// #define _GLIBCXX_DEBUG
#include <bits/stdc++.h>
// clang-format off
std::ostream&operator<<(std::ostream&os,std::int8_t x){return os<<(int)x;}
std::ostream&operator<<(std::ostream&os,std::uint8_t x){return os<<(int)x;}
std::ostream&operator<<(std::ostream&os,const __int128_t &v){if(!v)os<<"0";__int128_t tmp=v<0?(os<<"-",-v):v;std::string s;while(tmp)s+='0'+(tmp%10),tmp/=10;return std::reverse(s.begin(),s.end()),os<<s;}
std::ostream&operator<<(std::ostream&os,const __uint128_t &v){if(!v)os<<"0";__uint128_t tmp=v;std::string s;while(tmp)s+='0'+(tmp%10),tmp/=10;return std::reverse(s.begin(),s.end()),os<<s;}
#define checkpoint() (void(0))
#define debug(...) (void(0))
#define debugArray(x,n) (void(0))
#define debugMatrix(x,h,w) (void(0))
// clang-format on
#include <type_traits>
template <class Int> constexpr inline Int mod_inv(Int a, Int mod) {
 static_assert(std::is_signed_v<Int>);
 Int x= 1, y= 0, b= mod;
 for (Int q= 0, z= 0; b;) z= x, x= y, y= z - y * (q= a / b), z= a, a= b, b= z - b * q;
 return assert(a == 1), x < 0 ? mod - (-x) % mod : x % mod;
}
namespace math_internal {
using namespace std;
using u8= unsigned char;
using u32= unsigned;
using i64= long long;
using u64= unsigned long long;
using u128= __uint128_t;
#define CE constexpr
#define IL inline
#define NORM \
 if (n >= mod) n-= mod; \
 return n
#define PLUS(U, M) \
 CE IL U plus(U l, U r) const { \
  if (l+= r; l >= M) l-= M; \
  return l; \
 }
#define DIFF(U, C, M) \
 CE IL U diff(U l, U r) const { \
  if (l-= r; l >> C) l+= M; \
  return l; \
 }
#define SGN(U) \
 static CE IL U set(U n) { return n; } \
 static CE IL U get(U n) { return n; } \
 static CE IL U norm(U n) { return n; }
template <class u_t, class du_t, u8 B, u8 A> struct MP_Mo {
 u_t mod;
 CE MP_Mo(): mod(0), iv(0), r2(0) {}
 CE MP_Mo(u_t m): mod(m), iv(inv(m)), r2(-du_t(mod) % mod) {}
 CE IL u_t mul(u_t l, u_t r) const { return reduce(du_t(l) * r); }
 PLUS(u_t, mod << 1)
 DIFF(u_t, A, mod << 1)
 CE IL u_t set(u_t n) const { return mul(n, r2); }
 CE IL u_t get(u_t n) const {
  n= reduce(n);
  NORM;
 }
 CE IL u_t norm(u_t n) const { NORM; }
private:
 u_t iv, r2;
 static CE u_t inv(u_t n, int e= 6, u_t x= 1) { return e ? inv(n, e - 1, x * (2 - x * n)) : x; }
 CE IL u_t reduce(const du_t &w) const { return u_t(w >> B) + mod - ((du_t(u_t(w) * iv) * mod) >> B); }
};
struct MP_Na {
 u32 mod;
 CE MP_Na(): mod(0){};
 CE MP_Na(u32 m): mod(m) {}
 CE IL u32 mul(u32 l, u32 r) const { return u64(l) * r % mod; }
 PLUS(u32, mod) DIFF(u32, 31, mod) SGN(u32)
};
struct MP_Br {  // mod < 2^31
 u32 mod;
 CE MP_Br(): mod(0), s(0), x(0) {}
 CE MP_Br(u32 m): mod(m), s(95 - __builtin_clz(m - 1)), x(((u128(1) << s) + m - 1) / m) {}
 CE IL u32 mul(u32 l, u32 r) const { return rem(u64(l) * r); }
 PLUS(u32, mod) DIFF(u32, 31, mod) SGN(u32) private: u8 s;
 u64 x;
 CE IL u64 quo(u64 n) const { return (u128(x) * n) >> s; }
 CE IL u32 rem(u64 n) const { return n - quo(n) * mod; }
};
struct MP_Br2 {  // 2^20 < mod <= 2^41
 u64 mod;
 CE MP_Br2(): mod(0), x(0) {}
 CE MP_Br2(u64 m): mod(m), x((u128(1) << 84) / m) {}
 CE IL u64 mul(u64 l, u64 r) const { return rem(u128(l) * r); }
 PLUS(u64, mod << 1)
 DIFF(u64, 63, mod << 1)
 static CE IL u64 set(u64 n) { return n; }
 CE IL u64 get(u64 n) const { NORM; }
 CE IL u64 norm(u64 n) const { NORM; }
private:
 u64 x;
 CE IL u128 quo(const u128 &n) const { return (n * x) >> 84; }
 CE IL u64 rem(const u128 &n) const { return n - quo(n) * mod; }
};
struct MP_D2B1 {
 u8 s;
 u64 mod, d, v;
 CE MP_D2B1(): s(0), mod(0), d(0), v(0) {}
 CE MP_D2B1(u64 m): s(__builtin_clzll(m)), mod(m), d(m << s), v(u128(-1) / d) {}
 CE IL u64 mul(u64 l, u64 r) const { return rem((u128(l) * r) << s) >> s; }
 PLUS(u64, mod) DIFF(u64, 63, mod) SGN(u64) private: CE IL u64 rem(const u128 &u) const {
  u128 q= (u >> 64) * v + u;
  u64 r= u64(u) - (q >> 64) * d - d;
  if (r > u64(q)) r+= d;
  if (r >= d) r-= d;
  return r;
 }
};
template <class u_t, class MP> CE u_t pow(u_t x, u64 k, const MP &md) {
 for (u_t ret= md.set(1);; x= md.mul(x, x))
  if (k & 1 ? ret= md.mul(ret, x) : 0; !(k>>= 1)) return ret;
}
#undef NORM
#undef PLUS
#undef DIFF
#undef SGN
#undef CE
}
namespace math_internal {
struct m_b {};
struct s_b: m_b {};
}
template <class mod_t> constexpr bool is_modint_v= std::is_base_of_v<math_internal::m_b, mod_t>;
template <class mod_t> constexpr bool is_staticmodint_v= std::is_base_of_v<math_internal::s_b, mod_t>;
namespace math_internal {
#define CE constexpr
template <class MP, u64 MOD> struct SB: s_b {
protected:
 static CE MP md= MP(MOD);
};
template <class Int, class U, class B> struct MInt: public B {
 using Uint= U;
 static CE inline auto mod() { return B::md.mod; }
 CE MInt(): x(0) {}
 template <class T, enable_if_t<is_modint_v<T> && !is_same_v<T, MInt>, nullptr_t> = nullptr> CE MInt(T v): x(B::md.set(v.val() % B::md.mod)) {}
 CE MInt(__int128_t n): x(B::md.set((n < 0 ? ((n= (-n) % B::md.mod) ? B::md.mod - n : n) : n % B::md.mod))) {}
 CE MInt operator-() const { return MInt() - *this; }
#define FUNC(name, op) \
 CE MInt name const { \
  MInt ret; \
  ret.x= op; \
  return ret; \
 }
 FUNC(operator+(const MInt& r), B::md.plus(x, r.x))
 FUNC(operator-(const MInt& r), B::md.diff(x, r.x))
 FUNC(operator*(const MInt& r), B::md.mul(x, r.x))
 FUNC(pow(u64 k), math_internal::pow(x, k, B::md))
#undef FUNC
 CE MInt operator/(const MInt& r) const { return *this * r.inv(); }
 CE MInt& operator+=(const MInt& r) { return *this= *this + r; }
 CE MInt& operator-=(const MInt& r) { return *this= *this - r; }
 CE MInt& operator*=(const MInt& r) { return *this= *this * r; }
 CE MInt& operator/=(const MInt& r) { return *this= *this / r; }
 CE bool operator==(const MInt& r) const { return B::md.norm(x) == B::md.norm(r.x); }
 CE bool operator!=(const MInt& r) const { return !(*this == r); }
 CE bool operator<(const MInt& r) const { return B::md.norm(x) < B::md.norm(r.x); }
 CE inline MInt inv() const { return mod_inv<Int>(val(), B::md.mod); }
 CE inline Uint val() const { return B::md.get(x); }
 friend ostream& operator<<(ostream& os, const MInt& r) { return os << r.val(); }
 friend istream& operator>>(istream& is, MInt& r) {
  i64 v;
  return is >> v, r= MInt(v), is;
 }
private:
 Uint x;
};
template <u64 MOD> using ModInt= conditional_t < (MOD < (1 << 30)) & MOD, MInt<int, u32, SB<MP_Mo<u32, u64, 32, 31>, MOD>>, conditional_t < (MOD < (1ull << 62)) & MOD, MInt<i64, u64, SB<MP_Mo<u64, u128, 64, 63>, MOD>>, conditional_t<MOD<(1u << 31), MInt<int, u32, SB<MP_Na, MOD>>, conditional_t<MOD<(1ull << 32), MInt<i64, u32, SB<MP_Na, MOD>>, conditional_t<MOD <= (1ull << 41), MInt<i64, u64, SB<MP_Br2, MOD>>, MInt<i64, u64, SB<MP_D2B1, MOD>>>>>>>;
#undef CE
}
using math_internal::ModInt;
template <class mod_t, size_t LM> mod_t get_inv(int n) {
 static_assert(is_modint_v<mod_t>);
 static const auto m= mod_t::mod();
 static mod_t dat[LM];
 static int l= 1;
 if (l == 1) dat[l++]= 1;
 while (l <= n) dat[l++]= dat[m % l] * (m - m / l);
 return dat[n];
}
class UnionFind {
 std::vector<int> par;
public:
 UnionFind(int n): par(n, -1) {}
 bool unite(int u, int v) {
  if ((u= root(u)) == (v= root(v))) return false;
  if (par[u] > par[v]) std::swap(u, v);
  return par[u]+= par[v], par[v]= u, true;
 }
 bool same(int u, int v) { return root(u) == root(v); }
 int root(int u) { return par[u] < 0 ? u : par[u]= root(par[u]); }
 int size(int u) { return -par[root(u)]; }
};
template <class T> struct ListRange {
 using Iterator= typename std::vector<T>::const_iterator;
 Iterator bg, ed;
 Iterator begin() const { return bg; }
 Iterator end() const { return ed; }
 size_t size() const { return std::distance(bg, ed); }
 const T &operator[](int i) const { return bg[i]; }
};
template <class T> class CsrArray {
 std::vector<T> csr;
 std::vector<int> pos;
public:
 CsrArray()= default;
 CsrArray(const std::vector<T> &c, const std::vector<int> &p): csr(c), pos(p) {}
 size_t size() const { return pos.size() - 1; }
 const ListRange<T> operator[](int i) const { return {csr.cbegin() + pos[i], csr.cbegin() + pos[i + 1]}; }
};
template <class Cost= void, bool weight= false> class Tree {
 template <class D, class T> struct Edge_B {
  int to;
  T cost;
  operator int() const { return to; }
 };
 template <class D> struct Edge_B<D, void> {
  int to;
  operator int() const { return to; }
 };
 using Edge= Edge_B<void, Cost>;
 using C= std::conditional_t<std::is_void_v<Cost>, std::nullptr_t, Cost>;
 std::vector<std::conditional_t<std::is_void_v<Cost>, std::pair<int, int>, std::tuple<int, int, Cost>>> es;
 std::vector<Edge> g;
 std::vector<int> P, PP, D, I, L, R, pos;
 std::vector<C> DW, W;
public:
 Tree(int n): P(n, -2) {}
 template <class T= Cost> std::enable_if_t<std::is_void_v<T>, void> add_edge(int u, int v) { es.emplace_back(u, v), es.emplace_back(v, u); }
 template <class T> std::enable_if_t<std::is_convertible_v<T, Cost>, void> add_edge(int u, int v, T c) { es.emplace_back(u, v, c), es.emplace_back(v, u, c); }
 template <class T, class U, std::enable_if_t<std::conjunction_v<std::is_convertible<T, Cost>, std::is_convertible<U, Cost>>, std::nullptr_t> = nullptr> void add_edge(int u, int v, T c, U d) /* c:u->v, d:v->u */ { es.emplace_back(u, v, c), es.emplace_back(v, u, d); }
 void build(int root= 0) {
  size_t n= P.size();
  I.resize(n), PP.resize(n), std::iota(PP.begin(), PP.end(), 0), D.assign(n, 0), L.assign(n, 0), R.assign(n, 0), pos.resize(n + 1), g.resize(es.size());
  for (const auto &e: es) ++pos[std::get<0>(e)];
  std::partial_sum(pos.begin(), pos.end(), pos.begin());
  if constexpr (std::is_void_v<Cost>)
   for (const auto &[f, t]: es) g[--pos[f]]= {t};
  else
   for (const auto &[f, t, c]: es) g[--pos[f]]= {t, c};
  auto f= [&, i= 0, v= 0, t= 0](int r) mutable {
   for (P[r]= -1, I[t++]= r; i < t; ++i)
    for (int u: operator[](v= I[i]))
     if (P[v] != u) P[I[t++]= u]= v;
  };
  f(root);
  for (size_t r= 0; r < n; ++r)
   if (P[r] == -2) f(r);
  std::vector<int> Z(n, 1), nx(n, -1);
  for (int i= n, v; i--;) {
   if (P[v= I[i]] == -1) continue;
   if (Z[P[v]]+= Z[v]; nx[P[v]] == -1) nx[P[v]]= v;
   if (Z[nx[P[v]]] < Z[v]) nx[P[v]]= v;
  }
  for (int v: I)
   if (nx[v] != -1) PP[nx[v]]= v;
  for (int v: I)
   if (P[v] != -1) PP[v]= PP[PP[v]], D[v]= D[P[v]] + 1;
  for (int i= n; i--;) L[I[i]]= i;
  for (int v: I) {
   int ir= R[v]= L[v] + Z[v];
   for (int u: operator[](v))
    if (u != P[v] && u != nx[v]) L[u]= ir-= Z[u];
   if (nx[v] != -1) L[nx[v]]= L[v] + 1;
  }
  if constexpr (weight) {
   DW.resize(n), W.resize(n);
   for (int v: I)
    for (auto &[u, c]: operator[](v)) {
     if (u != P[v]) DW[u]= DW[v] + c;
     else W[v]= c;
    }
  }
  for (int i= n; i--;) I[L[i]]= i;
 }
 size_t size() const { return P.size(); }
 const ListRange<Edge> operator[](int v) const { return {g.cbegin() + pos[v], g.cbegin() + pos[v + 1]}; }
 int depth(int v) const { return D[v]; }
 C depth_w(int v) const {
  static_assert(weight, "\'depth_w\' is not available");
  return DW[v];
 }
 int to_seq(int v) const { return L[v]; }
 int to_node(int i) const { return I[i]; }
 int parent(int v) const { return P[v]; }
 int root(int v) const {
  for (v= PP[v];; v= PP[P[v]])
   if (P[v] == -1) return v;
 }
 bool connected(int u, int v) const { return root(u) == root(v); }
 int lca(int u, int v) const {
  for (;; v= P[PP[v]]) {
   if (L[u] > L[v]) std::swap(u, v);
   if (PP[u] == PP[v]) return u;
  }
 }
 int la(int v, int k) const {
  assert(k <= D[v]);
  for (int u;; k-= L[v] - L[u] + 1, v= P[u])
   if (L[v] - k >= L[u= PP[v]]) return I[L[v] - k];
 }
 int la_w(int v, C w) const {
  static_assert(weight, "\'la_w\' is not available");
  for (C c;; w-= c) {
   int u= PP[v];
   c= DW[v] - DW[u] + W[u];
   if (w < c) {
    int ok= L[v], ng= L[u] - 1;
    while (ok - ng > 1) {
     if (int m= (ok + ng) / 2; DW[v] - DW[I[m]] <= w) ok= m;
     else ng= m;
    }
    return I[ok];
   }
   if (v= P[u]; v == -1) return u;
  }
 }
 int jump(int u, int v, int k) const {
  if (!k) return u;
  if (u == v) return -1;
  if (k == 1) return in_subtree(v, u) ? la(v, D[v] - D[u] - 1) : P[u];
  int w= lca(u, v), d_uw= D[u] - D[w], d_vw= D[v] - D[w];
  return k > d_uw + d_vw ? -1 : k <= d_uw ? la(u, k) : la(v, d_uw + d_vw - k);
 }
 int jump_w(int u, int v, C w) const {
  static_assert(weight, "\'jump_w\' is not available");
  if (u == v) return u;
  int z= lca(u, v);
  C d_uz= DW[u] - DW[z], d_vz= DW[v] - DW[z];
  return w >= d_uz + d_vz ? v : w <= d_uz ? la_w(u, w) : la_w(v, d_uz + d_vz - w);
 }
 int dist(int u, int v) const { return D[u] + D[v] - D[lca(u, v)] * 2; }
 C dist_w(int u, int v) const {
  static_assert(weight, "\'dist_w\' is not available");
  return DW[u] + DW[v] - DW[lca(u, v)] * 2;
 }
 // u is in v
 bool in_subtree(int u, int v) const { return L[v] <= L[u] && L[u] < R[v]; }
 int subtree_size(int v) const { return R[v] - L[v]; }
 // half-open interval
 std::array<int, 2> subtree(int v) const { return std::array{L[v], R[v]}; }
 // sequence of closed intervals
 template <bool edge= 0> std::vector<std::array<int, 2>> path(int u, int v) const {
  std::vector<std::array<int, 2>> up, down;
  while (PP[u] != PP[v]) {
   if (L[u] < L[v]) down.emplace_back(std::array{L[PP[v]], L[v]}), v= P[PP[v]];
   else up.emplace_back(std::array{L[u], L[PP[u]]}), u= P[PP[u]];
  }
  if (L[u] < L[v]) down.emplace_back(std::array{L[u] + edge, L[v]});
  else if (L[v] + edge <= L[u]) up.emplace_back(std::array{L[u], L[v] + edge});
  return up.insert(up.end(), down.rbegin(), down.rend()), up;
 }
};
template <class T> static constexpr bool tuple_like_v= false;
template <class... Args> static constexpr bool tuple_like_v<std::tuple<Args...>> = true;
template <class T, class U> static constexpr bool tuple_like_v<std::pair<T, U>> = true;
template <class T, size_t K> static constexpr bool tuple_like_v<std::array<T, K>> = true;
template <class T> auto to_tuple(const T &t) {
 if constexpr (tuple_like_v<T>) return std::apply([](auto &&...x) { return std::make_tuple(x...); }, t);
}
template <class T> auto forward_tuple(const T &t) {
 if constexpr (tuple_like_v<T>) return std::apply([](auto &&...x) { return std::forward_as_tuple(x...); }, t);
}
template <class T> static constexpr bool array_like_v= false;
template <class T, size_t K> static constexpr bool array_like_v<std::array<T, K>> = true;
template <class T, class U> static constexpr bool array_like_v<std::pair<T, U>> = std::is_convertible_v<T, U>;
template <class T> static constexpr bool array_like_v<std::tuple<T>> = true;
template <class T, class U, class... Args> static constexpr bool array_like_v<std::tuple<T, U, Args...>> = array_like_v<std::tuple<T, Args...>> && std::is_convertible_v<U, T>;
template <class T> auto to_array(const T &t) {
 if constexpr (array_like_v<T>) return std::apply([](auto &&...x) { return std::array{x...}; }, t);
}
template <class T> using to_tuple_t= decltype(to_tuple(T()));
template <class T> using to_array_t= decltype(to_array(T()));
template <class pos_t, class M> class SegmentTree_2D {
public:
 using T= typename M::T;
 using Pos= std::array<pos_t, 2>;
 std::vector<pos_t> xs;
 std::vector<Pos> yxs;
 std::vector<int> id, tol;
 std::vector<T> val;
 template <class P> using canbe_Pos= std::is_convertible<to_tuple_t<P>, std::tuple<pos_t, pos_t>>;
 template <class P> using canbe_PosV= std::is_convertible<to_tuple_t<P>, std::tuple<pos_t, pos_t, T>>;
 template <class P, class U> static constexpr bool canbe_Pos_and_T_v= std::conjunction_v<canbe_Pos<P>, std::is_convertible<U, T>>;
 int sz;
 inline int x2i(pos_t x) const { return std::lower_bound(xs.begin(), xs.end(), x) - xs.begin(); }
 inline int y2i(pos_t y) const {
  return std::lower_bound(yxs.begin(), yxs.end(), Pos{y, 0}, [](const Pos &a, const Pos &b) { return a[0] < b[0]; }) - yxs.begin();
 }
 inline int xy2i(pos_t x, pos_t y) const {
  Pos p{y, x};
  auto it= std::lower_bound(yxs.begin(), yxs.end(), p);
  return assert(p == *it), it - yxs.begin();
 }
 template <bool z, size_t k, class P> inline auto get_(const P &p) {
  if constexpr (z) return std::get<k>(p);
  else return std::get<k>(p.first);
 }
 template <bool z, class XYW> inline void build(const XYW *xyw, int n, const T &v= M::ti()) {
  xs.resize(n), yxs.resize(n);
  for (int i= n; i--;) xs[i]= get_<z, 0>(xyw[i]);
  std::sort(xs.begin(), xs.end()), xs.erase(std::unique(xs.begin(), xs.end()), xs.end()), id.resize((sz= 1 << (32 - __builtin_clz(xs.size()))) * 2 + 1);
  std::vector<int> ix(n), ord(n);
  for (int i= n; i--;) ix[i]= x2i(get_<z, 0>(xyw[i]));
  for (int i: ix)
   for (i+= sz; i; i>>= 1) ++id[i + 1];
  for (int i= 1, e= sz * 2; i < e; ++i) id[i + 1]+= id[i];
  val.assign(id.back() * 2, M::ti()), tol.resize(id[sz] + 1), std::iota(ord.begin(), ord.end(), 0), std::sort(ord.begin(), ord.end(), [&](int i, int j) { return get_<z, 1>(xyw[i]) == get_<z, 1>(xyw[j]) ? get_<z, 0>(xyw[i]) < get_<z, 0>(xyw[j]) : get_<z, 1>(xyw[i]) < get_<z, 1>(xyw[j]); });
  for (int i= n; i--;) yxs[i]= {get_<z, 1>(xyw[ord[i]]), get_<z, 0>(xyw[ord[i]])};
  std::vector<int> ptr= id;
  for (int r: ord)
   for (int i= ix[r] + sz, j= -1; i; j= i, i>>= 1) {
    int p= ptr[i]++;
    if constexpr (z) {
     if constexpr (std::tuple_size_v<XYW> == 3) val[id[i + 1] + p]= std::get<2>(xyw[r]);
     else val[id[i + 1] + p]= v;
    } else val[id[i + 1] + p]= xyw[r].second;
    if (j != -1) tol[p + 1]= !(j & 1);
   }
  for (int i= 1, e= id[sz]; i < e; ++i) tol[i + 1]+= tol[i];
  for (int i= 0, e= sz * 2; i < e; ++i) {
   auto dat= val.begin() + id[i] * 2;
   for (int j= id[i + 1] - id[i]; --j > 0;) dat[j]= M::op(dat[j * 2], dat[j * 2 + 1]);
  }
 }
 inline T fold(int i, int a, int b) const {
  int n= id[i + 1] - id[i];
  T ret= M::ti();
  auto dat= val.begin() + id[i] * 2;
  for (a+= n, b+= n; a < b; a>>= 1, b>>= 1) {
   if (a & 1) ret= M::op(ret, dat[a++]);
   if (b & 1) ret= M::op(dat[--b], ret);
  }
  return ret;
 }
 template <bool z> inline void seti(int i, int j, T v) {
  auto dat= val.begin() + id[i] * 2;
  j+= id[i + 1] - id[i];
  if constexpr (z) dat[j]= v;
  else dat[j]= M::op(dat[j], v);
  for (; j;) j>>= 1, dat[j]= M::op(dat[2 * j], dat[2 * j + 1]);
 }
 template <bool z> inline void set_(pos_t x, pos_t y, T v) {
  for (int i= 1, p= xy2i(x, y);;) {
   if (seti<z>(i, p - id[i], v); i >= sz) break;
   if (int lc= tol[p] - tol[id[i]], rc= (p - id[i]) - lc; tol[p + 1] - tol[p]) p= id[2 * i] + lc, i= 2 * i;
   else p= id[2 * i + 1] + rc, i= 2 * i + 1;
  }
 }
public:
 template <class P, typename= std::enable_if_t<std::disjunction_v<canbe_Pos<P>, canbe_PosV<P>>>> SegmentTree_2D(const P *p, size_t n) { build<1>(p, n); }
 template <class P, typename= std::enable_if_t<std::disjunction_v<canbe_Pos<P>, canbe_PosV<P>>>> SegmentTree_2D(const std::vector<P> &p): SegmentTree_2D(p.data(), p.size()) {}
 template <class P, typename= std::enable_if_t<canbe_Pos<P>::value>> SegmentTree_2D(const std::set<P> &p): SegmentTree_2D(std::vector(p.begin(), p.end())) {}
 template <class P, class U, typename= std::enable_if_t<canbe_Pos_and_T_v<P, U>>> SegmentTree_2D(const P *p, size_t n, const U &v) { build<1>(p, n, v); }
 template <class P, class U, typename= std::enable_if_t<canbe_Pos_and_T_v<P, U>>> SegmentTree_2D(const std::vector<P> &p, const U &v): SegmentTree_2D(p.data(), p.size(), v) {}
 template <class P, class U, typename= std::enable_if_t<canbe_Pos_and_T_v<P, U>>> SegmentTree_2D(const std::set<P> &p, const U &v): SegmentTree_2D(std::vector(p.begin(), p.end()), v) {}
 template <class P, class U, typename= std::enable_if_t<canbe_Pos_and_T_v<P, U>>> SegmentTree_2D(const std::pair<P, U> *p, size_t n) { build<0>(p, n); }
 template <class P, class U, typename= std::enable_if_t<canbe_Pos_and_T_v<P, U>>> SegmentTree_2D(const std::vector<std::pair<P, U>> &p): SegmentTree_2D(p.data(), p.size()) {}
 template <class P, class U, typename= std::enable_if_t<canbe_Pos_and_T_v<P, U>>> SegmentTree_2D(const std::map<P, U> &p): SegmentTree_2D(std::vector(p.begin(), p.end())) {}
 // [l,r) x [u,d)
 T fold(pos_t l, pos_t r, pos_t u, pos_t d) const {
  T ret= M::ti();
  int L= x2i(l), R= x2i(r);
  auto dfs= [&](auto &dfs, int i, int a, int b, int c, int d) -> void {
   if (c == d || R <= a || b <= L) return;
   if (L <= a && b <= R) return ret= M::op(ret, fold(i, c, d)), void();
   int m= (a + b) / 2, ac= tol[id[i] + c] - tol[id[i]], bc= c - ac, ad= tol[id[i] + d] - tol[id[i]], bd= d - ad;
   dfs(dfs, i * 2, a, m, ac, ad), dfs(dfs, i * 2 + 1, m, b, bc, bd);
  };
  return dfs(dfs, 1, 0, sz, y2i(u), y2i(d)), ret;
 }
 void set(pos_t x, pos_t y, T v) { set_<1>(x, y, v); }
 void mul(pos_t x, pos_t y, T v) { set_<0>(x, y, v); }
 T get(pos_t x, pos_t y) const { return val[xy2i(x, y) + id[2]]; }
};
using namespace std;
struct RMQ {
 using T= int;
 static T ti() { return 0x7fffffff; }
 static T op(T a, T b) { return min(a, b); }
};
signed main() {
 cin.tie(0);
 ios::sync_with_stdio(0);
 using Mint= ModInt<1000000007>;
 int N, M;
 cin >> N >> M;
 vector<pair<int, int>> es;
 vector<char> used(M);
 UnionFind uf(N);
 Mint w= 1;
 Tree<Mint, true> tree(N);
 for (int i= 0; i < M; ++i) {
  int A, B;
  cin >> A >> B, --A, --B;
  es.emplace_back(A, B);
  w+= w;
  if (uf.unite(A, B)) {
   used[i]= true;
   tree.add_edge(A, B, w);
  }
 }
 tree.build();
 vector<array<int, 3>> xyw;
 for (int i= 0; i < M; ++i) {
  if (used[i]) continue;
  auto [A, B]= es[i];
  int a= tree.to_seq(A), b= tree.to_seq(B);
  if (a > b) swap(a, b);
  xyw.push_back({a, b, i});
 }
 SegmentTree_2D<int, RMQ> seg(xyw);
 int Q;
 cin >> Q;
 while (Q--) {
  int u, v, e;
  cin >> u >> v >> e, --u, --v, --e;
  auto [x, y]= es[e];
  if (tree.parent(y) == x) swap(x, y);
  bool u_in= tree.in_subtree(u, x);
  if (!used[e] || u_in == tree.in_subtree(v, x)) {
   cout << tree.dist_w(u, v) << '\n';
   continue;
  }
  auto [l, r]= tree.subtree(x);
  int i= min(seg.fold(0, l, l, r), seg.fold(l, r, r, N));
  if (i > M) {
   cout << -1 << '\n';
   continue;
  }
  auto [p, q]= es[i];
  if (!u_in) swap(u, v);
  if (tree.in_subtree(q, x)) swap(p, q);
  cout << tree.dist_w(u, p) + tree.dist_w(v, q) + Mint(2).pow(i + 1) << '\n';
 }
 return 0;
}