#include #include #include struct AdjacencyList{ public: struct AdjacencyListRange{ using iterator = typename std::vector::const_iterator; iterator begi, endi; iterator begin() const { return begi; } iterator end() const { return endi; } }; private: int mn; std::vector E; std::vector I; public: AdjacencyList(int n, std::vector> edges, bool rev){ if(n == 0){ mn = 0; I = {0}; E = {}; return; } mn = n; std::vector buf(n+1, 0); for(auto [u,v] : edges){ ++buf[u]; if(rev) ++buf[v]; } for(int i=1; i<=n; i++) buf[i] += buf[i-1]; E.resize(buf[n]); for(int i=(int)edges.size()-1; i>=0; i--){ auto [u,v] = edges[i]; E[--buf[u]] = v; if(rev) E[--buf[v]] = u; } I = std::move(buf); } AdjacencyListRange operator[](int u) const { return AdjacencyListRange{ E.begin() + I[u], E.begin() + I[u+1] }; } int num_vertices() const { return mn; } }; #include #include #include namespace nachia{ struct HeavyLightDecomposition{ private: int N; std::vector P; std::vector PP; std::vector PD; std::vector D; std::vector I; std::vector rangeL; std::vector rangeR; public: HeavyLightDecomposition(const AdjacencyList& E = AdjacencyList(1, {}, false)){ N = E.num_vertices(); P.assign(N, -1); I = {0}; I.reserve(N); for(int i=0; i<(int)I.size(); i++){ int p = I[i]; for(int e : E[p]) if(P[p] != e){ I.push_back(e); P[e] = p; } } std::vector Z(N, 1); std::vector nx(N, -1); PP.resize(N); for(int i=0; i=1; i--){ int p = I[i]; Z[P[p]] += Z[p]; if(nx[P[p]] == -1) nx[P[p]] = p; if(Z[nx[P[p]]] < Z[p]) nx[P[p]] = p; } for(int p : I) if(nx[p] != -1) PP[nx[p]] = p; PD.assign(N,N); PD[0] = 0; D.assign(N,0); for(int p : I) if(p != 0){ PP[p] = PP[PP[p]]; PD[p] = std::min(PD[PP[p]], PD[P[p]]+1); D[p] = D[P[p]]+1; } rangeL.assign(N,0); rangeR.assign(N,0); std::vector dfs; dfs.push_back(0); while(dfs.size()){ int p = dfs.back(); rangeR[p] = rangeL[p] + Z[p]; int ir = rangeR[p]; dfs.pop_back(); for(int e : E[p]) if(P[p] != e) if(e != nx[p]){ rangeL[e] = (ir -= Z[e]); dfs.push_back(e); } if(nx[p] != -1){ rangeL[nx[p]] = rangeL[p] + 1; dfs.push_back(nx[p]); } } I.resize(N); for(int i=0; i PD[v]) u = P[PP[u]]; while(PP[u] != PP[v]){ u = P[PP[u]]; v = P[PP[v]]; } return (D[u] > D[v]) ? v : u; } int dist(int u, int v) const { return depth(u) + depth(v) - depth(lca(u,v)) * 2; } std::vector> path(int r, int c, bool include_root = true, bool reverse_path = false) const { if(PD[c] < PD[r]) return {}; std::vector> res(PD[c]-PD[r]+1); for(int i=0; i<(int)res.size()-1; i++){ res[i] = std::make_pair(rangeL[PP[c]], rangeL[c]+1); c = P[PP[c]]; } if(PP[r] != PP[c] || D[r] > D[c]) return {}; res.back() = std::make_pair(rangeL[r]+(include_root?0:1), rangeL[c]+1); if(res.back().first == res.back().second) res.pop_back(); if(!reverse_path) std::reverse(res.begin(),res.end()); else for(auto& a : res) a = std::make_pair(N - a.second, N - a.first); return move(res); } std::pair subtree(int p){ return std::make_pair(rangeL[p], rangeR[p]); } int to_seq(int vertex) const { return rangeL[vertex]; } int to_vtx(int seqidx) const { return I[seqidx]; } int median(int x, int y, int z) const { if(to_seq(x) > to_seq(y)) std::swap(x,y); if(to_seq(y) > to_seq(z)) std::swap(y,z); if(to_seq(x) > to_seq(y)) std::swap(x,y); x = lca(x,y); y = lca(y,z); return depth(x) < depth(y) ? y : x; } int la(int from, int to, int d) const { if(d < 0) return -1; int g = lca(from,to); int dist0 = D[from] - D[g] * 2 + D[to]; if(dist0 < d) return -1; int p = from; if(D[from] - D[g] < d){ p = to; d = dist0 - d; } while(D[p] - D[PP[p]] < d){ d -= D[p] - D[PP[p]] + 1; p = P[PP[p]]; } return I[rangeL[p] - d]; } }; } // namespace nachia #include #include #include #include using namespace std; using ll = long long; using ull = unsigned long long; const ull MOD = 1000000007; #define rep(i,n) for(int i=0; i<(n); i++) struct mll{ using u32 = uint32_t; using u64 = uint64_t; u32 v; mll(u32 x = 0) : v(x) {} u32 val() const { return v; } mll& operator+=(const mll& r){ v += r.val(); if(v >= MOD) v -= MOD; return *this; } mll& operator-=(const mll& r){ v += MOD - r.val(); if(v >= MOD) v -= MOD; return *this; } mll& operator*=(const mll& r) { v = (u64)v * r.val() % MOD; return *this; } mll operator+(const mll& r) const { mll res = *this; res += r; return res; } mll operator-(const mll& r) const { mll res = *this; res -= r; return res; } mll operator*(const mll& r) const { mll res = *this; res *= r; return res; } mll operator-() const { return v ? mll(MOD-v) : mll(0); } }; struct DSU{ vector V; DSU(int n){ V.resize(n); rep(i,n) V[i] = i; } int leader(int a){ if(V[a] == a) return a; return V[a] = leader(V[a]); } void merge(int r,int c){ V[leader(c)] = leader(r); } }; struct Edge{ int u,v,i; }; int N, M; vector J; vector> E; vector flows; vector cost; vector P; vector Eidx; vector dep; vector iEidx; vector flowIdx; nachia::HeavyLightDecomposition hld; void read_graph(){ cin >> N >> M; E.resize(N); vector> idE; cost.resize(M); cost[0] = 2; for(int i=1; i> u >> v; u--; v--; J.push_back({u,v,i}); if(G1.leader(u) == G1.leader(v)){ flows.push_back({u,v,i}); } else{ G1.merge(u,v); E[u].push_back({u,v,i}); E[v].push_back({v,u,i}); idE.push_back(make_pair(u,v)); } } hld = nachia::HeavyLightDecomposition(AdjacencyList(N, idE, true)); } void initLCA(){ vector I; P.assign(N,-1); I.push_back(0); dep.assign(N,0); Eidx.assign(N,-1); rep(i,I.size()){ int p = I[i]; for(Edge e : E[p]) if(P[p] != e.v){ P[e.v] = p; dep[e.v] = dep[p] + cost[e.i]; Eidx[e.v] = e.i; I.push_back(e.v); } } } int LCA(int u,int v){ return hld.lca(u,v); } int dist0(int u,int v){ return hld.dist(u,v); } mll dist1(int u,int v){ int g = LCA(u,v); return dep[u] + dep[v] - dep[g] * 2; } void build_flows(){ iEidx.assign(M,-1); rep(i,N) if(Eidx[i] != -1) iEidx[Eidx[i]] = i; flowIdx.assign(N,-1); DSU G2(N); for(Edge e : flows){ int g = G2.leader(LCA(e.u,e.v)); for(int s : {e.u,e.v}){ int p = G2.leader(s); while(p != g){ flowIdx[p] = e.i; G2.merge(P[p],p); p = G2.leader(p); } } } } int path_includes(int u,int v,int z){ if(iEidx[z] == -1) return -1; if(hld.median(u,v,J[z].u) != J[z].u) return -1; if(hld.median(u,v,J[z].v) != J[z].v) return -1; int res = flowIdx[iEidx[z]]; if(res == -1) return -2; return res; } mll shortest_using(int u,int v,int z){ mll ans = cost[z]; if(dist0(u,J[z].u) + dist0(v,J[z].v) < dist0(u,J[z].v) + dist0(v,J[z].u)) ans += dist1(u,J[z].u) + dist1(v,J[z].v); else ans += dist1(u,J[z].v) + dist1(v,J[z].u); return ans; } int main(){ read_graph(); initLCA(); build_flows(); int Q; cin >> Q; rep(q,Q){ int u,v,z; cin >> u >> v >> z; u--; v--; z--; int inc = path_includes(u,v,z); if(inc == -2){ cout << "-1\n"; continue; } if(inc == -1){ cout << dist1(u,v).val() << "\n"; continue; } auto e = J[inc]; mll ans = shortest_using(u,v,e.i); cout << ans.val() << "\n"; } return 0; } struct ios_do_not_sync{ ios_do_not_sync(){ ios::sync_with_stdio(false); cin.tie(nullptr); } } ios_do_not_sync_inst;