#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 u32 = unsigned int;
using u64 = unsigned long long;
using i128 = __int128;
using u128 = unsigned __int128;
using f128 = __float128;

template <class T>
constexpr T infty = 0;
template <>
constexpr int infty<int> = 1'000'000'000;
template <>
constexpr ll infty<ll> = ll(infty<int>) * infty<int> * 2;
template <>
constexpr u32 infty<u32> = infty<int>;
template <>
constexpr u64 infty<u64> = infty<ll>;
template <>
constexpr i128 infty<i128> = i128(infty<ll>) * infty<ll>;
template <>
constexpr double infty<double> = infty<ll>;
template <>
constexpr long double infty<long double> = infty<ll>;

using pi = pair<ll, ll>;
using vi = vector<ll>;
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); }
int popcnt_mod_2(int x) { return __builtin_parity(x); }
int popcnt_mod_2(u32 x) { return __builtin_parity(x); }
int popcnt_mod_2(ll x) { return __builtin_parityll(x); }
int popcnt_mod_2(u64 x) { return __builtin_parityll(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 floor(T a, T b) {
  return a / b - (a % b && (a ^ b) < 0);
}
template <typename T>
T ceil(T x, T y) {
  return floor(x + y - 1, y);
}
template <typename T>
T bmod(T x, T y) {
  return x - y * floor(x, y);
}
template <typename T>
pair<T, T> divmod(T x, T y) {
  T q = floor(x, y);
  return {q, x - q * y};
}

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

#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) {
  T a = que.top();
  que.pop();
  return a;
}
template <typename T>
T POP(vc<T> &que) {
  T a = que.back();
  que.pop_back();
  return a;
}

template <typename F>
ll binary_search(F check, ll ok, ll ng, bool check_ok = true) {
  if (check_ok) assert(check(ok));
  while (abs(ok - ng) > 1) {
    auto x = (ng + ok) / 2;
    (check(x) ? ok : ng) = 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;
    (check(x) ? ok : ng) = 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"
#define FASTIO
#include <unistd.h>

// https://judge.yosupo.jp/submission/21623
namespace fastio {
static constexpr uint32_t SZ = 1 << 17;
char ibuf[SZ];
char obuf[SZ];
char out[100];
// pointer of ibuf, obuf
uint32_t pil = 0, pir = 0, por = 0;

struct Pre {
  char num[10000][4];
  constexpr Pre() : num() {
    for (int i = 0; i < 10000; i++) {
      int n = i;
      for (int j = 3; j >= 0; j--) {
        num[i][j] = n % 10 | '0';
        n /= 10;
      }
    }
  }
} constexpr pre;

inline void load() {
  memcpy(ibuf, ibuf + pil, pir - pil);
  pir = pir - pil + fread(ibuf + pir - pil, 1, SZ - pir + pil, stdin);
  pil = 0;
  if (pir < SZ) ibuf[pir++] = '\n';
}

inline void flush() {
  fwrite(obuf, 1, por, stdout);
  por = 0;
}

void rd(char &c) {
  do {
    if (pil + 1 > pir) load();
    c = ibuf[pil++];
  } while (isspace(c));
}

void rd(string &x) {
  x.clear();
  char c;
  do {
    if (pil + 1 > pir) load();
    c = ibuf[pil++];
  } while (isspace(c));
  do {
    x += c;
    if (pil == pir) load();
    c = ibuf[pil++];
  } while (!isspace(c));
}

template <typename T>
void rd_real(T &x) {
  string s;
  rd(s);
  x = stod(s);
}

template <typename T>
void rd_integer(T &x) {
  if (pil + 100 > pir) load();
  char c;
  do
    c = ibuf[pil++];
  while (c < '-');
  bool minus = 0;
  if constexpr (is_signed<T>::value || is_same_v<T, i128>) {
    if (c == '-') { minus = 1, c = ibuf[pil++]; }
  }
  x = 0;
  while ('0' <= c) { x = x * 10 + (c & 15), c = ibuf[pil++]; }
  if constexpr (is_signed<T>::value || is_same_v<T, i128>) {
    if (minus) x = -x;
  }
}

void rd(int &x) { rd_integer(x); }
void rd(ll &x) { rd_integer(x); }
void rd(i128 &x) { rd_integer(x); }
void rd(u32 &x) { rd_integer(x); }
void rd(u64 &x) { rd_integer(x); }
void rd(u128 &x) { rd_integer(x); }
void rd(double &x) { rd_real(x); }
void rd(long double &x) { rd_real(x); }
void rd(f128 &x) { rd_real(x); }

template <class T, class U>
void rd(pair<T, U> &p) {
  return rd(p.first), rd(p.second);
}
template <size_t N = 0, typename T>
void rd_tuple(T &t) {
  if constexpr (N < std::tuple_size<T>::value) {
    auto &x = std::get<N>(t);
    rd(x);
    rd_tuple<N + 1>(t);
  }
}
template <class... T>
void rd(tuple<T...> &tpl) {
  rd_tuple(tpl);
}

template <size_t N = 0, typename T>
void rd(array<T, N> &x) {
  for (auto &d: x) rd(d);
}
template <class T>
void rd(vc<T> &x) {
  for (auto &d: x) rd(d);
}

void read() {}
template <class H, class... T>
void read(H &h, T &... t) {
  rd(h), read(t...);
}

void wt(const char c) {
  if (por == SZ) flush();
  obuf[por++] = c;
}
void wt(const string s) {
  for (char c: s) wt(c);
}
void wt(const char *s) {
  size_t len = strlen(s);
  for (size_t i = 0; i < len; i++) wt(s[i]);
}

template <typename T>
void wt_integer(T x) {
  if (por > SZ - 100) flush();
  if (x < 0) { obuf[por++] = '-', x = -x; }
  int outi;
  for (outi = 96; x >= 10000; outi -= 4) {
    memcpy(out + outi, pre.num[x % 10000], 4);
    x /= 10000;
  }
  if (x >= 1000) {
    memcpy(obuf + por, pre.num[x], 4);
    por += 4;
  } else if (x >= 100) {
    memcpy(obuf + por, pre.num[x] + 1, 3);
    por += 3;
  } else if (x >= 10) {
    int q = (x * 103) >> 10;
    obuf[por] = q | '0';
    obuf[por + 1] = (x - q * 10) | '0';
    por += 2;
  } else
    obuf[por++] = x | '0';
  memcpy(obuf + por, out + outi + 4, 96 - outi);
  por += 96 - outi;
}

template <typename T>
void wt_real(T x) {
  ostringstream oss;
  oss << fixed << setprecision(15) << double(x);
  string s = oss.str();
  wt(s);
}

void wt(int x) { wt_integer(x); }
void wt(ll x) { wt_integer(x); }
void wt(i128 x) { wt_integer(x); }
void wt(u32 x) { wt_integer(x); }
void wt(u64 x) { wt_integer(x); }
void wt(u128 x) { wt_integer(x); }
void wt(double x) { wt_real(x); }
void wt(long double x) { wt_real(x); }
void wt(f128 x) { wt_real(x); }

template <class T, class U>
void wt(const pair<T, U> val) {
  wt(val.first);
  wt(' ');
  wt(val.second);
}
template <size_t N = 0, typename T>
void wt_tuple(const T t) {
  if constexpr (N < std::tuple_size<T>::value) {
    if constexpr (N > 0) { wt(' '); }
    const auto x = std::get<N>(t);
    wt(x);
    wt_tuple<N + 1>(t);
  }
}
template <class... T>
void wt(tuple<T...> tpl) {
  wt_tuple(tpl);
}
template <class T, size_t S>
void wt(const array<T, S> val) {
  auto n = val.size();
  for (size_t i = 0; i < n; i++) {
    if (i) wt(' ');
    wt(val[i]);
  }
}
template <class T>
void wt(const vector<T> val) {
  auto n = val.size();
  for (size_t i = 0; i < n; i++) {
    if (i) wt(' ');
    wt(val[i]);
  }
}

void print() { wt('\n'); }
template <class Head, class... Tail>
void print(Head &&head, Tail &&... tail) {
  wt(head);
  if (sizeof...(Tail)) wt(' ');
  print(forward<Tail>(tail)...);
}

// gcc expansion. called automaticall after main.
void __attribute__((destructor)) _d() { flush(); }
} // namespace fastio
using fastio::read;
using fastio::print;
using fastio::flush;

#define INT(...)   \
  int __VA_ARGS__; \
  read(__VA_ARGS__)
#define LL(...)   \
  ll __VA_ARGS__; \
  read(__VA_ARGS__)
#define U32(...)   \
  u32 __VA_ARGS__; \
  read(__VA_ARGS__)
#define U64(...)   \
  u64 __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 3 "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 {
  static constexpr bool is_directed = directed;
  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; }

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

  void build(int n) {
    N = n, M = 0;
    prepared = 0;
    edges.clear();
    indptr.clear();
    csr_edges.clear();
    vc_deg.clear();
    vc_indeg.clear();
    vc_outdeg.clear();
  }

  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;
  }

#ifdef FASTIO
  // 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();
  }
#endif

  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];
  }

#ifdef FASTIO
  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);
    }
  }
#endif

  vc<int> new_idx;
  vc<bool> used_e;

  // G における頂点 V[i] が、新しいグラフで i になるようにする
  // {G, es}
  Graph<T, directed> rearrange(vc<int> V, bool keep_eid = 0) {
    if (len(new_idx) != N) new_idx.assign(N, -1);
    if (len(used_e) != M) used_e.assign(M, 0);
    int n = len(V);
    FOR(i, n) new_idx[V[i]] = i;
    Graph<T, directed> G(n);
    vc<int> history;
    FOR(i, n) {
      for (auto&& e: (*this)[V[i]]) {
        if (used_e[e.id]) continue;
        int a = e.frm, b = e.to;
        if (new_idx[a] != -1 && new_idx[b] != -1) {
          history.eb(e.id);
          used_e[e.id] = 1;
          int eid = (keep_eid ? e.id : -1);
          G.add(new_idx[a], new_idx[b], e.cost, eid);
        }
      }
    }
    FOR(i, n) new_idx[V[i]] = -1;
    for (auto&& eid: history) used_e[eid] = 0;
    G.build();
    return G;
  }

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/shortest_path/bfs01.hpp"

template <typename T, typename GT>
pair<vc<T>, vc<int>> bfs01(GT& G, int v) {
  assert(G.is_prepared());
  int N = G.N;
  vc<T> dist(N, infty<T>);
  vc<int> par(N, -1);
  deque<int> que;

  dist[v] = 0;
  que.push_front(v);
  while (!que.empty()) {
    auto v = que.front();
    que.pop_front();
    for (auto&& e: G[v]) {
      if (dist[e.to] == infty<T> || dist[e.to] > dist[e.frm] + e.cost) {
        dist[e.to] = dist[e.frm] + e.cost;
        par[e.to] = e.frm;
        if (e.cost == 0)
          que.push_front(e.to);
        else
          que.push_back(e.to);
      }
    }
  }
  return {dist, par};
}

// 多点スタート。[dist, par, root]
template <typename T, typename GT>
tuple<vc<T>, vc<int>, vc<int>> bfs01(GT& G, vc<int> vs) {
  assert(G.is_prepared());
  int N = G.N;
  vc<T> dist(N, infty<T>);
  vc<int> par(N, -1);
  vc<int> root(N, -1);
  deque<int> que;

  for (auto&& v: vs) {
    dist[v] = 0;
    root[v] = v;
    que.push_front(v);
  }

  while (!que.empty()) {
    auto v = que.front();
    que.pop_front();
    for (auto&& e: G[v]) {
      if (dist[e.to] == infty<T> || dist[e.to] > dist[e.frm] + e.cost) {
        dist[e.to] = dist[e.frm] + e.cost;
        root[e.to] = root[e.frm];
        par[e.to] = e.frm;
        if (e.cost == 0)
          que.push_front(e.to);
        else
          que.push_back(e.to);
      }
    }
  }
  return {dist, par, root};
}
#line 3 "library/graph/centroid_decomposition.hpp"

/*
頂点ベースの重心分解
f(par, V, indptr)
*/
template <typename F>
void centroid_decomposition_0_dfs(vc<int>& par, vc<int>& vs, F f) {
  const int N = len(par);
  assert(N >= 1);
  int c = -1;
  vc<int> sz(N, 1);
  FOR_R(i, N) {
    if (sz[i] >= ceil<int>(N, 2)) {
      c = i;
      break;
    }
    sz[par[i]] += sz[i];
  }
  vc<int> color(N);
  vc<int> V = {c};
  int nc = 1;
  FOR(v, 1, N) {
    if (par[v] == c) { V.eb(v), color[v] = nc++; }
  }
  if (c > 0) {
    for (int a = par[c]; a != -1; a = par[a]) { color[a] = nc, V.eb(a); }
    ++nc;
  }
  FOR(i, N) {
    if (i != c && color[i] == 0) color[i] = color[par[i]], V.eb(i);
  }
  vc<int> indptr(nc + 1);
  FOR(i, N) indptr[1 + color[i]]++;
  FOR(i, nc) indptr[i + 1] += indptr[i];
  vc<int> counter = indptr;
  vc<int> ord(N);
  for (auto& v: V) { ord[counter[color[v]]++] = v; }
  vc<int> new_idx(N);
  FOR(i, N) new_idx[ord[i]] = i;
  vc<int> name(N);
  FOR(i, N) name[new_idx[i]] = vs[i];
  {
    vc<int> tmp(N, -1);
    FOR(i, 1, N) {
      int a = new_idx[i], b = new_idx[par[i]];
      if (a > b) swap(a, b);
      tmp[b] = a;
    }
    swap(par, tmp);
  }
  f(par, name, indptr);
  FOR(k, 1, nc) {
    int L = indptr[k], R = indptr[k + 1];
    vc<int> par1(R - L, -1);
    vc<int> name1(R - L, -1);
    name1[0] = name[0];
    FOR(i, L, R) name1[i - L] = name[i];
    FOR(i, L, R) { par1[i - L] = max(par[i] - L, -1); }
    centroid_decomposition_0_dfs(par1, name1, f);
  }
}

/*
https://maspypy.com/%e9%87%8d%e5%bf%83%e5%88%86%e8%a7%a3%e3%83%bb1-3%e9%87%8d%e5%bf%83%e5%88%86%e8%a7%a3%e3%81%ae%e3%81%8a%e7%b5%b5%e6%8f%8f%e3%81%8d
centroid_decomposition_1：長さ 2 以上のパス全体
f(par, V, n1, n2)
[1,1+n1]: color 1
[1+n1,1+n1+n2]: color 2
*/
template <typename F>
void centroid_decomposition_1_dfs(vc<int>& par, vc<int> vs, F f) {
  const int N = len(par);
  assert(N > 1);
  if (N == 2) { return; }
  int c = -1;
  vc<int> sz(N, 1);
  FOR_R(i, N) {
    if (sz[i] >= ceil<int>(N, 2)) {
      c = i;
      break;
    }
    sz[par[i]] += sz[i];
  }
  vc<int> color(N, -1);
  int take = 0;
  vc<int> ord(N, -1);
  ord[c] = 0;
  int p = 1;
  FOR(v, 1, N) {
    if (par[v] == c && take + sz[v] <= floor<int>(N - 1, 2)) {
      color[v] = 0, ord[v] = p++, take += sz[v];
    }
  }
  FOR(i, 1, N) {
    if (color[par[i]] == 0) color[i] = 0, ord[i] = p++;
  }
  int n0 = p - 1;
  for (int a = par[c]; a != -1; a = par[a]) { color[a] = 1, ord[a] = p++; }
  FOR(i, N) {
    if (i != c && color[i] == -1) color[i] = 1, ord[i] = p++;
  }
  assert(p == N);
  int n1 = N - 1 - n0;
  vc<int> par0(n0 + 1, -1), par1(n1 + 1, -1), par2(N, -1);
  vc<int> V0(n0 + 1), V1(n1 + 1), V2(N);
  FOR(v, N) {
    int i = ord[v];
    V2[i] = vs[v];
    if (color[v] != 1) { V0[i] = vs[v]; }
    if (color[v] != 0) { V1[max(i - n0, 0)] = vs[v]; }
  }
  FOR(v, 1, N) {
    int a = ord[v], b = ord[par[v]];
    if (a > b) swap(a, b);
    par2[b] = a;
    if (color[v] != 1 && color[par[v]] != 1) par0[b] = a;
    if (color[v] != 0 && color[par[v]] != 0)
      par1[max(b - n0, 0)] = max(a - n0, 0);
  }
  f(par2, V2, n0, n1);
  centroid_decomposition_1_dfs(par0, V0, f);
  centroid_decomposition_1_dfs(par1, V1, f);
}

/*
https://maspypy.com/%e9%87%8d%e5%bf%83%e5%88%86%e8%a7%a3%e3%83%bb1-3%e9%87%8d%e5%bf%83%e5%88%86%e8%a7%a3%e3%81%ae%e3%81%8a%e7%b5%b5%e6%8f%8f%e3%81%8d
f(par2, V2, color)
color in [-1,0,1], -1 is virtual.
*/
template <typename F>
void centroid_decomposition_2_dfs(vc<int>& par, vc<int>& vs, vc<int>& real,
                                  F f) {
  const int N = len(par);
  assert(N > 1);
  if (N == 2) {
    if (real[0] && real[1]) {
      vc<int> color = {0, 1};
      f(par, vs, color);
    }
    return;
  }
  int c = -1;
  vc<int> sz(N, 1);
  FOR_R(i, N) {
    if (sz[i] >= ceil<int>(N, 2)) {
      c = i;
      break;
    }
    sz[par[i]] += sz[i];
  }
  vc<int> color(N, -1);
  int take = 0;
  vc<int> ord(N, -1);
  ord[c] = 0;
  int p = 1;
  FOR(v, 1, N) {
    if (par[v] == c && take + sz[v] <= floor<int>(N - 1, 2)) {
      color[v] = 0, ord[v] = p++, take += sz[v];
    }
  }
  FOR(i, 1, N) {
    if (color[par[i]] == 0) color[i] = 0, ord[i] = p++;
  }
  int n0 = p - 1;
  for (int a = par[c]; a != -1; a = par[a]) { color[a] = 1, ord[a] = p++; }
  FOR(i, N) {
    if (i != c && color[i] == -1) color[i] = 1, ord[i] = p++;
  }
  assert(p == N);
  int n1 = N - 1 - n0;
  vc<int> par0(n0 + 1, -1), par1(n1 + 1, -1), par2(N, -1);
  vc<int> V0(n0 + 1), V1(n1 + 1), V2(N);
  vc<int> rea0(n0 + 1), rea1(n1 + 1), rea2(N);
  FOR(v, N) {
    int i = ord[v];
    V2[i] = vs[v], rea2[i] = real[v];
    if (color[v] != 1) { V0[i] = vs[v], rea0[i] = real[v]; }
    if (color[v] != 0) {
      V1[max(i - n0, 0)] = vs[v], rea1[max(i - n0, 0)] = real[v];
    }
  }
  FOR(v, 1, N) {
    int a = ord[v], b = ord[par[v]];
    if (a > b) swap(a, b);
    par2[b] = a;
    if (color[v] != 1 && color[par[v]] != 1) par0[b] = a;
    if (color[v] != 0 && color[par[v]] != 0)
      par1[max(b - n0, 0)] = max(a - n0, 0);
  }
  if (real[c]) {
    color.assign(N, -1);
    color[0] = 0;
    FOR(i, 1, N) color[i] = rea2[i] ? 1 : -1;
    f(par2, V2, color);
    rea0[0] = rea1[0] = rea2[0] = 0;
  }
  color.assign(N, -1);
  FOR(i, 1, N) if (rea2[i]) color[i] = (i <= n0 ? 0 : 1);
  f(par2, V2, color);
  centroid_decomposition_2_dfs(par0, V0, rea0, f);
  centroid_decomposition_2_dfs(par1, V1, rea1, f);
}

// f(par, V, color)
// V: label in original tree, dfs order
// color in [-1,0,1], color=-1: virtual
template <int MODE, typename GT, typename F>
void centroid_decomposition(GT& G, F f) {
  const int N = G.N;
  if (N == 1) return;
  vc<int> V(N), par(N, -1);
  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]) V[r++] = e.to, par[e.to] = v;
    }
  }
  assert(r == N);
  vc<int> new_idx(N);
  FOR(i, N) new_idx[V[i]] = i;
  vc<int> tmp(N, -1);
  FOR(i, 1, N) {
    int j = par[i];
    tmp[new_idx[i]] = new_idx[j];
  }
  swap(par, tmp);
  static_assert(MODE == 0 || MODE == 1 || MODE == 2);
  if constexpr (MODE == 0) { centroid_decomposition_0_dfs(par, V, f); }
  elif constexpr(MODE == 1) { centroid_decomposition_1_dfs(par, V, f); }
  else {
    vc<int> real(N, 1);
    centroid_decomposition_2_dfs(par, V, real, f);
  }
}
#line 7 "main.cpp"

struct Block {
  int N, off;
  vc<ll> A;
  vc<ll> SORTED_A;
  ll lazy = 0;

  Block(vc<ll>& B, int L, int R) : N(R - L), off(L) {
    A = {B.begin() + L, B.begin() + R};
    SORTED_A = A;
    sort(all(SORTED_A));
  }

  void apply(int l, int r, ll x) {
    l -= off, r -= off;
    chmax(l, 0), chmin(r, N);
    if (l >= r) return;
    if (r - l != N) {
      FOR(i, l, r) A[i] += x;
      SORTED_A = A;
      sort(all(SORTED_A));
      return;
    }
    assert(r - l == N);
    lazy += x;
  }

  ll get(int i) { return A[i - off] + lazy; }

  int query(int l, int r, ll x) {
    l -= off, r -= off;
    chmax(l, 0), chmin(r, N);
    if (l >= r) return 0;
    x -= lazy;
    if (r - l == N) { return UB(SORTED_A, x); }
    int cnt = 0;
    FOR(i, l, r) { cnt += (A[i] <= x); }
    return cnt;
  }
};

void solve() {
  INT(N, Q);
  Graph<int, 0> G0(N);
  G0.read_tree(1);
  vc<int> P0 = bfs01<int>(G0, 0).se;
  vc<int> v_to_e(N, -1);
  FOR(i, 1, N) {
    for (auto& e: G0[i]) {
      if (e.to == P0[i]) v_to_e[i] = e.id;
    }
  }

  vc<tuple<int, int, int>> QUERY;
  vvc<int> QID(N);
  FOR(q, Q) {
    INT(a, b, c);
    if (a == 1) {
      --b;
      QUERY.eb(a, b, c);
      auto& e = G0.edges[b];
      QID[e.frm].eb(q);
    }
    if (a == 2) {
      --b;
      QUERY.eb(a, b, c);
      QID[b].eb(q);
    }
  }

  vc<int> ANS(Q);
  vc<int> new_idx(N, -1);
  vc<int> new_idx_e(N, -1);

  auto work = [&](vc<int> par, vc<int> V, vc<int> indptr) -> void {
    int n = len(V);
    FOR(i, n) { new_idx[V[i]] = i; }
    Graph<int, 1> G(n);
    vi A(n);
    vc<int> NOW_LEN(n);
    FOR(i, 1, n) {
      int a = V[par[i]], b = V[i];
      int raw_idx = -1;
      if (P0[b] == a) {
        raw_idx = v_to_e[b];
      } else {
        raw_idx = v_to_e[a];
      }
      G.add(par[i], i, G0.edges[raw_idx].cost);
      new_idx_e[raw_idx] = i;
      NOW_LEN[i] = G0.edges[raw_idx].cost;
      A[i] = A[par[i]] + NOW_LEN[i];
    }
    G.build();
    vc<int> ord, LID(n), RID(n);
    auto dfs = [&](auto& dfs, int v) -> void {
      LID[v] = len(ord);
      ord.eb(v);
      for (auto& e: G[v]) dfs(dfs, e.to);
      RID[v] = len(ord);
    };
    dfs(dfs, 0);

    A = rearrange(A, ord);
    vc<int> SUB_L(n), SUB_R(n);
    FOR(i, 1, n) {
      if (par[i] == 0) {
        int a = LID[i], b = RID[i];
        FOR(k, a, b) {
          SUB_L[ord[k]] = a;
          SUB_R[ord[k]] = b;
        }
      }
    }

    // qid, 1, v, x
    // qid, 2, v, x
    vc<tuple<int, int, int, ll>> SUB_QUERY;
    for (auto& v: V) {
      for (auto q: QID[v]) {
        auto [t, a, b] = QUERY[q];
        if (t == 1) {
          int w = new_idx_e[a];
          if (w != -1) {
            SUB_QUERY.eb(q, 1, w, b - NOW_LEN[w]);
            NOW_LEN[w] = b;
          }
        }
        if (t == 2) {
          a = new_idx[a];
          SUB_QUERY.eb(q, 2, a, b);
        }
      }
    }

    int b_sz = sqrt(n);
    int b_num = ceil<int>(n, b_sz);
    vc<Block> BLOCK;
    FOR(b, b_num) {
      int L = b_sz * b;
      int R = min<int>(L + b_sz, n);
      BLOCK.eb(Block(A, L, R));
    }

    auto ADD = [&](int L, int R, ll x) -> void {
      FOR(b, b_num) BLOCK[b].apply(L, R, x);
    };
    auto GET = [&](int i) -> ll {
      int bid = i / b_sz;
      return BLOCK[bid].get(i);
    };
    auto COUNT = [&](int L, int R, ll x) -> int {
      int cnt = 0;
      FOR(b, b_num) cnt += BLOCK[b].query(L, R, x);
      return cnt;
    };

    sort(all(SUB_QUERY));
    for (auto& [q, t, v, x]: SUB_QUERY) {
      if (t == 1) { ADD(LID[v], RID[v], x); }
      if (t == 2) {
        int ans = 0;
        ll xx = x - GET(LID[v]);
        ans += COUNT(0, n, xx);
        ans -= COUNT(SUB_L[v], SUB_R[v], xx);
        ANS[q] += ans;
      }
    }

    // reset
    for (auto& v: V) { new_idx[v] = -1; }
    FOR(i, 1, n) {
      int a = V[par[i]], b = V[i];
      int raw_idx = -1;
      if (P0[b] == a) {
        raw_idx = v_to_e[b];
      } else {
        raw_idx = v_to_e[a];
      }
      new_idx_e[raw_idx] = -1;
    }
  };
  centroid_decomposition<0>(G0, work);

  FOR(q, Q) {
    int t = get<0>(QUERY[q]);
    if (t == 2) print(ANS[q]);
  }
}

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