#line 1 "Main.cpp" #define PROBLEM "https://yukicoder.me/problems/no/1600" #line 2 "nachia\\array\\csr-array.hpp" #include #include #include namespace nachia{ template class CsrArray{ public: struct ListRange{ using iterator = typename std::vector::iterator; iterator begi, endi; iterator begin() const { return begi; } iterator end() const { return endi; } int size() const { return (int)std::distance(begi, endi); } Elem& operator[](int i) const { return begi[i]; } }; struct ConstListRange{ using iterator = typename std::vector::const_iterator; iterator begi, endi; iterator begin() const { return begi; } iterator end() const { return endi; } int size() const { return (int)std::distance(begi, endi); } const Elem& operator[](int i) const { return begi[i]; } }; private: int m_n; std::vector m_list; std::vector m_pos; public: CsrArray() : m_n(0), m_list(), m_pos() {} static CsrArray Construct(int n, std::vector> items){ CsrArray res; res.m_n = n; std::vector buf(n+1, 0); for(auto& [u,v] : items){ ++buf[u]; } for(int i=1; i<=n; i++) buf[i] += buf[i-1]; res.m_list.resize(buf[n]); for(int i=(int)items.size()-1; i>=0; i--){ res.m_list[--buf[items[i].first]] = std::move(items[i].second); } res.m_pos = std::move(buf); return res; } static CsrArray FromRaw(std::vector list, std::vector pos){ CsrArray res; res.m_n = pos.size() - 1; res.m_list = std::move(list); res.m_pos = std::move(pos); return res; } ListRange operator[](int u) { return ListRange{ m_list.begin() + m_pos[u], m_list.begin() + m_pos[u+1] }; } ConstListRange operator[](int u) const { return ConstListRange{ m_list.begin() + m_pos[u], m_list.begin() + m_pos[u+1] }; } int size() const { return m_n; } int fullSize() const { return (int)m_list.size(); } }; } // namespace nachia #line 4 "nachia\\graph\\graph.hpp" #include #line 6 "nachia\\graph\\graph.hpp" namespace nachia{ struct Graph { public: struct Edge{ int from, to; void reverse(){ std::swap(from, to); } }; using Base = std::vector>; Graph(int n = 0, bool undirected = false) : m_n(n), m_e(), m_isUndir(undirected) {} Graph(int n, const std::vector>& edges, bool undirected = false) : m_n(n), m_isUndir(undirected){ m_e.resize(edges.size()); for(std::size_t i=0; i& edges, bool undirected = false) : m_n(n), m_e(edges), m_isUndir(undirected) {} Graph(int n, std::vector&& edges, bool undirected = false) : m_n(n), m_e(std::move(edges)), m_isUndir(undirected) {} int numVertices() const noexcept { return m_n; } int numEdges() const noexcept { return int(m_e.size()); } int addNode() noexcept { return m_n++; } int addEdge(int from, int to){ m_e.push_back({ from, to }); return numEdges() - 1; } Edge& operator[](int ei) noexcept { return m_e[ei]; } const Edge& operator[](int ei) const noexcept { return m_e[ei]; } Edge& at(int ei) { return m_e.at(ei); } const Edge& at(int ei) const { return m_e.at(ei); } auto begin(){ return m_e.begin(); } auto end(){ return m_e.end(); } auto begin() const { return m_e.begin(); } auto end() const { return m_e.end(); } bool isUndirected() const noexcept { return m_isUndir; } void reverseEdges() noexcept { for(auto& e : m_e) e.reverse(); } void contract(int newV, const std::vector& mapping){ assert(numVertices() == int(mapping.size())); for(int i=0; i induce(int num, const std::vector& mapping) const { int n = numVertices(); assert(n == int(mapping.size())); for(int i=0; i indexV(n), newV(num); for(int i=0; i= 0) indexV[i] = newV[mapping[i]]++; std::vector res; res.reserve(num); for(int i=0; i= 0) res[mapping[e.to]].addEdge(indexV[e.from], indexV[e.to]); return res; } CsrArray getEdgeIndexArray(bool undirected) const { std::vector> src; src.reserve(numEdges() * (undirected ? 2 : 1)); for(int i=0; i::Construct(numVertices(), src); } CsrArray getEdgeIndexArray() const { return getEdgeIndexArray(isUndirected()); } CsrArray getAdjacencyArray(bool undirected) const { std::vector> src; src.reserve(numEdges() * (undirected ? 2 : 1)); for(auto e : m_e){ src.emplace_back(e.from, e.to); if(undirected) src.emplace_back(e.to, e.from); } return CsrArray::Construct(numVertices(), src); } CsrArray getAdjacencyArray() const { return getAdjacencyArray(isUndirected()); } private: int m_n; std::vector m_e; bool m_isUndir; }; } // namespace nachia #line 6 "nachia\\tree\\heavy-light-decomposition.hpp" 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 CsrArray& E = CsrArray::Construct(1, {}), int root = 0){ N = E.size(); P.assign(N, -1); I = {root}; 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[root] = 0; D.assign(N,0); for(int p : I) if(p != root){ 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); for(int p : I){ rangeR[p] = rangeL[p] + Z[p]; int ir = rangeR[p]; for(int e : E[p]) if(P[p] != e) if(e != nx[p]){ rangeL[e] = (ir -= Z[e]); } if(nx[p] != -1){ rangeL[nx[p]] = rangeL[p] + 1; } } 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 res; } std::pair subtree(int p){ return std::make_pair(rangeL[p], rangeR[p]); } int median(int x, int y, int z) const { return lca(x,y) ^ lca(y,z) ^ lca(x,z); } 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 #line 4 "nachia\\set\\dsu.hpp" namespace nachia { struct Dsu{ private: int N; std::vector P; std::vector H; public: Dsu() : N(0) {} Dsu(int n) : N(n), P(n, -1), H(n) { for(int i=0; i= 0){ P[u] = P[v]; u = v; v = P[v]; } return P[u]; } int append(){ int n = P.size(); P.push_back(-1); H.push_back(n); return n; } int label(int u){ return H[leader(u)]; } int operator[](int u){ return H[leader(u)]; } void merge(int u, int v, int newLabel){ if(newLabel < 0) newLabel = u; u = leader(u); v = leader(v); if(u == v){ H[u] = newLabel; return; } N--; if(-P[u] < -P[v]) std::swap(u, v); P[u] += P[v]; H[P[v] = u] = newLabel; } int merge(int u, int v){ merge(u, v, u); return u; } int count(){ return N; } int size(int u){ return -P[leader(u)]; } bool same(int u, int v){ return leader(u) == leader(v); } }; } // namespace nachia #line 2 "nachia\\misc\\fastio.hpp" #include #include #include #include namespace nachia{ struct CInStream{ private: static const unsigned int INPUT_BUF_SIZE = 1 << 17; unsigned int p = INPUT_BUF_SIZE; static char Q[INPUT_BUF_SIZE]; public: using MyType = CInStream; char seekChar() noexcept { if(p == INPUT_BUF_SIZE){ size_t len = fread(Q, 1, INPUT_BUF_SIZE, stdin); if(len != INPUT_BUF_SIZE) Q[len] = '\0'; p = 0; } return Q[p]; } void skipSpace() noexcept { while(isspace(seekChar())) p++; } uint32_t nextU32() noexcept { skipSpace(); uint32_t buf = 0; while(true){ char tmp = seekChar(); if('9' < tmp || tmp < '0') break; buf = buf * 10 + (tmp - '0'); p++; } return buf; } int32_t nextI32() noexcept { skipSpace(); if(seekChar() == '-'){ p++; return (int32_t)(-nextU32()); } return (int32_t)nextU32(); } uint64_t nextU64() noexcept { skipSpace(); uint64_t buf = 0; while(true){ char tmp = seekChar(); if('9' < tmp || tmp < '0') break; buf = buf * 10 + (tmp - '0'); p++; } return buf; } int64_t nextI64() noexcept { skipSpace(); if(seekChar() == '-'){ p++; return (int64_t)(-nextU64()); } return (int64_t)nextU64(); } char nextChar() noexcept { skipSpace(); char buf = seekChar(); p++; return buf; } std::string nextToken(){ skipSpace(); std::string buf; while(true){ char ch = seekChar(); if(isspace(ch) || ch == '\0') break; buf.push_back(ch); p++; } return buf; } MyType& operator>>(unsigned int& dest) noexcept { dest = nextU32(); return *this; } MyType& operator>>(int& dest) noexcept { dest = nextI32(); return *this; } MyType& operator>>(unsigned long& dest) noexcept { dest = nextU64(); return *this; } MyType& operator>>(long& dest) noexcept { dest = nextI64(); return *this; } MyType& operator>>(unsigned long long& dest) noexcept { dest = nextU64(); return *this; } MyType& operator>>(long long& dest) noexcept { dest = nextI64(); return *this; } MyType& operator>>(std::string& dest){ dest = nextToken(); return *this; } MyType& operator>>(char& dest) noexcept { dest = nextChar(); return *this; } } cin; struct FastOutputTable{ char LZ[1000][4] = {}; char NLZ[1000][4] = {}; constexpr FastOutputTable(){ using u32 = uint_fast32_t; for(u32 d=0; d<1000; d++){ LZ[d][0] = ('0' + d / 100 % 10); LZ[d][1] = ('0' + d / 10 % 10); LZ[d][2] = ('0' + d / 1 % 10); LZ[d][3] = '\0'; } for(u32 d=0; d<1000; d++){ u32 i = 0; if(d >= 100) NLZ[d][i++] = ('0' + d / 100 % 10); if(d >= 10) NLZ[d][i++] = ('0' + d / 10 % 10); if(d >= 1) NLZ[d][i++] = ('0' + d / 1 % 10); NLZ[d][i++] = '\0'; } } }; struct COutStream{ private: using u32 = uint32_t; using u64 = uint64_t; using MyType = COutStream; static const u32 OUTPUT_BUF_SIZE = 1 << 17; static char Q[OUTPUT_BUF_SIZE]; static constexpr FastOutputTable TB = FastOutputTable(); u32 p = 0; static constexpr u32 P10(u32 d){ return d ? P10(d-1)*10 : 1; } static constexpr u64 P10L(u32 d){ return d ? P10L(d-1)*10 : 1; } template static void Fil(T& m, U& l, U x) noexcept { m = l/x; l -= m*x; } void next_dig9(u32 x){ u32 y; Fil(y, x, P10(6)); nextCstr(TB.LZ[y]); Fil(y, x, P10(3)); nextCstr(TB.LZ[y]); nextCstr(TB.LZ[x]); } public: void nextChar(char c){ Q[p++] = c; if(p == OUTPUT_BUF_SIZE){ fwrite(Q, p, 1, stdout); p = 0; } } void nextEoln(){ nextChar('\n'); } void nextCstr(const char* s){ while(*s) nextChar(*(s++)); } void nextU32(uint32_t x){ u32 y = 0; if(x >= P10(9)){ Fil(y, x, P10(9)); nextCstr(TB.NLZ[y]); next_dig9(x); } else if(x >= P10(6)){ Fil(y, x, P10(6)); nextCstr(TB.NLZ[y]); Fil(y, x, P10(3)); nextCstr(TB.LZ[y]); nextCstr(TB.LZ[x]); } else if(x >= P10(3)){ Fil(y, x, P10(3)); nextCstr(TB.NLZ[y]); nextCstr(TB.LZ[x]); } else if(x >= 1) nextCstr(TB.NLZ[x]); else nextChar('0'); } void nextI32(int32_t x){ if(x >= 0) nextU32(x); else{ nextChar('-'); nextU32((u32)-x); } } void nextU64(uint64_t x){ u32 y = 0; if(x >= P10L(18)){ Fil(y, x, P10L(18)); nextU32(y); Fil(y, x, P10L(9)); next_dig9(y); next_dig9(x); } else if(x >= P10L(9)){ Fil(y, x, P10L(9)); nextU32(y); next_dig9(x); } else nextU32(x); } void nextI64(int64_t x){ if(x >= 0) nextU64(x); else{ nextChar('-'); nextU64((u64)-x); } } void writeToFile(bool flush = false){ fwrite(Q, p, 1, stdout); if(flush) fflush(stdout); p = 0; } COutStream(){ Q[0] = 0; } ~COutStream(){ writeToFile(); } MyType& operator<<(unsigned int tg){ nextU32(tg); return *this; } MyType& operator<<(unsigned long tg){ nextU64(tg); return *this; } MyType& operator<<(unsigned long long tg){ nextU64(tg); return *this; } MyType& operator<<(int tg){ nextI32(tg); return *this; } MyType& operator<<(long tg){ nextI64(tg); return *this; } MyType& operator<<(long long tg){ nextI64(tg); return *this; } MyType& operator<<(const std::string& tg){ nextCstr(tg.c_str()); return *this; } MyType& operator<<(const char* tg){ nextCstr(tg); return *this; } MyType& operator<<(char tg){ nextChar(tg); return *this; } } cout; char CInStream::Q[INPUT_BUF_SIZE]; char COutStream::Q[OUTPUT_BUF_SIZE]; } // namespace nachia #line 8 "Main.cpp" #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<(int)(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 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(){ using nachia::cin; 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.same(u, 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({ u,v }); } } hld = nachia::HeavyLightDecomposition(nachia::Graph(N, idE, true).getAdjacencyArray()); } 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); nachia::Dsu G2(N); for(Edge e : flows){ int g = G2.label(LCA(e.u,e.v)); for(int s : {e.u,e.v}){ int p = G2.label(s); while(p != g){ flowIdx[p] = e.i; G2.merge(P[p], p, G2.label(P[p])); p = G2.label(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(){ using nachia::cin; using nachia::cout; 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; }