#include #include #include using namespace std; struct heavy_light_decomposition{ private: int N; vector P; vector PP; vector PD; vector D; vector I; vector rangeL; vector rangeR; public: heavy_light_decomposition(const vector>& E = {{}}){ N = E.size(); P.assign(N, -1); I = {0}; I.reserve(N); for(int i=0; i Z(N, 1); 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] = min(PD[PP[p]], PD[P[p]]+1); D[p] = D[P[p]]+1; } rangeL.assign(N,0); rangeR.assign(N,0); 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; } vector> path(int r, int c, bool include_root = true, bool reverse_path = false) const { vector> res; while(PD[r] < PD[c]){ res.push_back({ rangeL[PP[c]], rangeL[c]+1 }); c = P[PP[c]]; } if(PP[r] != PP[c]) return {}; if(D[r] > D[c]) return {}; res.push_back({ rangeL[r], rangeL[c]+1 }); if(!include_root){ res.back().first++; if(res.back().first == res.back().second) res.pop_back(); } if(!reverse_path) reverse(res.begin(),res.end()); return move(res); } const vector& idxs() const { return rangeL; } int meet(int x, int y, int z) const { //return lca(x,y) ^ lca(y,z) ^ lca(x,z); if(PD[x] > PD[y]) swap(x,y); if(PD[y] > PD[z]) swap(y,z); if(PD[x] > PD[y]) swap(x,y); while(PD[z] > PD[y]) z = P[PP[z]]; while(PD[y] > PD[x]){ if(PP[y] == PP[z]) return (D[y] > D[z]) ? z : y; y = P[PP[y]]; z = P[PP[z]]; } while(true){ if(PP[x] == PP[y]){ if(PP[y] == PP[z]){ if(D[x] > D[y]) swap(x,y); if(D[y] > D[z]) swap(y,z); if(D[x] > D[y]) swap(x,y); return y; } return (D[x] > D[y]) ? y : x; } if(PP[x] == PP[z]) return (D[x] > D[z]) ? z : x; if(PP[y] == PP[z]) return (D[y] > D[z]) ? z : y; x = P[PP[x]]; y = P[PP[y]]; z = P[PP[z]]; } return -1; } int jump(int from, int to, int d) const { 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]; } }; #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; heavy_light_decomposition hld; void read_graph(){ cin >> N >> M; E.resize(N); vector> idE(N); 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[u].push_back(v); idE[v].push_back(u); } } hld = heavy_light_decomposition(idE); } 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.meet(u,v,J[z].u) != J[z].u) return -1; if(hld.meet(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;