#line 1 "library/my_template.hpp"
#if defined(LOCAL)
#include <my_template_compiled.hpp>
#else
#pragma GCC optimize("Ofast")
#pragma GCC optimize("unroll-loops")

#include <bits/stdc++.h>

using namespace std;

using ll = long long;
using pi = pair<ll, ll>;
using vi = vector<ll>;
using u32 = unsigned int;
using u64 = unsigned long long;
using i128 = __int128;

template <class T>
using vc = vector<T>;
template <class T>
using vvc = vector<vc<T>>;
template <class T>
using vvvc = vector<vvc<T>>;
template <class T>
using vvvvc = vector<vvvc<T>>;
template <class T>
using vvvvvc = vector<vvvvc<T>>;
template <class T>
using pq = priority_queue<T>;
template <class T>
using pqg = priority_queue<T, vector<T>, greater<T>>;

#define vv(type, name, h, ...) \
  vector<vector<type>> name(h, vector<type>(__VA_ARGS__))
#define vvv(type, name, h, w, ...)   \
  vector<vector<vector<type>>> name( \
      h, vector<vector<type>>(w, vector<type>(__VA_ARGS__)))
#define vvvv(type, name, a, b, c, ...)       \
  vector<vector<vector<vector<type>>>> name( \
      a, vector<vector<vector<type>>>(       \
             b, vector<vector<type>>(c, vector<type>(__VA_ARGS__))))

// https://trap.jp/post/1224/
#define FOR1(a) for (ll _ = 0; _ < ll(a); ++_)
#define FOR2(i, a) for (ll i = 0; i < ll(a); ++i)
#define FOR3(i, a, b) for (ll i = a; i < ll(b); ++i)
#define FOR4(i, a, b, c) for (ll i = a; i < ll(b); i += (c))
#define FOR1_R(a) for (ll i = (a)-1; i >= ll(0); --i)
#define FOR2_R(i, a) for (ll i = (a)-1; i >= ll(0); --i)
#define FOR3_R(i, a, b) for (ll i = (b)-1; i >= ll(a); --i)
#define overload4(a, b, c, d, e, ...) e
#define overload3(a, b, c, d, ...) d
#define FOR(...) overload4(__VA_ARGS__, FOR4, FOR3, FOR2, FOR1)(__VA_ARGS__)
#define FOR_R(...) overload3(__VA_ARGS__, FOR3_R, FOR2_R, FOR1_R)(__VA_ARGS__)

#define FOR_subset(t, s) \
  for (ll t = (s); t >= 0; t = (t == 0 ? -1 : (t - 1) & (s)))
#define all(x) x.begin(), x.end()
#define len(x) ll(x.size())
#define elif else if

#define eb emplace_back
#define mp make_pair
#define mt make_tuple
#define fi first
#define se second

#define stoi stoll

int popcnt(int x) { return __builtin_popcount(x); }
int popcnt(u32 x) { return __builtin_popcount(x); }
int popcnt(ll x) { return __builtin_popcountll(x); }
int popcnt(u64 x) { return __builtin_popcountll(x); }
// (0, 1, 2, 3, 4) -> (-1, 0, 1, 1, 2)
int topbit(int x) { return (x == 0 ? -1 : 31 - __builtin_clz(x)); }
int topbit(u32 x) { return (x == 0 ? -1 : 31 - __builtin_clz(x)); }
int topbit(ll x) { return (x == 0 ? -1 : 63 - __builtin_clzll(x)); }
int topbit(u64 x) { return (x == 0 ? -1 : 63 - __builtin_clzll(x)); }
// (0, 1, 2, 3, 4) -> (-1, 0, 1, 0, 2)
int lowbit(int x) { return (x == 0 ? -1 : __builtin_ctz(x)); }
int lowbit(u32 x) { return (x == 0 ? -1 : __builtin_ctz(x)); }
int lowbit(ll x) { return (x == 0 ? -1 : __builtin_ctzll(x)); }
int lowbit(u64 x) { return (x == 0 ? -1 : __builtin_ctzll(x)); }

template <typename T, typename U>
T ceil(T x, U y) {
  return (x > 0 ? (x + y - 1) / y : x / y);
}
template <typename T, typename U>
T floor(T x, U y) {
  return (x > 0 ? x / y : (x - y + 1) / y);
}
template <typename T, typename U>
pair<T, T> divmod(T x, U y) {
  T q = floor(x, y);
  return {q, x - q * y};
}

template <typename T, typename U>
T SUM(const vector<U> &A) {
  T sum = 0;
  for (auto &&a: A) sum += a;
  return sum;
}

#define MIN(v) *min_element(all(v))
#define MAX(v) *max_element(all(v))
#define LB(c, x) distance((c).begin(), lower_bound(all(c), (x)))
#define UB(c, x) distance((c).begin(), upper_bound(all(c), (x)))
#define UNIQUE(x) \
  sort(all(x)), x.erase(unique(all(x)), x.end()), x.shrink_to_fit()

template <typename T>
T POP(deque<T> &que) {
  T a = que.front();
  que.pop_front();
  return a;
}
template <typename T>
T POP(pq<T> &que) {
  T a = que.top();
  que.pop();
  return a;
}
template <typename T>
T POP(pqg<T> &que) {
  assert(!que.empty());
  T a = que.top();
  que.pop();
  return a;
}
template <typename T>
T POP(vc<T> &que) {
  assert(!que.empty());
  T a = que.back();
  que.pop_back();
  return a;
}

template <typename F>
ll binary_search(F check, ll ok, ll ng) {
  assert(check(ok));
  while (abs(ok - ng) > 1) {
    auto x = (ng + ok) / 2;
    tie(ok, ng) = (check(x) ? mp(x, ng) : mp(ok, x));
  }
  return ok;
}
template <typename F>
double binary_search_real(F check, double ok, double ng, int iter = 100) {
  FOR(iter) {
    double x = (ok + ng) / 2;
    tie(ok, ng) = (check(x) ? mp(x, ng) : mp(ok, x));
  }
  return (ok + ng) / 2;
}

template <class T, class S>
inline bool chmax(T &a, const S &b) {
  return (a < b ? a = b, 1 : 0);
}
template <class T, class S>
inline bool chmin(T &a, const S &b) {
  return (a > b ? a = b, 1 : 0);
}

// ? は -1
vc<int> s_to_vi(const string &S, char first_char) {
  vc<int> A(S.size());
  FOR(i, S.size()) { A[i] = (S[i] != '?' ? S[i] - first_char : -1); }
  return A;
}

template <typename T, typename U>
vector<T> cumsum(vector<U> &A, int off = 1) {
  int N = A.size();
  vector<T> B(N + 1);
  FOR(i, N) { B[i + 1] = B[i] + A[i]; }
  if (off == 0) B.erase(B.begin());
  return B;
}

// stable sort
template <typename T>
vector<int> argsort(const vector<T> &A) {
  vector<int> ids(len(A));
  iota(all(ids), 0);
  sort(all(ids),
       [&](int i, int j) { return (A[i] == A[j] ? i < j : A[i] < A[j]); });
  return ids;
}

// A[I[0]], A[I[1]], ...
template <typename T>
vc<T> rearrange(const vc<T> &A, const vc<int> &I) {
  vc<T> B(len(I));
  FOR(i, len(I)) B[i] = A[I[i]];
  return B;
}
#endif
#line 1 "library/other/io.hpp"
// based on yosupo's fastio
#include <unistd.h>

namespace fastio {
#define FASTIO
// クラスが read(), print() を持っているかを判定するメタ関数
struct has_write_impl {
  template <class T>
  static auto check(T &&x) -> decltype(x.write(), std::true_type{});

  template <class T>
  static auto check(...) -> std::false_type;
};

template <class T>
class has_write : public decltype(has_write_impl::check<T>(std::declval<T>())) {
};

struct has_read_impl {
  template <class T>
  static auto check(T &&x) -> decltype(x.read(), std::true_type{});

  template <class T>
  static auto check(...) -> std::false_type;
};

template <class T>
class has_read : public decltype(has_read_impl::check<T>(std::declval<T>())) {};

struct Scanner {
  FILE *fp;
  char line[(1 << 15) + 1];
  size_t st = 0, ed = 0;
  void reread() {
    memmove(line, line + st, ed - st);
    ed -= st;
    st = 0;
    ed += fread(line + ed, 1, (1 << 15) - ed, fp);
    line[ed] = '\0';
  }
  bool succ() {
    while (true) {
      if (st == ed) {
        reread();
        if (st == ed) return false;
      }
      while (st != ed && isspace(line[st])) st++;
      if (st != ed) break;
    }
    if (ed - st <= 50) {
      bool sep = false;
      for (size_t i = st; i < ed; i++) {
        if (isspace(line[i])) {
          sep = true;
          break;
        }
      }
      if (!sep) reread();
    }
    return true;
  }
  template <class T, enable_if_t<is_same<T, string>::value, int> = 0>
  bool read_single(T &ref) {
    if (!succ()) return false;
    while (true) {
      size_t sz = 0;
      while (st + sz < ed && !isspace(line[st + sz])) sz++;
      ref.append(line + st, sz);
      st += sz;
      if (!sz || st != ed) break;
      reread();
    }
    return true;
  }
  template <class T, enable_if_t<is_integral<T>::value, int> = 0>
  bool read_single(T &ref) {
    if (!succ()) return false;
    bool neg = false;
    if (line[st] == '-') {
      neg = true;
      st++;
    }
    ref = T(0);
    while (isdigit(line[st])) { ref = 10 * ref + (line[st++] & 0xf); }
    if (neg) ref = -ref;
    return true;
  }
  template <typename T,
            typename enable_if<has_read<T>::value>::type * = nullptr>
  inline bool read_single(T &x) {
    x.read();
    return true;
  }
  bool read_single(double &ref) {
    string s;
    if (!read_single(s)) return false;
    ref = std::stod(s);
    return true;
  }
  bool read_single(char &ref) {
    string s;
    if (!read_single(s) || s.size() != 1) return false;
    ref = s[0];
    return true;
  }
  template <class T>
  bool read_single(vector<T> &ref) {
    for (auto &d: ref) {
      if (!read_single(d)) return false;
    }
    return true;
  }
  template <class T, class U>
  bool read_single(pair<T, U> &p) {
    return (read_single(p.first) && read_single(p.second));
  }
  template <size_t N = 0, typename T>
  void read_single_tuple(T &t) {
    if constexpr (N < std::tuple_size<T>::value) {
      auto &x = std::get<N>(t);
      read_single(x);
      read_single_tuple<N + 1>(t);
    }
  }
  template <class... T>
  bool read_single(tuple<T...> &tpl) {
    read_single_tuple(tpl);
    return true;
  }
  void read() {}
  template <class H, class... T>
  void read(H &h, T &... t) {
    bool f = read_single(h);
    assert(f);
    read(t...);
  }
  Scanner(FILE *fp) : fp(fp) {}
};

struct Printer {
  Printer(FILE *_fp) : fp(_fp) {}
  ~Printer() { flush(); }

  static constexpr size_t SIZE = 1 << 15;
  FILE *fp;
  char line[SIZE], small[50];
  size_t pos = 0;
  void flush() {
    fwrite(line, 1, pos, fp);
    pos = 0;
  }
  void write(const char val) {
    if (pos == SIZE) flush();
    line[pos++] = val;
  }
  template <class T, enable_if_t<is_integral<T>::value, int> = 0>
  void write(T val) {
    if (pos > (1 << 15) - 50) flush();
    if (val == 0) {
      write('0');
      return;
    }
    if (val < 0) {
      write('-');
      val = -val; // todo min
    }
    size_t len = 0;
    while (val) {
      small[len++] = char(0x30 | (val % 10));
      val /= 10;
    }
    for (size_t i = 0; i < len; i++) { line[pos + i] = small[len - 1 - i]; }
    pos += len;
  }
  void write(const string s) {
    for (char c: s) write(c);
  }
  void write(const char *s) {
    size_t len = strlen(s);
    for (size_t i = 0; i < len; i++) write(s[i]);
  }
  void write(const double x) {
    ostringstream oss;
    oss << fixed << setprecision(15) << x;
    string s = oss.str();
    write(s);
  }
  void write(const long double x) {
    ostringstream oss;
    oss << fixed << setprecision(15) << x;
    string s = oss.str();
    write(s);
  }
  template <typename T,
            typename enable_if<has_write<T>::value>::type * = nullptr>
  inline void write(T x) {
    x.write();
  }
  template <class T>
  void write(const vector<T> val) {
    auto n = val.size();
    for (size_t i = 0; i < n; i++) {
      if (i) write(' ');
      write(val[i]);
    }
  }
  template <class T, class U>
  void write(const pair<T, U> val) {
    write(val.first);
    write(' ');
    write(val.second);
  }
  template <size_t N = 0, typename T>
  void write_tuple(const T t) {
    if constexpr (N < std::tuple_size<T>::value) {
      if constexpr (N > 0) { write(' '); }
      const auto x = std::get<N>(t);
      write(x);
      write_tuple<N + 1>(t);
    }
  }
  template <class... T>
  bool write(tuple<T...> tpl) {
    write_tuple(tpl);
    return true;
  }
  template <class T, size_t S>
  void write(const array<T, S> val) {
    auto n = val.size();
    for (size_t i = 0; i < n; i++) {
      if (i) write(' ');
      write(val[i]);
    }
  }
  void write(i128 val) {
    string s;
    bool negative = 0;
    if (val < 0) {
      negative = 1;
      val = -val;
    }
    while (val) {
      s += '0' + int(val % 10);
      val /= 10;
    }
    if (negative) s += "-";
    reverse(all(s));
    if (len(s) == 0) s = "0";
    write(s);
  }
};
Scanner scanner = Scanner(stdin);
Printer printer = Printer(stdout);
void flush() { printer.flush(); }
void print() { printer.write('\n'); }
template <class Head, class... Tail>
void print(Head &&head, Tail &&... tail) {
  printer.write(head);
  if (sizeof...(Tail)) printer.write(' ');
  print(forward<Tail>(tail)...);
}

void read() {}
template <class Head, class... Tail>
void read(Head &head, Tail &... tail) {
  scanner.read(head);
  read(tail...);
}
} // namespace fastio
using fastio::print;
using fastio::flush;
using fastio::read;

#define INT(...)   \
  int __VA_ARGS__; \
  read(__VA_ARGS__)
#define LL(...)   \
  ll __VA_ARGS__; \
  read(__VA_ARGS__)
#define STR(...)      \
  string __VA_ARGS__; \
  read(__VA_ARGS__)
#define CHAR(...)   \
  char __VA_ARGS__; \
  read(__VA_ARGS__)
#define DBL(...)      \
  double __VA_ARGS__; \
  read(__VA_ARGS__)

#define VEC(type, name, size) \
  vector<type> name(size);    \
  read(name)
#define VV(type, name, h, w)                     \
  vector<vector<type>> name(h, vector<type>(w)); \
  read(name)

void YES(bool t = 1) { print(t ? "YES" : "NO"); }
void NO(bool t = 1) { YES(!t); }
void Yes(bool t = 1) { print(t ? "Yes" : "No"); }
void No(bool t = 1) { Yes(!t); }
void yes(bool t = 1) { print(t ? "yes" : "no"); }
void no(bool t = 1) { yes(!t); }
#line 2 "library/graph/base.hpp"

template <typename T>
struct Edge {
  int frm, to;
  T cost;
  int id;
};

template <typename T = int, bool directed = false>
struct Graph {
  int N, M;
  using cost_type = T;
  using edge_type = Edge<T>;
  vector<edge_type> edges;
  vector<int> indptr;
  vector<edge_type> csr_edges;
  vc<int> vc_deg, vc_indeg, vc_outdeg;
  bool prepared;

  class OutgoingEdges {
  public:
    OutgoingEdges(const Graph* G, int l, int r) : G(G), l(l), r(r) {}

    const edge_type* begin() const {
      if (l == r) { return 0; }
      return &G->csr_edges[l];
    }

    const edge_type* end() const {
      if (l == r) { return 0; }
      return &G->csr_edges[r];
    }

  private:
    const Graph* G;
    int l, r;
  };

  bool is_prepared() { return prepared; }
  constexpr bool is_directed() { return directed; }

  Graph() : N(0), M(0), prepared(0) {}
  Graph(int N) : N(N), M(0), prepared(0) {}

  void resize(int n) { N = n; }

  void add(int frm, int to, T cost = 1, int i = -1) {
    assert(!prepared);
    assert(0 <= frm && 0 <= to && to < N);
    if (i == -1) i = M;
    auto e = edge_type({frm, to, cost, i});
    edges.eb(e);
    ++M;
  }

  // wt, off
  void read_tree(bool wt = false, int off = 1) { read_graph(N - 1, wt, off); }

  void read_graph(int M, bool wt = false, int off = 1) {
    for (int m = 0; m < M; ++m) {
      INT(a, b);
      a -= off, b -= off;
      if (!wt) {
        add(a, b);
      } else {
        T c;
        read(c);
        add(a, b, c);
      }
    }
    build();
  }

  void read_parent(int off = 1) {
    for (int v = 1; v < N; ++v) {
      INT(p);
      p -= off;
      add(p, v);
    }
    build();
  }

  void build() {
    assert(!prepared);
    prepared = true;
    indptr.assign(N + 1, 0);
    for (auto&& e: edges) {
      indptr[e.frm + 1]++;
      if (!directed) indptr[e.to + 1]++;
    }
    for (int v = 0; v < N; ++v) { indptr[v + 1] += indptr[v]; }
    auto counter = indptr;
    csr_edges.resize(indptr.back() + 1);
    for (auto&& e: edges) {
      csr_edges[counter[e.frm]++] = e;
      if (!directed)
        csr_edges[counter[e.to]++] = edge_type({e.to, e.frm, e.cost, e.id});
    }
  }

  OutgoingEdges operator[](int v) const {
    assert(prepared);
    return {this, indptr[v], indptr[v + 1]};
  }

  vc<int> deg_array() {
    if (vc_deg.empty()) calc_deg();
    return vc_deg;
  }

  pair<vc<int>, vc<int>> deg_array_inout() {
    if (vc_indeg.empty()) calc_deg_inout();
    return {vc_indeg, vc_outdeg};
  }

  int deg(int v) {
    if (vc_deg.empty()) calc_deg();
    return vc_deg[v];
  }

  int in_deg(int v) {
    if (vc_indeg.empty()) calc_deg_inout();
    return vc_indeg[v];
  }

  int out_deg(int v) {
    if (vc_outdeg.empty()) calc_deg_inout();
    return vc_outdeg[v];
  }

  void debug() {
    print("Graph");
    if (!prepared) {
      print("frm to cost id");
      for (auto&& e: edges) print(e.frm, e.to, e.cost, e.id);
    } else {
      print("indptr", indptr);
      print("frm to cost id");
      FOR(v, N) for (auto&& e: (*this)[v]) print(e.frm, e.to, e.cost, e.id);
    }
  }

private:
  void calc_deg() {
    assert(vc_deg.empty());
    vc_deg.resize(N);
    for (auto&& e: edges) vc_deg[e.frm]++, vc_deg[e.to]++;
  }

  void calc_deg_inout() {
    assert(vc_indeg.empty());
    vc_indeg.resize(N);
    vc_outdeg.resize(N);
    for (auto&& e: edges) { vc_indeg[e.to]++, vc_outdeg[e.frm]++; }
  }
};
#line 3 "library/graph/tree.hpp"

// HLD euler tour をとっていろいろ。
// 木以外、非連結でも dfs 順序や親がとれる。
template <typename GT>
struct Tree {
  using Graph_type = GT;
  GT &G;
  using WT = typename GT::cost_type;
  int N;
  bool hld;
  vector<int> LID, RID, head, V, parent;
  vc<int> depth;
  vc<WT> depth_weighted;

  Tree(GT &G, int r = -1, bool hld = 1)
      : G(G),
        N(G.N),
        hld(hld),
        LID(G.N),
        RID(G.N),
        head(G.N, r),
        V(G.N),
        parent(G.N, -1),
        depth(G.N, -1),
        depth_weighted(G.N, 0) {
    assert(G.is_prepared());
    int t1 = 0;
    if (r != -1) {
      dfs_sz(r, -1);
      dfs_hld(r, t1);
    } else {
      for (int r = 0; r < N; ++r) {
        if (parent[r] == -1) {
          head[r] = r;
          dfs_sz(r, -1);
          dfs_hld(r, t1);
        }
      }
    }
  }

  void dfs_sz(int v, int p) {
    auto &sz = RID;
    parent[v] = p;
    depth[v] = (p == -1 ? 0 : depth[p] + 1);
    sz[v] = 1;
    int l = G.indptr[v], r = G.indptr[v + 1];
    auto &csr = G.csr_edges;
    // 使う辺があれば先頭にする
    for (int i = r - 2; i >= l; --i) {
      if (hld && depth[csr[i + 1].to] == -1) swap(csr[i], csr[i + 1]);
    }
    int hld_sz = 0;
    for (int i = l; i < r; ++i) {
      auto e = csr[i];
      if (depth[e.to] != -1) continue;
      depth_weighted[e.to] = depth_weighted[v] + e.cost;
      dfs_sz(e.to, v);
      sz[v] += sz[e.to];
      if (hld && chmax(hld_sz, sz[e.to]) && l < i) { swap(csr[l], csr[i]); }
    }
  }

  void dfs_hld(int v, int &times) {
    LID[v] = times++;
    RID[v] += LID[v];
    V[LID[v]] = v;
    bool heavy = true;
    for (auto &&e: G[v]) {
      if (depth[e.to] <= depth[v]) continue;
      head[e.to] = (heavy ? head[v] : e.to);
      heavy = false;
      dfs_hld(e.to, times);
    }
  }

  vc<int> heavy_path_at(int v) {
    vc<int> P = {v};
    while (1) {
      int a = P.back();
      for (auto &&e: G[a]) {
        if (e.to != parent[a] && head[e.to] == v) {
          P.eb(e.to);
          break;
        }
      }
      if (P.back() == a) break;
    }
    return P;
  }

  int e_to_v(int eid) {
    auto e = G.edges[eid];
    return (parent[e.frm] == e.to ? e.frm : e.to);
  }

  int ELID(int v) { return 2 * LID[v] - depth[v]; }
  int ERID(int v) { return 2 * RID[v] - depth[v] - 1; }

  /* k: 0-indexed */
  int LA(int v, int k) {
    assert(k <= depth[v]);
    while (1) {
      int u = head[v];
      if (LID[v] - k >= LID[u]) return V[LID[v] - k];
      k -= LID[v] - LID[u] + 1;
      v = parent[u];
    }
  }

  int LCA(int u, int v) {
    for (;; v = parent[head[v]]) {
      if (LID[u] > LID[v]) swap(u, v);
      if (head[u] == head[v]) return u;
    }
  }

  int lca(int u, int v) { return LCA(u, v); }
  int la(int u, int v) { return LA(u, v); }

  int subtree_size(int v) { return RID[v] - LID[v]; }

  int dist(int a, int b) {
    int c = LCA(a, b);
    return depth[a] + depth[b] - 2 * depth[c];
  }

  WT dist(int a, int b, bool weighted) {
    assert(weighted);
    int c = LCA(a, b);
    return depth_weighted[a] + depth_weighted[b] - WT(2) * depth_weighted[c];
  }

  // a is in b
  bool in_subtree(int a, int b) { return LID[b] <= LID[a] && LID[a] < RID[b]; }

  int jump(int a, int b, ll k) {
    if (k == 1) {
      if (a == b) return -1;
      return (in_subtree(b, a) ? LA(b, depth[b] - depth[a] - 1) : parent[a]);
    }
    int c = LCA(a, b);
    int d_ac = depth[a] - depth[c];
    int d_bc = depth[b] - depth[c];
    if (k > d_ac + d_bc) return -1;
    if (k <= d_ac) return LA(a, k);
    return LA(b, d_ac + d_bc - k);
  }

  vc<int> collect_child(int v) {
    vc<int> res;
    for (auto &&e: G[v])
      if (e.to != parent[v]) res.eb(e.to);
    return res;
  }

  vc<pair<int, int>> get_path_decomposition(int u, int v, bool edge) {
    // [始点, 終点] の"閉"区間列。
    vc<pair<int, int>> up, down;
    while (1) {
      if (head[u] == head[v]) break;
      if (LID[u] < LID[v]) {
        down.eb(LID[head[v]], LID[v]);
        v = parent[head[v]];
      } else {
        up.eb(LID[u], LID[head[u]]);
        u = parent[head[u]];
      }
    }
    if (LID[u] < LID[v]) down.eb(LID[u] + edge, LID[v]);
    elif (LID[v] + edge <= LID[u]) up.eb(LID[u], LID[v] + edge);
    reverse(all(down));
    up.insert(up.end(), all(down));
    return up;
  }

  vc<int> restore_path(int u, int v) {
    vc<int> P;
    for (auto &&[a, b]: get_path_decomposition(u, v, 0)) {
      if (a <= b) {
        FOR(i, a, b + 1) P.eb(V[i]);
      } else {
        FOR_R(i, b, a + 1) P.eb(V[i]);
      }
    }
    return P;
  }
};
#line 2 "library/graph/centroid.hpp"

template <typename GT>
vc<int> find_centroids(GT& G) {
  int N = G.N;
  vc<int> par(N, -1);
  vc<int> V(N);
  vc<int> sz(N);
  int l = 0, r = 0;
  V[r++] = 0;
  while (l < r) {
    int v = V[l++];
    for (auto&& e: G[v])
      if (e.to != par[v]) {
        par[e.to] = v;
        V[r++] = e.to;
      }
  }
  FOR_R(i, N) {
    int v = V[i];
    sz[v] += 1;
    int p = par[v];
    if (p != -1) sz[p] += sz[v];
  }

  int M = N / 2;
  auto check = [&](int v) -> bool {
    if (N - sz[v] > M) return false;
    for (auto&& e: G[v]) {
      if (e.to != par[v] && sz[e.to] > M) return false;
    }
    return true;
  };
  vc<int> ANS;
  FOR(v, N) if (check(v)) ANS.eb(v);
  return ANS;
}

template <typename GT>
struct Centroid_Decomposition {
  using edge_type = typename GT::edge_type;
  GT& G;
  int N;
  vc<int> sz;
  vc<int> par;
  vector<int> cdep; // depth in centroid tree
  bool calculated;

  Centroid_Decomposition(GT& G)
      : G(G), N(G.N), sz(G.N), par(G.N), cdep(G.N, -1) {
    calculated = 0;
    build();
  }

private:
  int find(int v) {
    vc<int> V = {v};
    par[v] = -1;
    int p = 0;
    while (p < len(V)) {
      int v = V[p++];
      sz[v] = 0;
      for (auto&& e: G[v]) {
        if (e.to == par[v] || cdep[e.to] != -1) continue;
        par[e.to] = v;
        V.eb(e.to);
      }
    }
    while (len(V)) {
      int v = V.back();
      V.pop_back();
      sz[v] += 1;
      if (p - sz[v] <= p / 2) return v;
      sz[par[v]] += sz[v];
    }
    return -1;
  }
  void build() {
    assert(G.is_prepared());
    assert(!G.is_directed());
    assert(!calculated);
    calculated = 1;

    vc<pair<int, int>> st;
    st.eb(0, 0);
    while (!st.empty()) {
      auto [lv, v] = st.back();
      st.pop_back();
      auto c = find(v);
      cdep[c] = lv;
      for (auto&& e: G[c]) {
        if (cdep[e.to] == -1) { st.eb(lv + 1, e.to); }
      }
    }
  }

public:
  /*
  root を重心とする木において、(v, path data v) の vector
  を、方向ごとに集めて返す ・0 番目：root からのパスすべて（root を含む）
  ・i番目：i 番目の方向
  f: E x edge -> E
  */
  template <typename E, typename F>
  vc<vc<pair<int, E>>> collect(int root, E root_val, F f) {
    vc<vc<pair<int, E>>> res = {{{root, root_val}}};
    for (auto&& e: G[root]) {
      int nxt = e.to;
      if (cdep[nxt] < cdep[root]) continue;
      vc<pair<int, E>> dat;
      int p = 0;
      dat.eb(nxt, f(root_val, e));
      par[nxt] = root;
      while (p < len(dat)) {
        auto [v, val] = dat[p++];
        for (auto&& e: G[v]) {
          if (e.to == par[v]) continue;
          if (cdep[e.to] < cdep[root]) continue;
          par[e.to] = v;
          dat.eb(e.to, f(val, e));
        }
      }
      res.eb(dat);
      res[0].insert(res[0].end(), all(dat));
    }
    return res;
  }

  vc<vc<pair<int, int>>> collect_dist(int root) {
    auto f = [&](int x, auto e) -> int { return x + 1; };
    return collect(root, 0, f);
  }

  // (V, H), V[i] は、H における頂点 i の G における番号
  // 頂点は EulerTour 順に並ぶ、V は sort されているとは限らない
  pair<vc<int>, Graph<typename GT::cost_type, true>> get_subgraph(int root) {
    static vc<int> conv;
    while (len(conv) < N) conv.eb(-1);

    vc<int> V;
    using cost_type = typename GT::cost_type;
    vc<tuple<int, int, cost_type>> edges;

    auto dfs = [&](auto& dfs, int v, int p) -> void {
      conv[v] = len(V);
      V.eb(v);
      for (auto&& e: G[v]) {
        int to = e.to;
        if (to == p) continue;
        if (cdep[to] < cdep[root]) continue;
        dfs(dfs, to, v);
        edges.eb(conv[v], conv[to], e.cost);
      }
    };
    dfs(dfs, root, -1);
    int n = len(V);
    Graph<typename GT::cost_type, true> H(n);
    for (auto&& [a, b, c]: edges) H.add(a, b, c);
    H.build();
    for (auto&& v: V) conv[v] = -1;
    return {V, H};
  }
};
#line 1 "library/graph/compress_tree.hpp"
// (圧縮された木の頂点ラベルたち、グラフ)
template <typename TREE>
pair<vc<int>, typename TREE::Graph_type> compress_tree(TREE& tree, vc<int> V) {
  // 大事な点をリストアップする
  // もともとの根は含まれるようにする
  sort(all(V), [&](auto& x, auto& y) { return tree.LID[x] < tree.LID[y]; });
  int n = len(V);
  FOR(i, n) {
    int j = (i + 1 == n ? 0 : i + 1);
    V.eb(tree.lca(V[i], V[j]));
  }
  V.eb(tree.V[0]);
  sort(all(V), [&](auto& x, auto& y) { return tree.LID[x] < tree.LID[y]; });
  V.erase(unique(all(V)), V.end());
  // 辺を張ってグラフを作る
  n = len(V);
  using GT = typename TREE::Graph_type;
  using WT = typename GT::cost_type;
  GT G(n);
  vc<int> st = {0};
  FOR(i, 1, n) {
    while (1) {
      int p = V[st.back()];
      int v = V[i];
      if (tree.in_subtree(v, p)) break;
      st.pop_back();
    }
    int p = V[st.back()];
    int v = V[i];
    WT d = tree.depth_weighted[v] - tree.depth_weighted[p];
    G.add(st.back(), i, d);
    st.eb(i);
  }
  G.build();
  return {V, G};
}
#line 6 "main.cpp"

void solve() {
  LL(N, Q);
  Graph<ll, 0> G1(N), G2(N);
  G1.read_tree(1);
  G2.read_tree(1);
  Tree<decltype(G2)> tree2(G2);

  vvc<pair<int, int>> query_at_A(N);
  FOR(q, Q) {
    LL(a, b);
    --a, --b;
    query_at_A[a].eb(q, b);
  }

  vi ANS(Q);
  Centroid_Decomposition<decltype(G1)> CD(G1);

  vc<bool> IN2(N);
  vc<int> new_idx_1(N, -1);
  vc<int> new_idx_2(N, -1);

  FOR(root, N) {
    auto [V1, H] = CD.get_subgraph(root);
    FOR(i, len(V1)) new_idx_1[V1[i]] = i;
    // (方向, 距離)
    vc<pair<int, ll>> dat(len(V1));
    auto dfs = [&](auto& dfs, int v, int p) -> void {
      for (auto&& e: H[v]) {
        dat[e.to].fi = dat[v].fi;
        dat[e.to].se = dat[v].se + e.cost;
        dfs(dfs, e.to, v);
      }
    };
    for (auto&& e: H[0]) {
      dat[e.to].fi = e.to;
      dat[e.to].se = e.cost;
      dfs(dfs, e.to, 0);
    }
    vc<int> V2;
    auto add_V2 = [&](int v) -> void {
      if (IN2[v]) return;
      IN2[v] = 1;
      V2.eb(v);
    };
    FOR(i, len(V1)) {
      auto a = V1[i];
      add_V2(a);
      for (auto&& [qid, b]: query_at_A[a]) { add_V2(b); }
    }
    // V2 で圧縮木を作る
    auto [V, G] = compress_tree<decltype(tree2)>(tree2, V2);
    FOR(i, len(V)) new_idx_2[V[i]] = i;

    // 全方位をやめる
    // 直径 bfs の変種で
    vc<int> que(G.N);
    auto bfs = [&](int s) -> vi {
      vi dist(G.N, -1);
      if (s == -1) return dist;
      int l = 0, r = 0;
      auto add = [&](int v, ll d) -> void { dist[v] = d, que[r++] = v; };
      add(s, 0);
      while (l < r) {
        int v = que[l++];
        for (auto&& e: G[v]) {
          if (dist[e.to] == -1) add(e.to, dist[v] + e.cost);
        }
      }
      return dist;
    };
    auto find_max2 = [&](vi& dist) -> pair<int, int> {
      if (dist[0] == -1) return {-1, -1};
      // 種類、点、距離
      using T = tuple<int, int, ll>;
      T x = {-1, -1, -1}, y = {-1, -1, -1};
      FOR(v, len(dist)) {
        int i = new_idx_1[V[v]];
        if (i == -1) continue;
        T p = {dat[i].fi, v, dist[v] + dat[i].se};
        if (get<2>(x) < get<2>(p)) {
          if (get<0>(x) == get<0>(p)) {
            x = p;
          } else {
            swap(x, y);
            x = p;
          }
        }
        elif (get<2>(y) < get<2>(p)) { y = p; }
      }
      return {get<1>(x), get<1>(y)};
    };

    // 適宜 unique してよい
    auto D0 = bfs(0);
    auto [A, B] = find_max2(D0);
    auto DA = bfs(A);
    auto DB = bfs(B);
    auto [C, D] = find_max2(DA);
    if (C == A || C == B) C = -1;
    if (D == A || D == B || D == C) D = -1;
    auto [E, F] = find_max2(DB);
    if (E == A || E == B || E == C || E == D) E = -1;
    if (F == A || F == B || F == C || F == D || F == E) F = -1;
    auto DC = bfs(C);
    auto DD = bfs(D);
    auto DE = bfs(E);
    auto DF = bfs(F);

    auto solve_query = [&](int qid, int b, int dir, ll dist) -> void {
      b = new_idx_2[b];
      auto upd = [&](int A, vi& DA) -> void {
        if (A == -1) return;
        auto [dir_A, dist_A] = dat[new_idx_1[V[A]]];
        if (dir != 0 && dir_A != 0 && dir == dir_A) return;
        chmax(ANS[qid], dist + DA[b] + dist_A);
      };
      upd(A, DA);
      upd(B, DB);
      upd(C, DC);
      upd(D, DD);
      upd(E, DE);
      upd(F, DF);
    };

    FOR(i, len(V1)) {
      auto a = V1[i];
      for (auto&& [qid, b]: query_at_A[a]) {
        solve_query(qid, b, dat[i].fi, dat[i].se);
      }
    }

    // reset
    for (auto&& v: V) {
      IN2[v] = 0;
      new_idx_1[v] = new_idx_2[v] = -1;
    }
  }
  for (auto&& x: ANS) print(x);
}

signed main() {
  solve();
  return 0;
}