#include using namespace std; using int64 = long long; //const int mod = 1e9 + 7; const int mod = 998244353; const int64 infll = (1LL << 62) - 1; const int inf = (1 << 30) - 1; struct IoSetup { IoSetup() { cin.tie(nullptr); ios::sync_with_stdio(false); cout << fixed << setprecision(10); cerr << fixed << setprecision(10); } } iosetup; template< typename T1, typename T2 > ostream &operator<<(ostream &os, const pair< T1, T2 > &p) { os << p.first << " " << p.second; return os; } template< typename T1, typename T2 > istream &operator>>(istream &is, pair< T1, T2 > &p) { is >> p.first >> p.second; return is; } template< typename T > ostream &operator<<(ostream &os, const vector< T > &v) { for(int i = 0; i < (int) v.size(); i++) { os << v[i] << (i + 1 != v.size() ? " " : ""); } return os; } template< typename T > istream &operator>>(istream &is, vector< T > &v) { for(T &in : v) is >> in; return is; } template< typename T1, typename T2 > inline bool chmax(T1 &a, T2 b) { return a < b && (a = b, true); } template< typename T1, typename T2 > inline bool chmin(T1 &a, T2 b) { return a > b && (a = b, true); } template< typename T = int64 > vector< T > make_v(size_t a) { return vector< T >(a); } template< typename T, typename... Ts > auto make_v(size_t a, Ts... ts) { return vector< decltype(make_v< T >(ts...)) >(a, make_v< T >(ts...)); } template< typename T, typename V > typename enable_if< is_class< T >::value == 0 >::type fill_v(T &t, const V &v) { t = v; } template< typename T, typename V > typename enable_if< is_class< T >::value != 0 >::type fill_v(T &t, const V &v) { for(auto &e : t) fill_v(e, v); } template< typename F > struct FixPoint : F { FixPoint(F &&f) : F(forward< F >(f)) {} template< typename... Args > decltype(auto) operator()(Args &&... args) const { return F::operator()(*this, forward< Args >(args)...); } }; template< typename F > inline decltype(auto) MFP(F &&f) { return FixPoint< F >{forward< F >(f)}; } template< typename T = int > struct Edge { int from, to; T cost; int idx; Edge() = default; Edge(int from, int to, T cost = 1, int idx = -1) : from(from), to(to), cost(cost), idx(idx) {} operator int() const { return to; } }; template< typename T = int > struct Graph { vector< vector< Edge< T > > > g; int es; Graph() = default; explicit Graph(int n) : g(n), es(0) {} size_t size() const { return g.size(); } void add_directed_edge(int from, int to, T cost = 1) { g[from].emplace_back(from, to, cost, es++); } void add_edge(int from, int to, T cost = 1) { g[from].emplace_back(from, to, cost, es); g[to].emplace_back(to, from, cost, es++); } void read(int M, int padding = -1, bool weighted = false, bool directed = false) { for(int i = 0; i < M; i++) { int a, b; cin >> a >> b; a += padding; b += padding; T c = T(1); if(weighted) cin >> c; if(directed) add_directed_edge(a, b, c); else add_edge(a, b, c); } } }; template< typename T = int > using Edges = vector< Edge< T > >; /** * @brief Low-Link(橋/関節点) * @see http://kagamiz.hatenablog.com/entry/2013/10/05/005213 * @docs docs/low-link.md */ template< typename T = int > struct LowLink : Graph< T > { public: using Graph< T >::Graph; vector< int > ord, low, articulation; vector< Edge< T > > bridge; using Graph< T >::g; virtual void build() { used.assign(g.size(), 0); ord.assign(g.size(), 0); low.assign(g.size(), 0); int k = 0; for(int i = 0; i < (int) g.size(); i++) { if(!used[i]) k = dfs(i, k, -1); } } explicit LowLink(const Graph< T > &g) : Graph< T >(g) {} private: vector< int > used; int dfs(int idx, int k, int par) { used[idx] = true; ord[idx] = k++; low[idx] = ord[idx]; bool is_articulation = false, beet = false; int cnt = 0; for(auto &to : g[idx]) { if(to == par && !exchange(beet, true)) { continue; } if(!used[to]) { ++cnt; k = dfs(to, k, idx); low[idx] = min(low[idx], low[to]); is_articulation |= par >= 0 && low[to] >= ord[idx]; if(ord[idx] < low[to]) bridge.emplace_back(to); } else { low[idx] = min(low[idx], ord[to]); } } is_articulation |= par == -1 && cnt > 1; if(is_articulation) articulation.push_back(idx); return k; } }; /** * @brief Bi-Connected-Components(二重頂点連結成分分解) * @docs docs/bi-connected-components.md */ template< typename T = int > struct BiConnectedComponents : LowLink< T > { public: using LowLink< T >::LowLink; using LowLink< T >::g; using LowLink< T >::ord; using LowLink< T >::low; vector< vector< Edge< T > > > bc; void build() override { LowLink< T >::build(); used.assign(g.size(), 0); for(int i = 0; i < used.size(); i++) { if(!used[i]) dfs(i, -1); } } explicit BiConnectedComponents(const Graph< T > &g) : Graph< T >(g) {} private: vector< int > used; vector< Edge< T > > tmp; void dfs(int idx, int par) { used[idx] = true; bool beet = false; for(auto &to : g[idx]) { if(to == par && !exchange(beet, true)) continue; if(!used[to] || ord[to] < ord[idx]) { tmp.emplace_back(to); } if(!used[to]) { dfs(to, idx); if(low[to] >= ord[idx]) { bc.emplace_back(); for(;;) { auto e = tmp.back(); bc.back().emplace_back(e); tmp.pop_back(); if(e.idx == to.idx) break; } } } } } }; /** * @brief Block-Cut-Tree * @see https://ei1333.hateblo.jp/entry/2020/03/25/010057 */ template< typename T = int > struct BlockCutTree : BiConnectedComponents< T > { public: using BiConnectedComponents< T >::BiConnectedComponents; using BiConnectedComponents< T >::g; using BiConnectedComponents< T >::articulation; using BiConnectedComponents< T >::bc; vector< int > rev; vector< vector< int > > group; Graph< T > tree; explicit BlockCutTree(const Graph< T > &g) : Graph< T >(g) {} int operator[](const int &k) const { return rev[k]; } void build() override { BiConnectedComponents< T >::build(); rev.assign(g.size(), -1); int ptr = (int) bc.size(); for(auto &idx : articulation) { rev[idx] = ptr++; } vector< int > last(ptr, -1); tree = Graph< T >(ptr); for(int i = 0; i < (int) bc.size(); i++) { for(auto &e : bc[i]) { for(auto &ver : {e.from, e.to}) { if(rev[ver] >= (int) bc.size()) { if(exchange(last[rev[ver]], i) != i) { tree.add_edge(rev[ver], i, e.cost); } } else { rev[ver] = i; } } } } group.resize(ptr); for(int i = 0; i < (int) g.size(); i++) { group[rev[i]].emplace_back(i); } } }; /** * @brief Sparse-Table(スパーステーブル) * @docs docs/sparse-table.md */ template< typename T, typename F > struct SparseTable { F f; vector< vector< T > > st; vector< int > lookup; SparseTable() = default; explicit SparseTable(const vector< T > &v, const F &f) : f(f) { const int n = (int) v.size(); const int b = 32 - __builtin_clz(n); st.assign(b, vector< T >(n)); for(int i = 0; i < v.size(); i++) { st[0][i] = v[i]; } for(int i = 1; i < b; i++) { for(int j = 0; j + (1 << i) <= n; j++) { st[i][j] = f(st[i - 1][j], st[i - 1][j + (1 << (i - 1))]); } } lookup.resize(v.size() + 1); for(int i = 2; i < lookup.size(); i++) { lookup[i] = lookup[i >> 1] + 1; } } inline T fold(int l, int r) const { int b = lookup[r - l]; return f(st[b][l], st[b][r - (1 << b)]); } }; template< typename T, typename F > SparseTable< T, F > get_sparse_table(const vector< T > &v, const F &f) { return SparseTable< T, F >(v, f); } /** * @brief Plus-Minus-One-RMQ **/ template< typename T > struct PlusMinusOneRMQ { using F = function< int(int, int) >; int backet; vector< T > vs; vector< int > bidx, bbit; SparseTable< int, F > st; vector< vector< vector< int > > > lookup; explicit PlusMinusOneRMQ() = default; explicit PlusMinusOneRMQ(const vector< T > &vs) : vs(vs) { int n = (int) vs.size(); backet = max(1, (31 - __builtin_clz(n)) / 2); int sz = (n + backet - 1) / backet; bidx.assign(sz, -1); bbit.assign(sz, 0); for(int i = 0; i < sz; i++) { int l = i * backet; int r = min(l + backet, n); bidx[i] = l; for(int j = l + 1; j < r; j++) { if(vs[j] < vs[bidx[i]]) bidx[i] = j; if(vs[j - 1] < vs[j]) bbit[i] |= 1 << (j - l - 1); } } F f = [&](int a, int b) { return vs[a] < vs[b] ? a : b; }; st = get_sparse_table(bidx, f); lookup.assign(1 << (backet - 1), vector< vector< int > >(backet, vector< int >(backet + 1))); for(int i = 0; i < (1 << (backet - 1)); i++) { for(int j = 0; j < backet; j++) { int sum = 0, ret = 0, pos = j; for(int k = j + 1; k <= backet; k++) { lookup[i][j][k] = pos; if(i & (1 << (k - 1))) ++sum; else --sum; if(sum < ret) { pos = k; ret = sum; } } } } } pair< T, int > fold(int l, int r) const { int lb = l / backet; int rb = r / backet; if(lb == rb) { int pos = lb * backet + lookup[bbit[lb]][l % backet][r % backet]; return {vs[pos], pos}; } int pos = lb * backet + lookup[bbit[lb]][l % backet][backet]; if(r % backet > 0) { int sub = rb * backet + lookup[bbit[rb]][0][r % backet]; if(vs[sub] < vs[pos]) pos = sub; } if(lb + 1 == rb) { return {vs[pos], pos}; } else { int sub = st.fold(lb + 1, rb); if(vs[sub] < vs[pos]) pos = sub; return {vs[pos], pos}; } } }; /** * @brief PMORMQ-Lowest-Common-Ancestor(最小共通祖先) * @docs docs/pmormq-lowest-common-ancestor.md **/ template< typename T = int > struct PMORMQLowestCommonAncestor : Graph< T > { public: using Graph< T >::Graph; using Graph< T >::g; using F = function< int(int, int) >; void build(int root = 0) { ord.reserve(g.size() * 2 - 1); dep.reserve(g.size() * 2 - 1); in.resize(g.size()); dfs(root, -1, 0); vector< int > vs(g.size() * 2 - 1); iota(begin(vs), end(vs), 0); st = PlusMinusOneRMQ< int >(dep); } int lca(int x, int y) const { if(in[x] > in[y]) swap(x, y); return ord[st.fold(in[x], in[y] + 1).second]; } explicit PMORMQLowestCommonAncestor(const Graph< T > &g) : Graph< T >(g) {} private: vector< int > ord, dep, in; PlusMinusOneRMQ< int > st; void dfs(int idx, int par, int d) { in[idx] = (int) ord.size(); ord.emplace_back(idx); dep.emplace_back(d); for(auto &to : g[idx]) { if(to != par) { dfs(to, idx, d + 1); ord.emplace_back(idx); dep.emplace_back(d); } } } }; int main() { int N, M; cin >> N >> M; BlockCutTree<> g(N); g.read(M); g.build(); PMORMQLowestCommonAncestor<> bct(g.tree); bct.build(); vector< int > sum(g.tree.size()); MFP([&](auto rec, int idx, int par) -> void { if(idx >= g.bc.size()) { sum[idx]++; } for(auto &to : g.tree.g[idx]) { if(to != par) { sum[to] += sum[idx]; rec(to, idx); } } })(0, -1); int Q; cin >> Q; while(Q--) { int X, Y; cin >> X >> Y; --X, --Y; X = g[X]; Y = g[Y]; if(X == Y) { cout << 0 << "\n"; continue; } int lca = bct.lca(X, Y); if(X == lca) { swap(X, Y); } if(Y == lca) { int ans = sum[X] - sum[Y]; ans -= X >= g.bc.size(); cout << ans << "\n"; continue; } int ans = sum[X] + sum[Y] - 2 * sum[lca]; ans -= X >= g.bc.size(); ans -= Y >= g.bc.size(); ans += lca >= g.bc.size(); cout << ans << "\n"; } }