in09.txt	AC	5 ms	4 MB
clang++-18	in10.txt	AC	4 ms	4 MB
clang++-18	in11.txt	AC	131 ms	36 MB
clang++-18	in12.txt	AC	165 ms	44 MB
clang++-18	in13.txt	AC	192 ms	41 MB
clang++-18	in14.txt	AC	181 ms	27 MB
clang++-18	in15.txt	AC	165 ms	18 MB
clang++-18	in16.txt	AC	5 ms	4 MB
clang++-18	in17.txt	AC	5 ms	4 MB
clang++-18	in18.txt	AC	185 ms	34 MB
clang++-18	in19.txt	AC	167 ms	18 MB
clang++-18	in20.txt	AC	5 ms	4 MB
clang++-18	in21.txt	AC	5 ms	4 MB
clang++-18	in22.txt	AC	183 ms	34 MB
clang++-18	in23.txt	AC	5 ms	4 MB
clang++-18	in24.txt	AC	4 ms	4 MB
clang++-18	in25.txt	AC	164 ms	18 MB
clang++-18	in26.txt	AC	5 ms	4 MB
clang++-18	in27.txt	AC	5 ms	4 MB
clang++-18	in28.txt	AC	5 ms	4 MB
clang++-18	in29.txt	AC	4 ms	4 MB
clang++-18	in30.txt	AC	186 ms	34 MB
clang++-18	in31.txt	AC	216 ms	34 MB
clang++-18	in32.txt	AC	175 ms	34 MB
clang++-18	in33.txt	AC	171 ms	34 MB
clang++-18	in34.txt	AC	5 ms	4 MB
clang++-18	in35.txt	AC	5 ms	4 MB
clang++-18	in36.txt	AC	146 ms	18 MB
clang++-18	in37.txt	AC	97 ms	18 MB
clang++-18	in38.txt	AC	5 ms	4 MB
clang++-18	in39.txt	AC	116 ms	17 MB
clang++-18	in40.txt	AC	5 ms	4 MB
clang++-18	in41.txt	AC	220 ms	34 MB
clang++-18	in42.txt	AC	144 ms	34 MB
clang++-18	in43.txt	AC	147 ms	34 MB
clang++-18	in44.txt	AC	152 ms	34 MB
clang++-18	in45.txt	AC	159 ms	34 MB
clang++-18	in46.txt	AC	165 ms	34 MB
clang++-18	in47.txt	AC	135 ms	34 MB
clang++-18	in48.txt	AC	196 ms	34 MB
clang++-18	in49.txt	AC	143 ms	34 MB
clang++-18	in50.txt	AC	5 ms	4 MB
clang++-18	in51.txt	AC	4 ms	4 MB
clang++-18	sample_01.txt	AC	4 ms	4 MB
clang++-18	sample_02.txt	AC	4 ms	4 MB
clang++-18	sample_03.txt	AC	4 ms	4 MB

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