#include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include using namespace std; using lint = long long; using pint = pair; using plint = pair; struct fast_ios { fast_ios(){ cin.tie(nullptr), ios::sync_with_stdio(false), cout << fixed << setprecision(20); }; } fast_ios_; #define ALL(x) (x).begin(), (x).end() #define FOR(i, begin, end) for(int i=(begin),i##_end_=(end);i=i##_begin_;i--) #define REP(i, n) FOR(i,0,n) #define IREP(i, n) IFOR(i,0,n) template void ndarray(vector& vec, const V& val, int len) { vec.assign(len, val); } template void ndarray(vector& vec, const V& val, int len, Args... args) { vec.resize(len), for_each(begin(vec), end(vec), [&](T& v) { ndarray(v, val, args...); }); } template bool chmax(T &m, const T q) { return m < q ? (m = q, true) : false; } template bool chmin(T &m, const T q) { return m > q ? (m = q, true) : false; } int floor_lg(long long x) { return x <= 0 ? -1 : 63 - __builtin_clzll(x); } template pair operator+(const pair &l, const pair &r) { return make_pair(l.first + r.first, l.second + r.second); } template pair operator-(const pair &l, const pair &r) { return make_pair(l.first - r.first, l.second - r.second); } template vector sort_unique(vector vec) { sort(vec.begin(), vec.end()), vec.erase(unique(vec.begin(), vec.end()), vec.end()); return vec; } template int arglb(const std::vector &v, const T &x) { return std::distance(v.begin(), std::lower_bound(v.begin(), v.end(), x)); } template int argub(const std::vector &v, const T &x) { return std::distance(v.begin(), std::upper_bound(v.begin(), v.end(), x)); } template istream &operator>>(istream &is, vector &vec) { for (auto &v : vec) is >> v; return is; } template ostream &operator<<(ostream &os, const vector &vec) { os << '['; for (auto v : vec) os << v << ','; os << ']'; return os; } template ostream &operator<<(ostream &os, const array &arr) { os << '['; for (auto v : arr) os << v << ','; os << ']'; return os; } #if __cplusplus >= 201703L template istream &operator>>(istream &is, tuple &tpl) { std::apply([&is](auto &&... args) { ((is >> args), ...);}, tpl); return is; } template ostream &operator<<(ostream &os, const tuple &tpl) { os << '('; std::apply([&os](auto &&... args) { ((os << args << ','), ...);}, tpl); return os << ')'; } #endif template ostream &operator<<(ostream &os, const deque &vec) { os << "deq["; for (auto v : vec) os << v << ','; os << ']'; return os; } template ostream &operator<<(ostream &os, const set &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; } template ostream &operator<<(ostream &os, const unordered_set &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; } template ostream &operator<<(ostream &os, const multiset &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; } template ostream &operator<<(ostream &os, const unordered_multiset &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; } template ostream &operator<<(ostream &os, const pair &pa) { os << '(' << pa.first << ',' << pa.second << ')'; return os; } template ostream &operator<<(ostream &os, const map &mp) { os << '{'; for (auto v : mp) os << v.first << "=>" << v.second << ','; os << '}'; return os; } template ostream &operator<<(ostream &os, const unordered_map &mp) { os << '{'; for (auto v : mp) os << v.first << "=>" << v.second << ','; os << '}'; return os; } #ifdef HITONANODE_LOCAL const string COLOR_RESET = "\033[0m", BRIGHT_GREEN = "\033[1;32m", BRIGHT_RED = "\033[1;31m", BRIGHT_CYAN = "\033[1;36m", NORMAL_CROSSED = "\033[0;9;37m", RED_BACKGROUND = "\033[1;41m", NORMAL_FAINT = "\033[0;2m"; #define dbg(x) cerr << BRIGHT_CYAN << #x << COLOR_RESET << " = " << (x) << NORMAL_FAINT << " (L" << __LINE__ << ") " << __FILE__ << COLOR_RESET << endl #define dbgif(cond, x) ((cond) ? cerr << BRIGHT_CYAN << #x << COLOR_RESET << " = " << (x) << NORMAL_FAINT << " (L" << __LINE__ << ") " << __FILE__ << COLOR_RESET << endl : cerr) #else #define dbg(x) (x) #define dbgif(cond, x) 0 #endif template struct ModInt { #if __cplusplus >= 201402L #define MDCONST constexpr #else #define MDCONST #endif using lint = long long; MDCONST static int mod() { return md; } static int get_primitive_root() { static int primitive_root = 0; if (!primitive_root) { primitive_root = [&]() { std::set fac; int v = md - 1; for (lint i = 2; i * i <= v; i++) while (v % i == 0) fac.insert(i), v /= i; if (v > 1) fac.insert(v); for (int g = 1; g < md; g++) { bool ok = true; for (auto i : fac) if (ModInt(g).pow((md - 1) / i) == 1) { ok = false; break; } if (ok) return g; } return -1; }(); } return primitive_root; } int val; MDCONST ModInt() : val(0) {} MDCONST ModInt &_setval(lint v) { return val = (v >= md ? v - md : v), *this; } MDCONST ModInt(lint v) { _setval(v % md + md); } MDCONST explicit operator bool() const { return val != 0; } MDCONST ModInt operator+(const ModInt &x) const { return ModInt()._setval((lint)val + x.val); } MDCONST ModInt operator-(const ModInt &x) const { return ModInt()._setval((lint)val - x.val + md); } MDCONST ModInt operator*(const ModInt &x) const { return ModInt()._setval((lint)val * x.val % md); } MDCONST ModInt operator/(const ModInt &x) const { return ModInt()._setval((lint)val * x.inv() % md); } MDCONST ModInt operator-() const { return ModInt()._setval(md - val); } MDCONST ModInt &operator+=(const ModInt &x) { return *this = *this + x; } MDCONST ModInt &operator-=(const ModInt &x) { return *this = *this - x; } MDCONST ModInt &operator*=(const ModInt &x) { return *this = *this * x; } MDCONST ModInt &operator/=(const ModInt &x) { return *this = *this / x; } friend MDCONST ModInt operator+(lint a, const ModInt &x) { return ModInt()._setval(a % md + x.val); } friend MDCONST ModInt operator-(lint a, const ModInt &x) { return ModInt()._setval(a % md - x.val + md); } friend MDCONST ModInt operator*(lint a, const ModInt &x) { return ModInt()._setval(a % md * x.val % md); } friend MDCONST ModInt operator/(lint a, const ModInt &x) { return ModInt()._setval(a % md * x.inv() % md); } MDCONST bool operator==(const ModInt &x) const { return val == x.val; } MDCONST bool operator!=(const ModInt &x) const { return val != x.val; } MDCONST bool operator<(const ModInt &x) const { return val < x.val; } // To use std::map friend std::istream &operator>>(std::istream &is, ModInt &x) { lint t; return is >> t, x = ModInt(t), is; } MDCONST friend std::ostream &operator<<(std::ostream &os, const ModInt &x) { return os << x.val; } MDCONST ModInt pow(lint n) const { ModInt ans = 1, tmp = *this; while (n) { if (n & 1) ans *= tmp; tmp *= tmp, n >>= 1; } return ans; } static std::vector facs, facinvs, invs; MDCONST static void _precalculation(int N) { int l0 = facs.size(); if (N > md) N = md; if (N <= l0) return; facs.resize(N), facinvs.resize(N), invs.resize(N); for (int i = l0; i < N; i++) facs[i] = facs[i - 1] * i; facinvs[N - 1] = facs.back().pow(md - 2); for (int i = N - 2; i >= l0; i--) facinvs[i] = facinvs[i + 1] * (i + 1); for (int i = N - 1; i >= l0; i--) invs[i] = facinvs[i] * facs[i - 1]; } MDCONST lint inv() const { if (this->val < std::min(md >> 1, 1 << 21)) { while (this->val >= int(facs.size())) _precalculation(facs.size() * 2); return invs[this->val].val; } else { return this->pow(md - 2).val; } } MDCONST ModInt fac() const { while (this->val >= int(facs.size())) _precalculation(facs.size() * 2); return facs[this->val]; } MDCONST ModInt facinv() const { while (this->val >= int(facs.size())) _precalculation(facs.size() * 2); return facinvs[this->val]; } MDCONST ModInt doublefac() const { lint k = (this->val + 1) / 2; return (this->val & 1) ? ModInt(k * 2).fac() / (ModInt(2).pow(k) * ModInt(k).fac()) : ModInt(k).fac() * ModInt(2).pow(k); } MDCONST ModInt nCr(const ModInt &r) const { return (this->val < r.val) ? 0 : this->fac() * (*this - r).facinv() * r.facinv(); } MDCONST ModInt nPr(const ModInt &r) const { return (this->val < r.val) ? 0 : this->fac() * (*this - r).facinv(); } ModInt sqrt() const { if (val == 0) return 0; if (md == 2) return val; if (pow((md - 1) / 2) != 1) return 0; ModInt b = 1; while (b.pow((md - 1) / 2) == 1) b += 1; int e = 0, m = md - 1; while (m % 2 == 0) m >>= 1, e++; ModInt x = pow((m - 1) / 2), y = (*this) * x * x; x *= (*this); ModInt z = b.pow(m); while (y != 1) { int j = 0; ModInt t = y; while (t != 1) j++, t *= t; z = z.pow(1LL << (e - j - 1)); x *= z, z *= z, y *= z; e = j; } return ModInt(std::min(x.val, md - x.val)); } }; template std::vector> ModInt::facs = {1}; template std::vector> ModInt::facinvs = {1}; template std::vector> ModInt::invs = {0}; using mint = ModInt<1000000007>; // UnionFind Tree (0-indexed), based on size of each disjoint set struct UnionFind { std::vector par, cou; UnionFind(int N = 0) : par(N), cou(N, 1) { iota(par.begin(), par.end(), 0); } int find(int x) { return (par[x] == x) ? x : (par[x] = find(par[x])); } bool unite(int x, int y) { x = find(x), y = find(y); if (x == y) return false; if (cou[x] < cou[y]) std::swap(x, y); par[y] = x, cou[x] += cou[y]; return true; } int count(int x) { return cou[find(x)]; } bool same(int x, int y) { return find(x) == find(y); } }; // Incremental Bridge-Connectivity // two-edge-connected components // Reference: // struct IncrementalBridgeConnectivity { int V; int nb_bridge; UnionFind con, bicon; std::vector bbf; int _bicon_par(int x) { return bbf[x] == -1 ? -1 : bicon.find(bbf[x]); } int _lca(int x, int y) { std::unordered_set us; while (true) { if (x != -1) { if (!us.insert(x).second) { return x; } x = _bicon_par(x); } std::swap(x, y); } } void _compress(int now, int lca) { while (bicon.find(now) != bicon.find(lca)) { int nxt = _bicon_par(now); bbf[now] = bbf[lca], bicon.unite(now, lca), now = nxt, nb_bridge--; } } IncrementalBridgeConnectivity(int v = 0) : V(v), nb_bridge(0), con(v), bicon(v), bbf(v, -1) {} void add_edge(int u, int v) { assert(u >= 0 and u < V); assert(v >= 0 and v < V); u = bicon.find(u), v = bicon.find(v); if (con.find(u) == con.find(v)) { int lca = _lca(u, v); _compress(u, lca), _compress(v, lca); } else { if (con.count(u) > con.count(v)) std::swap(u, v); for (int now = u, pre = v; now != -1;) { int nxt = _bicon_par(now); bbf[now] = pre, pre = now, now = nxt; } con.unite(u, v), nb_bridge++; } } int count_bridge() const { return nb_bridge; } bool two_edge_connected(int x, int y) { return bicon.same(x, y); } int find(int x) { return bicon.find(x); } }; // lowest common ancestor (LCA) class for undirected weighted tree // 無向重み付きグラフの最小共通祖先 // struct UndirectedWeightedTree { using T = long long; // Arbitrary data structure (operator+, operator- must be defined) int INVALID = -1; int V, lgV; int E; int root; std::vector>> adj; // (nxt_vertex, edge_id) // vector edge; // edges[edge_id] = (vertex_id, vertex_id) std::vector weight; // w[edge_id] std::vector par; // parent_vertex_id[vertex_id] std::vector depth; // depth_from_root[vertex_id] std::vector acc_weight; // w_sum_from_root[vertex_id] void _fix_root_dfs(int now, int prv, int prv_edge_id) { par[now] = prv; if (prv_edge_id != INVALID) acc_weight[now] = acc_weight[prv] + weight[prv_edge_id]; for (auto nxt : adj[now]) if (nxt.first != prv) { depth[nxt.first] = depth[now] + 1; _fix_root_dfs(nxt.first, now, nxt.second); } } UndirectedWeightedTree() = default; UndirectedWeightedTree(int N) : V(N), E(0), adj(N) { lgV = 1; while (1 << lgV < V) lgV++; } void add_edge(int u, int v, T w) { adj[u].emplace_back(v, E); adj[v].emplace_back(u, E); // edge.emplace_back(u, v); weight.emplace_back(w); E++; } void fix_root(int r) { root = r; par.resize(V); depth.resize(V); depth[r] = 0; acc_weight.resize(V); acc_weight[r] = 0; _fix_root_dfs(root, INVALID, INVALID); } std::vector> doubling; void doubling_precalc() { doubling.assign(lgV, std::vector(V)); doubling[0] = par; for (int d = 0; d < lgV - 1; d++) for (int i = 0; i < V; i++) { if (doubling[d][i] == INVALID) doubling[d + 1][i] = INVALID; else doubling[d + 1][i] = doubling[d][doubling[d][i]]; } } int kth_parent(int x, int k) { if (depth[x] < k) return INVALID; for (int d = 0; d < lgV; d++) { if (x == INVALID) return INVALID; if (k & (1 << d)) x = doubling[d][x]; } return x; } int lowest_common_ancestor(int u, int v) { if (depth[u] > depth[v]) std::swap(u, v); v = kth_parent(v, depth[v] - depth[u]); if (u == v) return u; for (int d = lgV - 1; d >= 0; d--) { if (doubling[d][u] != doubling[d][v]) u = doubling[d][u], v = doubling[d][v]; } return par[u]; } T path_length(int u, int v) { // Not distance, but the sum of weights int r = lowest_common_ancestor(u, v); return (acc_weight[u] - acc_weight[r]) + (acc_weight[v] - acc_weight[r]); } }; // Range Minimum Query for static sequence by sparse table // Complexity: (N \log N)$ for precalculation, (1)$ per query template struct StaticRMQ { inline T func(const T &l, const T &r) const noexcept { return std::min(l, r); } int N, lgN; T defaultT; std::vector> data; std::vector lgx_table; StaticRMQ() = default; StaticRMQ(const std::vector &sequence, T defaultT) : N(sequence.size()), defaultT(defaultT) { lgx_table.resize(N + 1); for (int i = 2; i < N + 1; i++) lgx_table[i] = lgx_table[i >> 1] + 1; lgN = lgx_table[N] + 1; data.assign(lgN, std::vector(N, defaultT)); data[0] = sequence; for (int d = 1; d < lgN; d++) { for (int i = 0; i + (1 << d) <= N; i++) { data[d][i] = func(data[d - 1][i], data[d - 1][i + (1 << (d - 1))]); } } } T get(int l, int r) const { // [l, r), 0-indexed assert(l >= 0 and r <= N); if (l >= r) return defaultT; int d = lgx_table[r - l]; return func(data[d][l], data[d][r - (1 << d)]); } }; struct TreeLCA { const int N; std::vector> to; bool built; TreeLCA(int V = 0) : N(V), to(V), built(false) {} void add_edge(int u, int v) { assert(0 <= u and u < N); assert(0 <= v and v < N); assert(u != v); to[u].push_back(v); to[v].push_back(u); } using P = std::pair; std::vector subtree_begin; std::vector

vis_order; std::vector depth; void _build_dfs(int now, int prv, int dnow) { subtree_begin[now] = vis_order.size(); vis_order.emplace_back(dnow, now); depth[now] = dnow; for (auto &&nxt : to[now]) { if (nxt != prv) { _build_dfs(nxt, now, dnow + 1); vis_order.emplace_back(dnow, now); } } } StaticRMQ

rmq; void build(int root = 0) { assert(root >= 0 and root < N); built = true; subtree_begin.resize(N); vis_order.reserve(N * 2); depth.resize(N); _build_dfs(root, -1, 0); rmq = {vis_order, P{N, -1}}; } int lca(int u, int v) { assert(0 <= u and u < N); assert(0 <= v and v < N); if (!built) build(); auto a = subtree_begin[u], b = subtree_begin[v]; if (a > b) std::swap(a, b); return rmq.get(a, b + 1).second; }; int lca3(int a, int b, int c) { return lca(a, b) ^ lca(b, c) ^ lca(c, a); } int distance(int u, int v) { return depth[u] + depth[v] - 2 * depth[lca(u, v)]; } }; int main() { int N, M; cin >> N >> M; UndirectedWeightedTree tree(N); TreeLCA tree1(N); vector edges, tree_edges; vector pow2{1}; UnionFind uf(N); vector additional_eids; REP(e, M) { int a, b; cin >> a >> b; a--, b--; edges.emplace_back(a, b); auto p = pow2.back() * 2; pow2.push_back(p); if (uf.unite(a, b)) { tree.add_edge(a, b, p.val); tree1.add_edge(a, b); tree_edges.emplace_back(a, b); } else { additional_eids.push_back(e); } } tree.fix_root(0); tree1.build(); tree.doubling_precalc(); int Q; cin >> Q; vector x(Q), y(Q), z(Q), u(Q), v(Q); vector ret(Q, -1); vector lo(Q, -1), hi(Q, additional_eids.size() + 1); REP(q, Q) { cin >> x[q] >> y[q] >> z[q]; x[q]--, y[q]--, z[q]--; bool edge_on_line = false; if (!binary_search(additional_eids.begin(), additional_eids.end(), z[q])) { tie(u[q], v[q]) = edges[z[q]]; if (tree1.lca3(x[q], y[q], u[q]) == u[q] and tree1.lca3(x[q], y[q], v[q]) == v[q]) { edge_on_line = true; } } if (!edge_on_line) { lo[q] = -1, hi[q] = 0; ret[q] = mint(tree.path_length(x[q], y[q])).val; } else { lo[q] = 0; } } dbg("OK"); IncrementalBridgeConnectivity conn_(N); for (auto [a, b] : tree_edges) conn_.add_edge(a, b); while (true) { vector t2q; REP(q, Q) { if (lo[q] + 1 < hi[q]) { int n = (lo[q] + hi[q]) / 2; t2q.emplace_back(n, q); } } if (t2q.empty()) break; sort(t2q.begin(), t2q.end()); int added = 0; auto conn = conn_; for (auto [t, q] : t2q) { while (added < t) { auto [u, v] = edges[additional_eids[added++]]; conn.add_edge(u, v); } (conn.two_edge_connected(u[q], v[q]) ? hi[q] : lo[q]) = t; } } REP(q, Q) if (ret[q] < 0) { if (lo[q] < int(additional_eids.size())) { int e = additional_eids[lo[q]]; auto [u, v] = edges[e]; if (tree1.distance(x[q], u) > tree1.distance(x[q], v)) swap(u, v); ret[q] = mint(tree.path_length(x[q], u) + tree.path_length(y[q], v) + pow2[e + 1]).val; } } for (auto x : ret) cout << x << '\n'; }