#line 1 "main.cpp"
#define PROBLEM "https://yukicoder.me/problems/no/1197"

#line 1 "library/my_template.hpp"
#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 vec(type, name, ...) vector<type> name(__VA_ARGS__)
#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 FOR4_R(i, a, b, c) for (ll i = (b)-1; i >= ll(a); i -= (c))
#define overload4(a, b, c, d, e, ...) e
#define FOR(...) overload4(__VA_ARGS__, FOR4, FOR3, FOR2, FOR1)(__VA_ARGS__)
#define FOR_R(...) \
  overload4(__VA_ARGS__, FOR4_R, 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

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())

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>
T pick(deque<T> &que) {
  T a = que.front();
  que.pop_front();
  return a;
}

template <typename T>
T pick(pq<T> &que) {
  T a = que.top();
  que.pop();
  return a;
}

template <typename T>
T pick(pqg<T> &que) {
  assert(que.size());
  T a = que.top();
  que.pop();
  return a;
}

template <typename T>
T pick(vc<T> &que) {
  assert(que.size());
  T a = que.back();
  que.pop_back();
  return a;
}

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 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);
}

vc<int> s_to_vi(const string &S, char first_char) {
  vc<int> A(S.size());
  FOR(i, S.size()) { A[i] = S[i] - first_char; }
  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;
}

template <typename CNT, typename T>
vc<CNT> bincount(const vc<T> &A, int size) {
  vc<CNT> C(size);
  for (auto &&x: A) { ++C[x]; }
  return C;
}

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

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

namespace 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 5 "main.cpp"

#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 {
  GT &G;
  using WT = typename GT::cost_type;
  int N;
  bool hld;
  vector<int> LID, RID, head, V, parent, root;
  vc<int> depth;
  vc<WT> depth_weighted;
  vector<bool> in_tree;

  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),
        root(G.N, -1),
        depth(G.N, -1),
        depth_weighted(G.N, 0),
        in_tree(G.M, 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);
        }
      }
    }
    for (auto &&v: V) root[v] = (parent[v] == -1 ? v : root[parent[v]]);
  }

  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;
      in_tree[e.id] = 1;
      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 (!in_tree[e.id] || 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;
  }

  void debug() {
    print("V", V);
    print("LID", LID);
    print("RID", RID);
    print("parent", parent);
    print("depth", depth);
    print("head", head);
    print("in_tree(edge)", in_tree);
    print("root", root);
  }
};
#line 2 "library/alg/monoid/add.hpp"

template <typename X>
struct Monoid_Add {
  using value_type = X;
  static constexpr X op(const X &x, const X &y) noexcept { return x + y; }
  static constexpr X inverse(const X &x) noexcept { return -x; }
  static constexpr X power(const X &x, ll n) noexcept { return X(n) * x; }
  static constexpr X unit() { return X(0); }
  static constexpr bool commute = true;
};
#line 2 "library/alg/acted_monoid/sum_add.hpp"

template <typename E>
struct ActedMonoid_Sum_Add {
  using Monoid_X = Monoid_Add<E>;
  using Monoid_A = Monoid_Add<E>;
  using X = typename Monoid_X::value_type;
  using A = typename Monoid_A::value_type;
  static constexpr X act(const X &x, const A &a, const ll &size) {
    return x + a * E(size);
  }
};
#line 2 "library/ds/segtree/lazy_segtree.hpp"

template <typename ActedMonoid>
struct Lazy_SegTree {
  using AM = ActedMonoid;
  using MX = typename AM::Monoid_X;
  using MA = typename AM::Monoid_A;
  static_assert(MX::commute);
  using X = typename MX::value_type;
  using A = typename MA::value_type;
  int n, log, size;
  vc<X> dat;
  vc<A> laz;

  Lazy_SegTree() {}
  Lazy_SegTree(int n) { build(n); }
  template <typename F>
  Lazy_SegTree(int n, F f) {
    build(n, f);
  }
  Lazy_SegTree(const vc<X>& v) { build(v); }

  void build(int m) {
    build(m, [](int i) -> X { return MX::unit(); });
  }
  void build(const vc<X>& v) {
    build(len(v), [&](int i) -> X { return v[i]; });
  }
  template <typename F>
  void build(int m, F f) {
    n = m, log = 1;
    while ((1 << log) < n) ++log;
    size = 1 << log;
    dat.assign(size << 1, MX::unit());
    laz.assign(size, MA::unit());
    FOR(i, n) dat[size + i] = f(i);
    FOR_R(i, 1, size) update(i);
  }

  void update(int k) { dat[k] = MX::op(dat[2 * k], dat[2 * k + 1]); }
  void set(int p, X x) {
    assert(0 <= p && p < n);
    p += size;
    for (int i = log; i >= 1; i--) push(p >> i);
    dat[p] = x;
    for (int i = 1; i <= log; i++) update(p >> i);
  }

  X get(int p) {
    assert(0 <= p && p < n);
    p += size;
    for (int i = log; i >= 1; i--) push(p >> i);
    return dat[p];
  }

  vc<X> get_all() {
    FOR(k, 1, size) { push(k); }
    return {dat.begin() + size, dat.begin() + size + n};
  }

  X prod(int l, int r) {
    assert(0 <= l && l <= r && r <= n);
    if (l == r) return MX::unit();
    l += size, r += size;
    for (int i = log; i >= 1; i--) {
      if (((l >> i) << i) != l) push(l >> i);
      if (((r >> i) << i) != r) push((r - 1) >> i);
    }
    X x = MX::unit();
    while (l < r) {
      if (l & 1) x = MX::op(x, dat[l++]);
      if (r & 1) x = MX::op(x, dat[--r]);
      l >>= 1, r >>= 1;
    }
    return x;
  }

  X prod_all() { return dat[1]; }

  void apply(int l, int r, A a) {
    assert(0 <= l && l <= r && r <= n);
    if (l == r) return;
    l += size, r += size;
    for (int i = log; i >= 1; i--) {
      if (((l >> i) << i) != l) push(l >> i);
      if (((r >> i) << i) != r) push((r - 1) >> i);
    }
    int l2 = l, r2 = r;
    while (l < r) {
      if (l & 1) apply_at(l++, a);
      if (r & 1) apply_at(--r, a);
      l >>= 1, r >>= 1;
    }
    l = l2, r = r2;
    for (int i = 1; i <= log; i++) {
      if (((l >> i) << i) != l) update(l >> i);
      if (((r >> i) << i) != r) update((r - 1) >> i);
    }
  }

  template <typename F>
  int max_right(const F check, int l) {
    assert(0 <= l && l <= n);
    assert(check(MX::unit()));
    if (l == n) return n;
    l += size;
    for (int i = log; i >= 1; i--) push(l >> i);
    X sm = MX::unit();
    do {
      while (l % 2 == 0) l >>= 1;
      if (!check(MX::op(sm, dat[l]))) {
        while (l < size) {
          push(l);
          l = (2 * l);
          if (check(MX::op(sm, dat[l]))) { sm = MX::op(sm, dat[l++]); }
        }
        return l - size;
      }
      sm = MX::op(sm, dat[l++]);
    } while ((l & -l) != l);
    return n;
  }

  template <typename F>
  int min_left(const F check, int r) {
    assert(0 <= r && r <= n);
    assert(check(MX::unit()));
    if (r == 0) return 0;
    r += size;
    for (int i = log; i >= 1; i--) push((r - 1) >> i);
    X sm = MX::unit();
    do {
      r--;
      while (r > 1 && (r % 2)) r >>= 1;
      if (!check(MX::op(dat[r], sm))) {
        while (r < size) {
          push(r);
          r = (2 * r + 1);
          if (check(MX::op(dat[r], sm))) { sm = MX::op(dat[r--], sm); }
        }
        return r + 1 - size;
      }
      sm = MX::op(dat[r], sm);
    } while ((r & -r) != r);
    return 0;
  }

private:
  void apply_at(int k, A a) {
    int sz = 1 << (log - topbit(k));
    dat[k] = AM::act(dat[k], a, sz);
    if (k < size) laz[k] = MA::op(laz[k], a);
  }
  void push(int k) {
    if (laz[k] == MA::unit()) return;
    apply_at(2 * k, laz[k]), apply_at(2 * k + 1, laz[k]);
    laz[k] = MA::unit();
  }
};
#line 3 "library/graph/ds/lazy_tree_monoid.hpp"

template <typename TREE, typename ActedMonoid, bool edge = false>
struct Lazy_Tree_Monoid {
  using MonoX = typename ActedMonoid::Monoid_X;
  using MonoA = typename ActedMonoid::Monoid_A;
  using X = typename MonoX::value_type;
  using A = typename MonoA::value_type;
  TREE &tree;
  int N;
  Lazy_SegTree<ActedMonoid> seg;

  Lazy_Tree_Monoid(TREE &tree) : tree(tree), N(tree.N), seg(tree.N) {
    assert(MonoX::commute);
  }

  Lazy_Tree_Monoid(TREE &tree, vc<X> dat) : tree(tree), N(tree.N) {
    vc<X> seg_raw(N, MonoX::unit());
    if (!edge) {
      FOR(v, N) seg_raw[tree.LID[v]] = dat[v];
    } else {
      FOR(e, N - 1) {
        int v = tree.e_to_v(e);
        seg_raw[tree.LID[v]] = dat[e];
      }
    }
    seg = Lazy_SegTree<ActedMonoid>(seg_raw);
    assert(MonoX::commute);
  }

  void set(int i, X x) {
    if (edge) i = tree.e_to_v(i);
    i = tree.LID[i];
    seg.set(i, x);
  }

  X prod_path(int u, int v) {
    auto pd = tree.get_path_decomposition(u, v, edge);
    X val = MonoX::unit();
    for (auto &&[a, b]: pd) {
      X x = (a <= b ? seg.prod(a, b + 1) : seg.prod(b, a + 1));
      val = MonoX::op(val, x);
    }
    return val;
  }

  X prod_subtree(int u) {
    int l = tree.LID[u], r = tree.RID[u];
    return seg.prod(l + edge, r);
  }

  X prod_all() { return seg.prod_all(); }

  void apply_path(int u, int v, A a) {
    auto pd = tree.get_path_decomposition(u, v, edge);
    for (auto &&[x, y]: pd) {
      int l = min(x, y), r = max(x, y);
      seg.apply(l, r + 1, a);
    }
  }

  void apply_subtree(int u, A a) {
    int l = tree.LID[u], r = tree.RID[u];
    return seg.apply(l + edge, r, a);
  }

  template <class F>
  int max_path(F &check, int u, int v) {
    if (edge) return max_path_edge(check, u, v);
    if (!check(prod_path(u, u))) return -1;
    auto pd = tree.get_path_decomposition(u, v, edge);
    X val = MonoX::unit();
    for (auto &&[a, b]: pd) {
      X x = (a <= b ? seg.prod(a, b + 1) : seg.prod(b, a + 1));
      if (check(MonoX::op(val, x))) {
        val = MonoX::op(val, x);
        u = (tree.V[b]);
        continue;
      }
      auto check_tmp = [&](X x) -> bool { return check(MonoX::op(val, x)); };
      if (a <= b) {
        // 下り
        auto i = seg.max_right(check_tmp, a);
        return (i == a ? u : tree.V[i - 1]);
      } else {
        // 上り
        auto i = seg.min_left(check_tmp, a + 1);
        if (i == a + 1) return u;
        return tree.V[i];
      }
    }
    return v;
  }

private:
  template <class F>
  int max_path_edge(F &check, int u, int v) {
    assert(edge);
    if (!check(MonoX::unit())) return -1;
    int lca = tree.lca(u, v);
    auto pd = tree.get_path_decomposition(u, lca, edge);
    X val = MonoX::unit();

    // climb
    for (auto &&[a, b]: pd) {
      assert(a >= b);
      X x = seg.prod(b, a + 1);
      if (check(MonoX::op(val, x))) {
        val = MonoX::op(val, x);
        u = (tree.parent[tree.V[b]]);
        continue;
      }
      auto check_tmp = [&](X x) -> bool { return check(MonoX::op(val, x)); };
      auto i = seg.min_left(check_tmp, a + 1);
      if (i == a + 1) return u;
      return tree.parent[tree.V[i]];
    }
    // down
    pd = tree.get_path_decomposition(lca, v, edge);
    for (auto &&[a, b]: pd) {
      assert(a <= b);
      X x = seg.prod(a, b + 1);
      if (check(MonoX::op(val, x))) {
        val = MonoX::op(val, x);
        u = (tree.V[b]);
        continue;
      }
      auto check_tmp = [&](X x) -> bool { return check(MonoX::op(val, x)); };
      auto i = seg.max_right(check_tmp, a);
      return (i == a ? u : tree.V[i - 1]);
    }
    return v;
  }
};
#line 9 "main.cpp"

void solve() {
  LL(N, K, Q);
  VEC(int, C, K);
  for (auto&& v: C) --v;

  Graph<int, 0> G(N);
  G.read_tree();

  TREE<decltype(G)> tree(G);
  using AM = ActedMonoid_Sum_Add<ll>;

  Lazy_Tree_Monoid<decltype(tree), AM> X(tree, vi(N, 0));

  FOR(i, K) { X.apply_path(0, C[i], 1); }

  ll d_sm = 0;
  auto& dep = tree.depth;
  FOR(i, K) d_sm += dep[C[i]];

  bool out = 0;

  FOR(Q) {
    LL(t);
    if (t == 1) {
      LL(k, d);
      --k;
      --d;
      d_sm -= dep[C[k]];
      X.apply_path(0, C[k], -1);
      C[k] = d;
      d_sm += dep[C[k]];
      X.apply_path(0, C[k], 1);
    }
    if (t == 2) {
      LL(v);
      --v;
      ll ANS = dep[v] * K + d_sm;
      ANS -= 2 * X.prod_path(0, v);
      ANS += 2 * K;
      print(ANS);
      out = 1;
    }
  }
  if (!out) print();
}

signed main() {
  cout << fixed << setprecision(15);

  ll T = 1;
  // LL(T);
  FOR(T) solve();

  return 0;
}