// >>> TEMPLATES #include using namespace std; using ll = long long; using ld = long double; using i32 = int32_t; using i64 = int64_t; using u32 = uint32_t; using u64 = uint64_t; #define int ll #define rep(i, n) for (int i = 0; i < (int)(n); i++) #define rep1(i, n) for (int i = 1; i <= (int)(n); i++) #define repR(i, n) for (int i = (int)(n)-1; i >= 0; i--) #define rep1R(i, n) for (int i = (int)(n); i >= 1; i--) #define loop(i, a, B) for (int i = a; i B; i++) #define loopR(i, a, B) for (int i = a; i B; i--) #define all(x) begin(x), end(x) #define allR(x) rbegin(x), rend(x) #define rng(x, l, r) begin(x) + (l), begin(x) + (r) #define pb push_back #define eb emplace_back #define fst first #define snd second template constexpr auto mp(A &&a, B &&b) { return make_pair(forward(a), forward(b)); } template constexpr auto mt(T&&... x) { return make_tuple(forward(x)...); } template auto constexpr inf_ = numeric_limits::max()/2-1; auto constexpr INF32 = inf_; auto constexpr INF64 = inf_; auto constexpr INF = inf_; #ifdef LOCAL #include "debug.hpp" #else #define dump(...) (void)(0) #define say(x) (void)(0) #define debug if (0) #endif template struct pque : priority_queue, Comp> { vector &data() { return this->c; } void clear() { this->c.clear(); } }; template using pque_max = pque>; template using pque_min = pque>; template ::value, int> = 0> ostream& operator<<(ostream& os, T const& a) { bool f = true; for (auto const& x : a) os << (f ? "" : " ") << x, f = false; return os; } template ::value, int> = 0> ostream& operator<<(ostream& os, const T (&a)[N]) { bool f = true; for (auto const& x : a) os << (f ? "" : " ") << x, f = false; return os; } template ())), class = typename enable_if::value>::type> istream& operator>>(istream& is, T &a) { for (auto& x : a) is >> x; return is; } template ostream& operator<<(ostream& os, pair const& p) { return os << p.first << " " << p.second; } template istream& operator>>(istream& is, pair& p) { return is >> p.first >> p.second; } struct IOSetup { IOSetup() { cin.tie(nullptr); ios::sync_with_stdio(false); cout << fixed << setprecision(15); } } iosetup; template struct FixPoint : private F { constexpr FixPoint(F&& f) : F(forward(f)) {} template constexpr auto operator()(T&&... x) const { return F::operator()(*this, forward(x)...); } }; struct MakeFixPoint { template constexpr auto operator|(F&& f) const { return FixPoint(forward(f)); } }; #define MFP MakeFixPoint()| #define def(name, ...) auto name = MFP [&](auto &&name, __VA_ARGS__) template struct vec_impl { using type = vector::type>; template static type make_v(size_t n, U&&... x) { return type(n, vec_impl::make_v(forward(x)...)); } }; template struct vec_impl { using type = T; static type make_v(T const& x = {}) { return x; } }; template using vec = typename vec_impl::type; template auto make_v(Args&&... args) { return vec_impl::make_v(forward(args)...); } template void quit(T const& x) { cout << x << endl; exit(0); } template constexpr bool chmin(T& x, U const& y) { if (x > (T)y) { x = (T)y; return true; } return false; } template constexpr bool chmax(T& x, U const& y) { if (x < (T)y) { x = (T)y; return true; } return false; } template constexpr auto sumof(It b, It e) { return accumulate(b, e, typename iterator_traits::value_type{}); } template int sz(T const& x) { return x.size(); } template int lbd(C const& v, T const& x) { return lower_bound(begin(v), end(v), x)-begin(v); } template int ubd(C const& v, T const& x) { return upper_bound(begin(v), end(v), x)-begin(v); } constexpr int64_t mod(int64_t x, int64_t m) { assert(m > 0); return (x %= m) < 0 ? x+m : x; } constexpr int64_t div_floor(int64_t x, int64_t y) { assert(y != 0); return x/y - ((x^y) < 0 and x%y); } constexpr int64_t div_ceil(int64_t x, int64_t y) { assert(y != 0); return x/y + ((x^y) > 0 and x%y); } constexpr int dx[] = { 1, 0, -1, 0, 1, -1, -1, 1 }; constexpr int dy[] = { 0, 1, 0, -1, 1, 1, -1, -1 }; constexpr int popcnt(ll x) { return __builtin_popcountll(x); } mt19937_64 seed_{random_device{}()}; template Int rand(Int a, Int b) { return uniform_int_distribution(a, b)(seed_); } i64 irand(i64 a, i64 b) { return rand(a, b); } // [a, b] u64 urand(u64 a, u64 b) { return rand(a, b); } // template void shuffle(It l, It r) { shuffle(l, r, seed_); } template vector &operator--(vector &v) { for (T &x : v) --x; return v; } template vector &operator++(vector &v) { for (T &x : v) ++x; return v; } // <<< // >>> modint template class modint { static_assert(md < (1u<<31), ""); using M = modint; using i64 = int64_t; uint32_t x; public: static constexpr uint32_t mod = md; constexpr modint(i64 x = 0) : x((x%=md) < 0 ? x+md : x) { } constexpr i64 val() const { return x; } constexpr explicit operator i64() const { return x; } constexpr bool operator==(M r) const { return x == r.x; } constexpr bool operator!=(M r) const { return x != r.x; } constexpr M operator+() const { return *this; } constexpr M operator-() const { return M()-*this; } constexpr M& operator+=(M r) { x += r.x; x = (x < md ? x : x-md); return *this; } constexpr M& operator-=(M r) { x += md-r.x; x = (x < md ? x : x-md); return *this; } constexpr M& operator*=(M r) { x = (uint64_t(x)*r.x)%md; return *this; } constexpr M& operator/=(M r) { return *this *= r.inv(); } constexpr M operator+(M r) const { return M(*this) += r; } constexpr M operator-(M r) const { return M(*this) -= r; } constexpr M operator*(M r) const { return M(*this) *= r; } constexpr M operator/(M r) const { return M(*this) /= r; } friend constexpr M operator+(i64 x, M y) { return M(x)+y; } friend constexpr M operator-(i64 x, M y) { return M(x)-y; } friend constexpr M operator*(i64 x, M y) { return M(x)*y; } friend constexpr M operator/(i64 x, M y) { return M(x)/y; } constexpr M inv() const { assert(x > 0); return pow(md-2); } constexpr M pow(i64 n) const { assert(not (x == 0 and n == 0)); if (n < 0) return inv().pow(-n); M v = *this, r = 1; for (; n > 0; n >>= 1, v *= v) if (n&1) r *= v; return r; } #ifdef LOCAL friend string to_s(M r) { return to_s(r.val(), mod); } #endif friend ostream& operator<<(ostream& os, M r) { return os << r.val(); } friend istream& operator>>(istream& is, M &r) { i64 x; is >> x; r = x; return is; } }; // <<< //constexpr int64_t MOD = 998244353; constexpr int64_t MOD = 1e9+7; using mint = modint; mint sign(int n) { return n & 1 ? -1 : +1; } // >>> mod table template struct ModTable { vector fact, finv; void calc(int n) { int old = fact.size(); if (n < old) return; n += 1000; fact.resize(n+1); finv.resize(n+1); if (old == 0) { fact[0] = fact[1] = finv[0] = finv[1] = 1; old = 2; } for (auto i = old; i <= n; i++) fact[i] = fact[i-1] * i; finv[n] = mint(1) / fact[n]; for (auto i = n-1; i >= old; i--) finv[i] = finv[i+1] * (i+1); } }; ModTable mod_tab; mint fact(int n) { assert(0 <= n); return mod_tab.calc(n), mod_tab.fact[n]; } mint finv(int n) { assert(0 <= n); return mod_tab.calc(n), mod_tab.finv[n]; } mint comb(int n, int k) { if (n < 0 || k < 0 || n < k) return 0; mod_tab.calc(n); return mod_tab.fact[n] * mod_tab.finv[k] * mod_tab.finv[n-k]; } mint perm(int n, int k) { assert(k >= 0); assert(n >= k); mod_tab.calc(n); return mod_tab.fact[n] * mod_tab.finv[n-k]; } // <<< // >>> HLD #ifndef EDGE_INFO #define EDGE_INFO constexpr int dest(int v) { return v; } template ().to)> constexpr int dest(E const& e) { return e.to; } constexpr int cost(...) { return 1; } template ().cost)> constexpr auto cost(E const& e) { return e.cost; } template using cost_t = decltype(cost(declval())); #endif template struct HLD { int n, m = 0, root; vector roots; vector> g; vector id, inv, head, sz, par; vector> dep; bool built = false; HLD() : n(0), root(-1) {}; HLD(int n, int root = 0) : n(n), root(root), g(n), id(n), inv(n), head(n), sz(n), par(n), dep(n) { // if (n == 1) build(); } vector const& operator[](int i) const { assert(built); assert(0 <= i); assert(i < (int)g.size()); return g[i]; } template void add_edge(int x, int y, Args&&... args) { g[x].push_back({y, args...}); g[y].push_back({x, args...}); // if (++m == n-1) build(); } void build() { // assert(m == n-1); fill(sz.begin(), sz.end(), 1); fill(all(par), -1); dep[root] = 0, par[root] = -1, head[root] = root; int time = 0; // dfs1(root), dfs2(root, time); roots.clear(); rep (x, n) if (par[x] < 0) roots.push_back(x), dfs1(x), dfs2(x, time); rep (x, g.size()) inv[id[x]] = x; built = true; } int lca(int x, int y) const { assert(built); while (true) { if (id[x] > id[y]) swap(x, y); if (head[x] == head[y]) return x; y = par[head[y]]; } } cost_t dist(int x, int y) const { assert(built); return dep[x] + dep[y] - 2*dep[lca(x, y)]; } int eid(int x, int y) const { assert(built); if (x == par[y]) return id[y]; if (y == par[x]) return id[x]; assert(false); return -1; } int vid(int x) const { assert(built); return id[x]; } int in(int x) const { assert(built); return id[x]; } int out(int x) const { assert(built); return id[x] + sz[x]; } pair subtree(int x) const { return { in(x), out(x) }; } pair split_size(int x, int y) const { assert(built); if (x == par[y]) return { n-sz[y], sz[y] }; if (y == par[x]) return { sz[x], n-sz[y] }; assert(false); return { -1, -1 }; } int meet(int x, int y, int z) const { return lca(x, y) ^ lca(y, z) ^ lca(z, x); } bool is_ancestor(int x, int y) const { // excluding x == y return in(x) < in(y) and out(y) <= out(x); } int step(int x, int y) const { // move one step from x toward y assert(built); assert(x != y); if (not is_ancestor(x, y)) return par[x]; while (true) { if (head[x] == head[y]) return dest(g[x][0]); y = head[y]; if (x == par[y]) return y; y = par[y]; } } int climb(int x, cost_t d) const { assert(built); assert(0 <= d); assert(d <= dep[x]); auto const dep_y = dep[x] - d; while (true) { x = head[x]; if (dep[x] <= dep_y) return inv[id[x] + dep_y - dep[x]]; x = par[x]; } } // jump from x toward y by distance d int jump(int x, int y, cost_t d) const { assert(built); auto const z = lca(x, y); auto const dist = dep[x] + dep[y] - 2*dep[z]; return d <= dep[x] - dep[z] ? climb(x, d) : climb(y, dist-d); } vector> path(int x, int y, bool with_lca) const { assert(built); static vector> ret; ret.clear(); while (true) { if (id[x] > id[y]) swap(x, y); if (head[x] == head[y]) { ret.emplace_back(id[x] + (with_lca ? 0 : 1), id[y]+1); return ret; } else { ret.emplace_back(id[head[y]], id[y]+1); y = par[head[y]]; } } } auto vertices(int x, int y) const { return path(x, y, true); } auto edges(int x, int y) const { return path(x, y, false); } void dfs1(int x) { for (auto &e : g[x]) { if (dest(e) == par[x]) { swap(e, g[x].back()); g[x].pop_back(); break; } } for (auto &e : g[x]) { const int y = dest(e); par[y] = x; dep[y] = dep[x] + cost(e); dfs1(y); sz[x] += sz[y]; if (sz[y] > sz[dest(g[x][0])]) swap(e, g[x][0]); } } void dfs2(int x, int &time) { id[x] = time++; for (auto const& e : g[x]) { const int y = dest(e); head[y] = (y == dest(g[x][0]) ? head[x] : y); dfs2(y, time); } } }; // <<< // >>> union find struct UnionFind { int n, sz; // id : 0...n-1 vector par; UnionFind(int n = 0) : n(n), sz(n), par(n, -1) { } void clear() { rep (i, n) par[i] = -1; sz = n; } int root(int x) { assert(0 <= x); assert(x < n); return par[x] < 0 ? x : par[x] = root(par[x]); } bool unite(int x, int y) { x = root(x), y = root(y); if (x == y) return false; sz--; if (par[x] < par[y]) swap(x, y); par[y] += par[x]; par[x] = y; return true; } bool same(int x, int y) { return root(x) == root(y); } int size(int x) { return -par[root(x)]; } int size() const { return sz; } vector> groups() { vector> g(n); rep (i, n) if (par[i] < 0) g[i].reserve(-par[i]); rep (i, n) g[root(i)].push_back(i); vector> grp; grp.reserve(size()); rep (i, n) if (g[i].size()) grp.emplace_back(move(g[i])); return grp; } }; // <<< // >>> lazy segment tree template struct LazySegtree : Handler { using Value = typename Handler::Value; using Action = typename Handler::Action; using Handler::unit_value; // () -> Value using Handler::unit_action; // () -> Action using Handler::merge; // (Value, Value) -> Value using Handler::compose; // (Action, Action) -> Action using Handler::act; // (Action, Value) -> Value vector v; vector a; int n, lg; LazySegtree() {} template LazySegtree(T&&... x) { init(forward(x)...); } template ()(0))> void init(int n, F gen) { assert(n >= 0); this->n = n; this->lg = (n == 0 ? 0 : __lg(2*n-1)); v.resize(2*n); a.assign(n, unit_action()); for (int i = 0; i < n; i++) v[n+i] = gen(i); for (int i = n-1; i >= 1; i--) v[i] = merge(v[i<<1], v[i<<1|1]); } // void init(int n) { init(n, [&](int) { return unit_value(); }); } void init(int n, Value const& x) { init(n, [&](int) { return x; }); } void init(vector const& v) { init(v.size(), [&](int i) { return v[i]; }); } int size() const { return n; } void act_at(Action const& x, int i) { if (i < n) a[i] = compose(x, a[i]); v[i] = act(x, v[i]); } void flush(int k) { if (n <= k || a[k] == unit_action()) return; act_at(a[k], k<<1); act_at(a[k], k<<1|1); a[k] = unit_action(); } void flush(int l, int r) { for (int p = lg; p; --p) flush(l >> p), flush((r - 1) >> p); } Value get(int l, int r) { assert(0 <= l); assert(l <= r); assert(r <= n); l += n, r += n; flush(l, r); Value x = unit_value(), y = unit_value(); for ( ; l < r; l >>= 1, r >>= 1) { if (l & 1) x = merge(x, v[l++]); if (r & 1) y = merge(v[--r], y); } return merge(x, y); } void build(int i) { i >>= __builtin_ctz(i); while (i >>= 1) v[i] = merge(v[i<<1], v[i<<1|1]); } void apply(int l, int r, Action const& x) { assert(0 <= l); assert(l <= r); assert(r <= n); l += n, r += n; flush(l, r); for (int a = l, b = r; a < b; a >>= 1, b >>= 1) { if (a & 1) act_at(x, a++); if (b & 1) act_at(x, --b); } build(l); build(r); } Value operator[](int i) const { return get(i); } Value get(int i) const { assert(0 <= i); assert(i < n); Value x = v[i += n]; while (i >>= 1) x = act(a[i], x); return x; } void set(int i, Value const& x) { assert(0 <= i); assert(i < n); i += n; for (int p = lg; p; --p) flush(i >> p); v[i] = x; while (i >>= 1) v[i] = merge(v[i<<1], v[i<<1|1]); } template int max_right(int l, F f) { assert(0 <= l); assert(l <= size()); assert(f(unit_value())); l += n; const int r = size() << 1; for (int p = lg; p; p--) flush(l >> p); Value x = unit_value(); while (true) { if (l == r) return size(); int k = __builtin_ctz(l | 1 << __lg(r - l)); auto y = merge(x, v[l >> k]); if (not f(y)) { l >>= k; break; } x = y, l += 1 << k; } while (l < size()) { flush(l); auto y = merge(x, v[l <<= 1]); if (f(y)) x = y, l++; } return l - size(); } template int min_left(int r, F f) { assert(0 <= r); assert(r <= size()); assert(f(unit_value())); r += n; const int l = size(); for (int p = lg; p; p--) flush((r - 1) >> p); Value x = unit_value(); while (true) { if (l == r) return 0; int k = __builtin_ctz(r | 1 << __lg(r - l)); auto y = merge(v[(r >> k) - 1], x); if (not f(y)) { r >>= k; --r; break; } x = y, r -= 1 << k; } while (r < size()) { flush(r); r = r << 1 | 1; auto y = merge(v[r], x); if (f(y)) x = y, r--; } return r + 1 - size(); } vector dat() const { vector ret(size()); for (int i = 0; i < size(); i++) ret[i] = get(i); return ret; } }; template struct Handler { using Value = _Value; using Action = _Action; constexpr static Value unit_value() { return {}; } constexpr static Action unit_action() { return {}; } constexpr static Value merge(Value const& x, Value const& y) { return x * y; } constexpr static Action compose(Action const& x, Action const& y) { return x * y; } constexpr static Value act(Action const& x, Value const& y) { return x(y); } }; // <<< struct MinChmin { using Value = int; using Action = int; constexpr static Value unit_value() { return INF; } constexpr static Action unit_action() { return INF; } constexpr static Value merge(Value const& x, Value const& y) { return min(x, y); } constexpr static Action compose(Action const& x, Action const& y) { return min(x, y); } constexpr static Value act(Action const& x, Value const& y) { return min(x, y); } }; int32_t main() { int n, m; cin >> n >> m; vector> es; rep (_, m) { int x, y; cin >> x >> y; x--, y--; es.eb(x, y); } UnionFind uf(n); struct edge { int to, id; }; HLD g(n); vector used(m); rep (i, m) { auto [x, y] = es[i]; if (uf.unite(x, y)) { used[i] = true; g.add_edge(x, y, i); } } g.build(); LazySegtree seg(n, INF); rep (i, m) if (not used[i]) { auto [x, y] = es[i]; for (auto [l, r] : g.edges(x, y)) { seg.apply(l, r, i); } } dump(seg.dat()); vector dep(n); { def (dfs, int x) -> void { for (auto [y, id] : g[x]) { dep[y] = dep[x] + mint(2).pow(id+1); dfs(y); } }; for (int x : g.roots) dfs(x); } auto wdist = [&](int x, int y) { int z = g.lca(x, y); return dep[x] + dep[y] - 2*dep[z]; }; int Q; cin >> Q; while (Q--) { int x, y, z; cin >> x >> y >> z; x--, y--, z--; auto [a, b] = es[z]; dump(x, y, z, a, b); if (not uf.same(x, y)) { cout << -1 << '\n'; } else if (used[z] and uf.same(x, a) and uf.same(x, b) and g.dist(x, y) == min(g.dist(x, a) + 1 + g.dist(b, y), g.dist(x, b) + 1 + g.dist(a, y))) { int w = seg[g.eid(a, b)]; if (w == INF) { say("2"); cout << -1 << '\n'; } else { say("3"); auto [a, b] = es[w]; if (g.dist(x, a) + 1 + g.dist(b, y) > g.dist(x, b) + 1 + g.dist(a, y)) { swap(a, b); } cout << wdist(x, a) + mint(2).pow(w+1) + wdist(b, y) << '\n'; } } else { say("4"); cout << wdist(x, y) << '\n'; } } }