#line 1 "main.cpp"
#define PROBLEM "https://yukicoder.me/problems/no/1038"

#line 1 "/home/maspy/compro/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 "/home/maspy/compro/library/other/io.hpp"
// based on yosupo's fastio
#include <unistd.h>

namespace fastio {
#define FASTIO
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 "/home/maspy/compro/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;
  }

  // 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 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);
    }
  }

  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 "/home/maspy/compro/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 "/home/maspy/compro/library/graph/centroid_decomposition.hpp"

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
1/3 CD のみ扱う
centroid_decomposition_1：長さ 2 以上のパス全体
*/
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
1/3 CD のみ扱う
centroid_decomposition_1：長さ 2 以上のパス全体
*/

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 2 "/home/maspy/compro/library/graph/ds/contour_query_range.hpp"

template <typename GT, bool WEIGHTED>
struct Contour_Query_Range {
  using WT = std::conditional_t<WEIGHTED, typename GT::cost_type, int>;
  int N;
  vc<int> V;
  vc<int> comp;
  vc<WT> dep;
  vc<int> info_idx, info_indptr;
  vc<int> comp_range;

  Contour_Query_Range(GT& G0) : N(G0.N) {
    int p = 0;
    comp_range = {0};
    auto f = [&](vc<int>& par, vc<int>& vs, vc<int>& color) -> void {
      const int n = len(par);
      vc<WT> dist(n);
      vc<int> A, B;
      FOR(v, 1, n) {
        static_assert(!WEIGHTED);
        dist[v] = dist[par[v]] + 1;
      }
      FOR(v, n) {
        if (color[v] == 0) A.eb(v);
        if (color[v] == 1) B.eb(v);
      }
      if (A.empty() || B.empty()) return;
      int mx_A = 0, mx_B = 0;
      for (auto& v: A) {
        V.eb(vs[v]), comp.eb(p), dep.eb(dist[v]), chmax(mx_A, dist[v]);
      }
      comp_range.eb(comp_range.back() + mx_A + 1), ++p;
      for (auto& v: B) {
        V.eb(vs[v]), comp.eb(p), dep.eb(dist[v]), chmax(mx_B, dist[v]);
      }
      comp_range.eb(comp_range.back() + mx_B + 1), ++p;
    };
    centroid_decomposition<2>(G0, f);
    info_indptr.assign(N + 1, 0);
    for (auto& v: V) info_indptr[1 + v]++;
    FOR(v, N) { info_indptr[v + 1] += info_indptr[v]; }
    auto counter = info_indptr;
    info_idx.resize(info_indptr.back());
    FOR(i, len(V)) { info_idx[counter[V[i]]++] = i; }
  }

  int size() { return comp_range.back(); }

  vc<pair<int, int>> get_contour_range(int v, WT l, WT r) {
    vc<pair<int, int>> res;
    FOR(k, info_indptr[v], info_indptr[v + 1]) {
      int idx = info_idx[k];
      int p = comp[idx] ^ 1;
      int lo = l - dep[idx], hi = r - dep[idx];
      int L = comp_range[p], R = comp_range[p + 1];
      int n = R - L;
      chmax(lo, 0), chmin(hi, n);
      if (lo < hi) { res.eb(comp_range[p] + lo, comp_range[p] + hi); }
    }
    return res;
  }

  vc<int> get_indices(int v) {
    vc<int> res;
    FOR(k, info_indptr[v], info_indptr[v + 1]) {
      int idx = info_idx[k];
      int p = comp[idx];
      res.eb(comp_range[p] + dep[idx]);
    }
    return res;
  }
};
#line 2 "/home/maspy/compro/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 3 "/home/maspy/compro/library/ds/fenwicktree/fenwicktree.hpp"

template <typename Monoid>
struct FenwickTree {
  using G = Monoid;
  using E = typename G::value_type;
  int n;
  vector<E> dat;
  E total;

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

  void build(int m) {
    n = m;
    dat.assign(m, G::unit());
    total = G::unit();
  }
  void build(const vc<E>& v) {
    build(len(v), [&](int i) -> E { return v[i]; });
  }
  template <typename F>
  void build(int m, F f) {
    n = m;
    dat.clear();
    dat.reserve(n);
    total = G::unit();
    FOR(i, n) { dat.eb(f(i)); }
    for (int i = 1; i <= n; ++i) {
      int j = i + (i & -i);
      if (j <= n) dat[j - 1] = G::op(dat[i - 1], dat[j - 1]);
    }
    total = prefix_sum(m);
  }

  E prod_all() { return total; }
  E sum_all() { return total; }
  E sum(int k) { return prefix_sum(k); }
  E prod(int k) { return prefix_prod(k); }
  E prefix_sum(int k) { return prefix_prod(k); }
  E prefix_prod(int k) {
    chmin(k, n);
    E ret = G::unit();
    for (; k > 0; k -= k & -k) ret = G::op(ret, dat[k - 1]);
    return ret;
  }
  E sum(int L, int R) { return prod(L, R); }
  E prod(int L, int R) {
    chmax(L, 0), chmin(R, n);
    if (L == 0) return prefix_prod(R);
    assert(0 <= L && L <= R && R <= n);
    E pos = G::unit(), neg = G::unit();
    while (L < R) { pos = G::op(pos, dat[R - 1]), R -= R & -R; }
    while (R < L) { neg = G::op(neg, dat[L - 1]), L -= L & -L; }
    return G::op(pos, G::inverse(neg));
  }

  void add(int k, E x) { multiply(k, x); }
  void multiply(int k, E x) {
    static_assert(G::commute);
    total = G::op(total, x);
    for (++k; k <= n; k += k & -k) dat[k - 1] = G::op(dat[k - 1], x);
  }

  template <class F>
  int max_right(const F check) {
    assert(check(G::unit()));
    int i = 0;
    E s = G::unit();
    int k = 1;
    while (2 * k <= n) k *= 2;
    while (k) {
      if (i + k - 1 < len(dat)) {
        E t = G::op(s, dat[i + k - 1]);
        if (check(t)) { i += k, s = t; }
      }
      k >>= 1;
    }
    return i;
  }

  // check(i, x)
  template <class F>
  int max_right_with_index(const F check) {
    assert(check(0, G::unit()));
    int i = 0;
    E s = G::unit();
    int k = 1;
    while (2 * k <= n) k *= 2;
    while (k) {
      if (i + k - 1 < len(dat)) {
        E t = G::op(s, dat[i + k - 1]);
        if (check(i + k, t)) { i += k, s = t; }
      }
      k >>= 1;
    }
    return i;
  }

  int kth(E k) {
    return max_right([&k](E x) -> bool { return x <= k; });
  }
};
#line 8 "main.cpp"

void solve() {
  LL(N, Q);
  Graph<int, 0> G(N);
  G.read_tree();

  Contour_Query_Range<decltype(G), false> X(G);
  FenwickTree<Monoid_Add<ll>> bit(len(X) + 1);
  vi A(N);

  FOR(Q) {
    INT(v, d, x);
    --v;
    ll ans = A[v];
    for (auto& i: X.get_indices(v)) { ans += bit.sum(1 + i); }
    print(ans);

    for (auto& [a, b]: X.get_contour_range(v, 0, 1 + d)) {
      bit.add(a, x), bit.add(b, -x);
    }
    A[v] += x;
  }
}

signed main() {
  int T = 1;
  // INT(T);
  FOR(T) solve();
  return 0;
}