verify/verify-yosupo-graph/yosupo-frequency-table-of-tree-distance.test.cpp

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Last update: 2024-05-03 23:21:26+09:00
Problem: https://judge.yosupo.jp/problem/frequency_table_of_tree_distance

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Code

#define PROBLEM "https://judge.yosupo.jp/problem/frequency_table_of_tree_distance"

#include "../../template/template.hpp"

#include "../../graph/graph-template.hpp"

#include "../../misc/fastio.hpp"

#include "../../tree/frequency-table-of-tree-distance.hpp"

using namespace Nyaan; void Nyaan::solve() {
  int N;
  rd(N);
  vvi g(N);
  rep(_, N - 1) {
    int u, v;
    rd(u, v);
    g[u].push_back(v);
    g[v].push_back(u);
  }
  FrequencyTableOfTreeDistance<vvi> ft(g);
  auto d = ft.get();
  d.resize(N);
  rep1(i, N - 1) {
    if (i != 1) wt(' ');
    wt(d[i]);
  }
  wt('\n');
}

#line 1 "verify/verify-yosupo-graph/yosupo-frequency-table-of-tree-distance.test.cpp"
#define PROBLEM "https://judge.yosupo.jp/problem/frequency_table_of_tree_distance"

#line 2 "template/template.hpp"
using namespace std;

// intrinstic
#include <immintrin.h>

#include <algorithm>
#include <array>
#include <bitset>
#include <cassert>
#include <cctype>
#include <cfenv>
#include <cfloat>
#include <chrono>
#include <cinttypes>
#include <climits>
#include <cmath>
#include <complex>
#include <cstdarg>
#include <cstddef>
#include <cstdint>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <deque>
#include <fstream>
#include <functional>
#include <initializer_list>
#include <iomanip>
#include <ios>
#include <iostream>
#include <istream>
#include <iterator>
#include <limits>
#include <list>
#include <map>
#include <memory>
#include <new>
#include <numeric>
#include <ostream>
#include <queue>
#include <random>
#include <set>
#include <sstream>
#include <stack>
#include <streambuf>
#include <string>
#include <tuple>
#include <type_traits>
#include <typeinfo>
#include <unordered_map>
#include <unordered_set>
#include <utility>
#include <vector>

// utility
#line 1 "template/util.hpp"
namespace Nyaan {
using ll = long long;
using i64 = long long;
using u64 = unsigned long long;
using i128 = __int128_t;
using u128 = __uint128_t;

template <typename T>
using V = vector<T>;
template <typename T>
using VV = vector<vector<T>>;
using vi = vector<int>;
using vl = vector<long long>;
using vd = V<double>;
using vs = V<string>;
using vvi = vector<vector<int>>;
using vvl = vector<vector<long long>>;
template <typename T>
using minpq = priority_queue<T, vector<T>, greater<T>>;

template <typename T, typename U>
struct P : pair<T, U> {
  template <typename... Args>
  P(Args... args) : pair<T, U>(args...) {}

  using pair<T, U>::first;
  using pair<T, U>::second;

  P &operator+=(const P &r) {
    first += r.first;
    second += r.second;
    return *this;
  }
  P &operator-=(const P &r) {
    first -= r.first;
    second -= r.second;
    return *this;
  }
  P &operator*=(const P &r) {
    first *= r.first;
    second *= r.second;
    return *this;
  }
  template <typename S>
  P &operator*=(const S &r) {
    first *= r, second *= r;
    return *this;
  }
  P operator+(const P &r) const { return P(*this) += r; }
  P operator-(const P &r) const { return P(*this) -= r; }
  P operator*(const P &r) const { return P(*this) *= r; }
  template <typename S>
  P operator*(const S &r) const {
    return P(*this) *= r;
  }
  P operator-() const { return P{-first, -second}; }
};

using pl = P<ll, ll>;
using pi = P<int, int>;
using vp = V<pl>;

constexpr int inf = 1001001001;
constexpr long long infLL = 4004004004004004004LL;

template <typename T>
int sz(const T &t) {
  return t.size();
}

template <typename T, typename U>
inline bool amin(T &x, U y) {
  return (y < x) ? (x = y, true) : false;
}
template <typename T, typename U>
inline bool amax(T &x, U y) {
  return (x < y) ? (x = y, true) : false;
}

template <typename T>
inline T Max(const vector<T> &v) {
  return *max_element(begin(v), end(v));
}
template <typename T>
inline T Min(const vector<T> &v) {
  return *min_element(begin(v), end(v));
}
template <typename T>
inline long long Sum(const vector<T> &v) {
  return accumulate(begin(v), end(v), 0LL);
}

template <typename T>
int lb(const vector<T> &v, const T &a) {
  return lower_bound(begin(v), end(v), a) - begin(v);
}
template <typename T>
int ub(const vector<T> &v, const T &a) {
  return upper_bound(begin(v), end(v), a) - begin(v);
}

constexpr long long TEN(int n) {
  long long ret = 1, x = 10;
  for (; n; x *= x, n >>= 1) ret *= (n & 1 ? x : 1);
  return ret;
}

template <typename T, typename U>
pair<T, U> mkp(const T &t, const U &u) {
  return make_pair(t, u);
}

template <typename T>
vector<T> mkrui(const vector<T> &v, bool rev = false) {
  vector<T> ret(v.size() + 1);
  if (rev) {
    for (int i = int(v.size()) - 1; i >= 0; i--) ret[i] = v[i] + ret[i + 1];
  } else {
    for (int i = 0; i < int(v.size()); i++) ret[i + 1] = ret[i] + v[i];
  }
  return ret;
};

template <typename T>
vector<T> mkuni(const vector<T> &v) {
  vector<T> ret(v);
  sort(ret.begin(), ret.end());
  ret.erase(unique(ret.begin(), ret.end()), ret.end());
  return ret;
}

template <typename F>
vector<int> mkord(int N, F f) {
  vector<int> ord(N);
  iota(begin(ord), end(ord), 0);
  sort(begin(ord), end(ord), f);
  return ord;
}

template <typename T>
vector<int> mkinv(vector<T> &v) {
  int max_val = *max_element(begin(v), end(v));
  vector<int> inv(max_val + 1, -1);
  for (int i = 0; i < (int)v.size(); i++) inv[v[i]] = i;
  return inv;
}

vector<int> mkiota(int n) {
  vector<int> ret(n);
  iota(begin(ret), end(ret), 0);
  return ret;
}

template <typename T>
T mkrev(const T &v) {
  T w{v};
  reverse(begin(w), end(w));
  return w;
}

template <typename T>
bool nxp(T &v) {
  return next_permutation(begin(v), end(v));
}

// 返り値の型は入力の T に依存
// i 要素目 : [0, a[i])
template <typename T>
vector<vector<T>> product(const vector<T> &a) {
  vector<vector<T>> ret;
  vector<T> v;
  auto dfs = [&](auto rc, int i) -> void {
    if (i == (int)a.size()) {
      ret.push_back(v);
      return;
    }
    for (int j = 0; j < a[i]; j++) v.push_back(j), rc(rc, i + 1), v.pop_back();
  };
  dfs(dfs, 0);
  return ret;
}

// F : function(void(T&)), mod を取る操作
// T : 整数型のときはオーバーフローに注意する
template <typename T>
T Power(T a, long long n, const T &I, const function<void(T &)> &f) {
  T res = I;
  for (; n; f(a = a * a), n >>= 1) {
    if (n & 1) f(res = res * a);
  }
  return res;
}
// T : 整数型のときはオーバーフローに注意する
template <typename T>
T Power(T a, long long n, const T &I = T{1}) {
  return Power(a, n, I, function<void(T &)>{[](T &) -> void {}});
}

template <typename T>
T Rev(const T &v) {
  T res = v;
  reverse(begin(res), end(res));
  return res;
}

template <typename T>
vector<T> Transpose(const vector<T> &v) {
  using U = typename T::value_type;
  if(v.empty()) return {};
  int H = v.size(), W = v[0].size();
  vector res(W, T(H, U{}));
  for (int i = 0; i < H; i++) {
    for (int j = 0; j < W; j++) {
      res[j][i] = v[i][j];
    }
  }
  return res;
}

template <typename T>
vector<T> Rotate(const vector<T> &v, int clockwise = true) {
  using U = typename T::value_type;
  int H = v.size(), W = v[0].size();
  vector res(W, T(H, U{}));
  for (int i = 0; i < H; i++) {
    for (int j = 0; j < W; j++) {
      if (clockwise) {
        res[W - 1 - j][i] = v[i][j];
      } else {
        res[j][H - 1 - i] = v[i][j];
      }
    }
  }
  return res;
}

}  // namespace Nyaan
#line 58 "template/template.hpp"

// bit operation
#line 1 "template/bitop.hpp"
namespace Nyaan {
__attribute__((target("popcnt"))) inline int popcnt(const u64 &a) {
  return __builtin_popcountll(a);
}
inline int lsb(const u64 &a) { return a ? __builtin_ctzll(a) : 64; }
inline int ctz(const u64 &a) { return a ? __builtin_ctzll(a) : 64; }
inline int msb(const u64 &a) { return a ? 63 - __builtin_clzll(a) : -1; }
template <typename T>
inline int gbit(const T &a, int i) {
  return (a >> i) & 1;
}
template <typename T>
inline void sbit(T &a, int i, bool b) {
  if (gbit(a, i) != b) a ^= T(1) << i;
}
constexpr long long PW(int n) { return 1LL << n; }
constexpr long long MSK(int n) { return (1LL << n) - 1; }
}  // namespace Nyaan
#line 61 "template/template.hpp"

// inout
#line 1 "template/inout.hpp"
namespace Nyaan {

template <typename T, typename U>
ostream &operator<<(ostream &os, const pair<T, U> &p) {
  os << p.first << " " << p.second;
  return os;
}
template <typename T, typename U>
istream &operator>>(istream &is, pair<T, U> &p) {
  is >> p.first >> p.second;
  return is;
}

template <typename T>
ostream &operator<<(ostream &os, const vector<T> &v) {
  int s = (int)v.size();
  for (int i = 0; i < s; i++) os << (i ? " " : "") << v[i];
  return os;
}
template <typename T>
istream &operator>>(istream &is, vector<T> &v) {
  for (auto &x : v) is >> x;
  return is;
}

istream &operator>>(istream &is, __int128_t &x) {
  string S;
  is >> S;
  x = 0;
  int flag = 0;
  for (auto &c : S) {
    if (c == '-') {
      flag = true;
      continue;
    }
    x *= 10;
    x += c - '0';
  }
  if (flag) x = -x;
  return is;
}

istream &operator>>(istream &is, __uint128_t &x) {
  string S;
  is >> S;
  x = 0;
  for (auto &c : S) {
    x *= 10;
    x += c - '0';
  }
  return is;
}

ostream &operator<<(ostream &os, __int128_t x) {
  if (x == 0) return os << 0;
  if (x < 0) os << '-', x = -x;
  string S;
  while (x) S.push_back('0' + x % 10), x /= 10;
  reverse(begin(S), end(S));
  return os << S;
}
ostream &operator<<(ostream &os, __uint128_t x) {
  if (x == 0) return os << 0;
  string S;
  while (x) S.push_back('0' + x % 10), x /= 10;
  reverse(begin(S), end(S));
  return os << S;
}

void in() {}
template <typename T, class... U>
void in(T &t, U &...u) {
  cin >> t;
  in(u...);
}

void out() { cout << "\n"; }
template <typename T, class... U, char sep = ' '>
void out(const T &t, const U &...u) {
  cout << t;
  if (sizeof...(u)) cout << sep;
  out(u...);
}

struct IoSetupNya {
  IoSetupNya() {
    cin.tie(nullptr);
    ios::sync_with_stdio(false);
    cout << fixed << setprecision(15);
    cerr << fixed << setprecision(7);
  }
} iosetupnya;

}  // namespace Nyaan
#line 64 "template/template.hpp"

// debug
#line 1 "template/debug.hpp"
namespace DebugImpl {

template <typename U, typename = void>
struct is_specialize : false_type {};
template <typename U>
struct is_specialize<
    U, typename conditional<false, typename U::iterator, void>::type>
    : true_type {};
template <typename U>
struct is_specialize<
    U, typename conditional<false, decltype(U::first), void>::type>
    : true_type {};
template <typename U>
struct is_specialize<U, enable_if_t<is_integral<U>::value, void>> : true_type {
};

void dump(const char& t) { cerr << t; }

void dump(const string& t) { cerr << t; }

void dump(const bool& t) { cerr << (t ? "true" : "false"); }

void dump(__int128_t t) {
  if (t == 0) cerr << 0;
  if (t < 0) cerr << '-', t = -t;
  string S;
  while (t) S.push_back('0' + t % 10), t /= 10;
  reverse(begin(S), end(S));
  cerr << S;
}

void dump(__uint128_t t) {
  if (t == 0) cerr << 0;
  string S;
  while (t) S.push_back('0' + t % 10), t /= 10;
  reverse(begin(S), end(S));
  cerr << S;
}

template <typename U,
          enable_if_t<!is_specialize<U>::value, nullptr_t> = nullptr>
void dump(const U& t) {
  cerr << t;
}

template <typename T>
void dump(const T& t, enable_if_t<is_integral<T>::value>* = nullptr) {
  string res;
  if (t == Nyaan::inf) res = "inf";
  if constexpr (is_signed<T>::value) {
    if (t == -Nyaan::inf) res = "-inf";
  }
  if constexpr (sizeof(T) == 8) {
    if (t == Nyaan::infLL) res = "inf";
    if constexpr (is_signed<T>::value) {
      if (t == -Nyaan::infLL) res = "-inf";
    }
  }
  if (res.empty()) res = to_string(t);
  cerr << res;
}

template <typename T, typename U>
void dump(const pair<T, U>&);
template <typename T>
void dump(const pair<T*, int>&);

template <typename T>
void dump(const T& t,
          enable_if_t<!is_void<typename T::iterator>::value>* = nullptr) {
  cerr << "[ ";
  for (auto it = t.begin(); it != t.end();) {
    dump(*it);
    cerr << (++it == t.end() ? "" : ", ");
  }
  cerr << " ]";
}

template <typename T, typename U>
void dump(const pair<T, U>& t) {
  cerr << "( ";
  dump(t.first);
  cerr << ", ";
  dump(t.second);
  cerr << " )";
}

template <typename T>
void dump(const pair<T*, int>& t) {
  cerr << "[ ";
  for (int i = 0; i < t.second; i++) {
    dump(t.first[i]);
    cerr << (i == t.second - 1 ? "" : ", ");
  }
  cerr << " ]";
}

void trace() { cerr << endl; }
template <typename Head, typename... Tail>
void trace(Head&& head, Tail&&... tail) {
  cerr << " ";
  dump(head);
  if (sizeof...(tail) != 0) cerr << ",";
  trace(std::forward<Tail>(tail)...);
}

}  // namespace DebugImpl

#ifdef NyaanDebug
#define trc(...)                            \
  do {                                      \
    cerr << "## " << #__VA_ARGS__ << " = "; \
    DebugImpl::trace(__VA_ARGS__);          \
  } while (0)
#else
#define trc(...) (void(0))
#endif

#ifdef NyaanLocal
#define trc2(...)                           \
  do {                                      \
    cerr << "## " << #__VA_ARGS__ << " = "; \
    DebugImpl::trace(__VA_ARGS__);          \
  } while (0)
#else
#define trc2(...) (void(0))
#endif
#line 67 "template/template.hpp"

// macro
#line 1 "template/macro.hpp"
#define each(x, v) for (auto&& x : v)
#define each2(x, y, v) for (auto&& [x, y] : v)
#define all(v) (v).begin(), (v).end()
#define rep(i, N) for (long long i = 0; i < (long long)(N); i++)
#define repr(i, N) for (long long i = (long long)(N)-1; i >= 0; i--)
#define rep1(i, N) for (long long i = 1; i <= (long long)(N); i++)
#define repr1(i, N) for (long long i = (N); (long long)(i) > 0; i--)
#define reg(i, a, b) for (long long i = (a); i < (b); i++)
#define regr(i, a, b) for (long long i = (b)-1; i >= (a); i--)
#define fi first
#define se second
#define ini(...)   \
  int __VA_ARGS__; \
  in(__VA_ARGS__)
#define inl(...)         \
  long long __VA_ARGS__; \
  in(__VA_ARGS__)
#define ins(...)      \
  string __VA_ARGS__; \
  in(__VA_ARGS__)
#define in2(s, t)                           \
  for (int i = 0; i < (int)s.size(); i++) { \
    in(s[i], t[i]);                         \
  }
#define in3(s, t, u)                        \
  for (int i = 0; i < (int)s.size(); i++) { \
    in(s[i], t[i], u[i]);                   \
  }
#define in4(s, t, u, v)                     \
  for (int i = 0; i < (int)s.size(); i++) { \
    in(s[i], t[i], u[i], v[i]);             \
  }
#define die(...)             \
  do {                       \
    Nyaan::out(__VA_ARGS__); \
    return;                  \
  } while (0)
#line 70 "template/template.hpp"

namespace Nyaan {
void solve();
}
int main() { Nyaan::solve(); }
#line 4 "verify/verify-yosupo-graph/yosupo-frequency-table-of-tree-distance.test.cpp"

#line 2 "graph/graph-template.hpp"

template <typename T>
struct edge {
  int src, to;
  T cost;

  edge(int _to, T _cost) : src(-1), to(_to), cost(_cost) {}
  edge(int _src, int _to, T _cost) : src(_src), to(_to), cost(_cost) {}

  edge &operator=(const int &x) {
    to = x;
    return *this;
  }

  operator int() const { return to; }
};
template <typename T>
using Edges = vector<edge<T>>;
template <typename T>
using WeightedGraph = vector<Edges<T>>;
using UnweightedGraph = vector<vector<int>>;

// Input of (Unweighted) Graph
UnweightedGraph graph(int N, int M = -1, bool is_directed = false,
                      bool is_1origin = true) {
  UnweightedGraph g(N);
  if (M == -1) M = N - 1;
  for (int _ = 0; _ < M; _++) {
    int x, y;
    cin >> x >> y;
    if (is_1origin) x--, y--;
    g[x].push_back(y);
    if (!is_directed) g[y].push_back(x);
  }
  return g;
}

// Input of Weighted Graph
template <typename T>
WeightedGraph<T> wgraph(int N, int M = -1, bool is_directed = false,
                        bool is_1origin = true) {
  WeightedGraph<T> g(N);
  if (M == -1) M = N - 1;
  for (int _ = 0; _ < M; _++) {
    int x, y;
    cin >> x >> y;
    T c;
    cin >> c;
    if (is_1origin) x--, y--;
    g[x].emplace_back(x, y, c);
    if (!is_directed) g[y].emplace_back(y, x, c);
  }
  return g;
}

// Input of Edges
template <typename T>
Edges<T> esgraph([[maybe_unused]] int N, int M, int is_weighted = true,
                 bool is_1origin = true) {
  Edges<T> es;
  for (int _ = 0; _ < M; _++) {
    int x, y;
    cin >> x >> y;
    T c;
    if (is_weighted)
      cin >> c;
    else
      c = 1;
    if (is_1origin) x--, y--;
    es.emplace_back(x, y, c);
  }
  return es;
}

// Input of Adjacency Matrix
template <typename T>
vector<vector<T>> adjgraph(int N, int M, T INF, int is_weighted = true,
                           bool is_directed = false, bool is_1origin = true) {
  vector<vector<T>> d(N, vector<T>(N, INF));
  for (int _ = 0; _ < M; _++) {
    int x, y;
    cin >> x >> y;
    T c;
    if (is_weighted)
      cin >> c;
    else
      c = 1;
    if (is_1origin) x--, y--;
    d[x][y] = c;
    if (!is_directed) d[y][x] = c;
  }
  return d;
}

/**
 * @brief グラフテンプレート
 * @docs docs/graph/graph-template.md
 */
#line 6 "verify/verify-yosupo-graph/yosupo-frequency-table-of-tree-distance.test.cpp"

#line 2 "misc/fastio.hpp"

#line 8 "misc/fastio.hpp"

using namespace std;

#line 2 "internal/internal-type-traits.hpp"

#line 4 "internal/internal-type-traits.hpp"
using namespace std;

namespace internal {
template <typename T>
using is_broadly_integral =
    typename conditional_t<is_integral_v<T> || is_same_v<T, __int128_t> ||
                               is_same_v<T, __uint128_t>,
                           true_type, false_type>::type;

template <typename T>
using is_broadly_signed =
    typename conditional_t<is_signed_v<T> || is_same_v<T, __int128_t>,
                           true_type, false_type>::type;

template <typename T>
using is_broadly_unsigned =
    typename conditional_t<is_unsigned_v<T> || is_same_v<T, __uint128_t>,
                           true_type, false_type>::type;

#define ENABLE_VALUE(x) \
  template <typename T> \
  constexpr bool x##_v = x<T>::value;

ENABLE_VALUE(is_broadly_integral);
ENABLE_VALUE(is_broadly_signed);
ENABLE_VALUE(is_broadly_unsigned);
#undef ENABLE_VALUE

#define ENABLE_HAS_TYPE(var)                                   \
  template <class, class = void>                               \
  struct has_##var : false_type {};                            \
  template <class T>                                           \
  struct has_##var<T, void_t<typename T::var>> : true_type {}; \
  template <class T>                                           \
  constexpr auto has_##var##_v = has_##var<T>::value;

#define ENABLE_HAS_VAR(var)                                     \
  template <class, class = void>                                \
  struct has_##var : false_type {};                             \
  template <class T>                                            \
  struct has_##var<T, void_t<decltype(T::var)>> : true_type {}; \
  template <class T>                                            \
  constexpr auto has_##var##_v = has_##var<T>::value;

}  // namespace internal
#line 12 "misc/fastio.hpp"

namespace fastio {
static constexpr int SZ = 1 << 17;
static constexpr int offset = 64;
char inbuf[SZ], outbuf[SZ];
int in_left = 0, in_right = 0, out_right = 0;

struct Pre {
  char num[40000];
  constexpr Pre() : num() {
    for (int i = 0; i < 10000; i++) {
      int n = i;
      for (int j = 3; j >= 0; j--) {
        num[i * 4 + j] = n % 10 + '0';
        n /= 10;
      }
    }
  }
} constexpr pre;

void load() {
  int len = in_right - in_left;
  memmove(inbuf, inbuf + in_left, len);
  in_right = len + fread(inbuf + len, 1, SZ - len, stdin);
  in_left = 0;
}
void flush() {
  fwrite(outbuf, 1, out_right, stdout);
  out_right = 0;
}
void skip_space() {
  if (in_left + offset > in_right) load();
  while (inbuf[in_left] <= ' ') in_left++;
}

void single_read(char& c) {
  if (in_left + offset > in_right) load();
  skip_space();
  c = inbuf[in_left++];
}
void single_read(string& S) {
  skip_space();
  while (true) {
    if (in_left == in_right) load();
    int i = in_left;
    for (; i != in_right; i++) {
      if (inbuf[i] <= ' ') break;
    }
    copy(inbuf + in_left, inbuf + i, back_inserter(S));
    in_left = i;
    if (i != in_right) break;
  }
}
template <typename T,
          enable_if_t<internal::is_broadly_integral_v<T>>* = nullptr>
void single_read(T& x) {
  if (in_left + offset > in_right) load();
  skip_space();
  char c = inbuf[in_left++];
  [[maybe_unused]] bool minus = false;
  if constexpr (internal::is_broadly_signed_v<T>) {
    if (c == '-') minus = true, c = inbuf[in_left++];
  }
  x = 0;
  while (c >= '0') {
    x = x * 10 + (c & 15);
    c = inbuf[in_left++];
  }
  if constexpr (internal::is_broadly_signed_v<T>) {
    if (minus) x = -x;
  }
}
void rd() {}
template <typename Head, typename... Tail>
void rd(Head& head, Tail&... tail) {
  single_read(head);
  rd(tail...);
}

void single_write(const char& c) {
  if (out_right > SZ - offset) flush();
  outbuf[out_right++] = c;
}
void single_write(const bool& b) {
  if (out_right > SZ - offset) flush();
  outbuf[out_right++] = b ? '1' : '0';
}
void single_write(const string& S) {
  flush(), fwrite(S.data(), 1, S.size(), stdout);
}
void single_write(const char* p) { flush(), fwrite(p, 1, strlen(p), stdout); }
template <typename T,
          enable_if_t<internal::is_broadly_integral_v<T>>* = nullptr>
void single_write(const T& _x) {
  if (out_right > SZ - offset) flush();
  if (_x == 0) {
    outbuf[out_right++] = '0';
    return;
  }
  T x = _x;
  if constexpr (internal::is_broadly_signed_v<T>) {
    if (x < 0) outbuf[out_right++] = '-', x = -x;
  }
  constexpr int buffer_size = sizeof(T) * 10 / 4;
  char buf[buffer_size];
  int i = buffer_size;
  while (x >= 10000) {
    i -= 4;
    memcpy(buf + i, pre.num + (x % 10000) * 4, 4);
    x /= 10000;
  }
  if (x < 100) {
    if (x < 10) {
      outbuf[out_right] = '0' + x;
      ++out_right;
    } else {
      uint32_t q = (uint32_t(x) * 205) >> 11;
      uint32_t r = uint32_t(x) - q * 10;
      outbuf[out_right] = '0' + q;
      outbuf[out_right + 1] = '0' + r;
      out_right += 2;
    }
  } else {
    if (x < 1000) {
      memcpy(outbuf + out_right, pre.num + (x << 2) + 1, 3);
      out_right += 3;
    } else {
      memcpy(outbuf + out_right, pre.num + (x << 2), 4);
      out_right += 4;
    }
  }
  memcpy(outbuf + out_right, buf + i, buffer_size - i);
  out_right += buffer_size - i;
}
void wt() {}
template <typename Head, typename... Tail>
void wt(const Head& head, const Tail&... tail) {
  single_write(head);
  wt(std::forward<const Tail>(tail)...);
}
template <typename... Args>
void wtn(const Args&... x) {
  wt(std::forward<const Args>(x)...);
  wt('\n');
}

struct Dummy {
  Dummy() { atexit(flush); }
} dummy;

}  // namespace fastio
using fastio::rd;
using fastio::skip_space;
using fastio::wt;
using fastio::wtn;
#line 8 "verify/verify-yosupo-graph/yosupo-frequency-table-of-tree-distance.test.cpp"

#line 2 "tree/frequency-table-of-tree-distance.hpp"

#line 2 "ntt/arbitrary-ntt-mod18446744069414584321.hpp"

#line 7 "ntt/arbitrary-ntt-mod18446744069414584321.hpp"
using namespace std;

struct ModInt18446744069414584321 {
  using M = ModInt18446744069414584321;
  using U = unsigned long long;
  using U128 = __uint128_t;

  static constexpr U mod = 18446744069414584321uLL;
  U x;

  static constexpr U modulo(U128 y) {
    U l = y & U(-1);
    U m = (y >> 64) & unsigned(-1);
    U h = y >> 96;
    U u = h + m + (m ? mod - (m << 32) : 0);
    U v = mod <= l ? l - mod : l;
    return v - u + (v < u ? mod : 0);
  }

  ModInt18446744069414584321() : x(0) {}
  ModInt18446744069414584321(U _x) : x(_x) {}
  U get() const { return x; }
  static U get_mod() { return mod; }

  friend M operator+(const M& l, const M& r) {
    U y = l.x - (mod - r.x);
    if (l.x < mod - r.x) y += mod;
    return M{y};
  }
  friend M operator-(const M& l, const M& r) {
    U y = l.x - r.x;
    if (l.x < r.x) y += mod;
    return M{y};
  }
  friend M operator*(const M& l, const M& r) {
    return M{modulo(U128(l.x) * r.x)};
  }
  friend M operator/(const M& l, const M& r) {
    return M{modulo(U128(l.x) * r.inverse().x)};
  }

  M& operator+=(const M& r) { return *this = *this + r; }
  M& operator-=(const M& r) { return *this = *this - r; }
  M& operator*=(const M& r) { return *this = *this * r; }
  M& operator/=(const M& r) { return *this = *this / r; }
  M operator-() const { return M{x ? mod - x : 0uLL}; }
  M operator+() const { return *this; }

  M pow(U e) const {
    M res{1}, a{*this};
    while (e) {
      if (e & 1) res = res * a;
      a = a * a;
      e >>= 1;
    }
    return res;
  }
  M inverse() const {
    assert(x != 0);
    return this->pow(mod - 2);
  }

  friend bool operator==(const M& l, const M& r) { return l.x == r.x; }
  friend bool operator!=(const M& l, const M& r) { return l.x != r.x; }
  friend ostream& operator<<(ostream& os, const M& r) { return os << r.x; }
};

struct NTT18446744069414584321 {
  using mint = ModInt18446744069414584321;
  using U = typename mint::U;

  static constexpr U mod = mint::mod;
  static constexpr U pr = 7;
  static constexpr int level = 32;
  mint dw[level], dy[level];

  void setwy(int k) {
    mint w[level], y[level];
    w[k - 1] = mint(pr).pow((mod - 1) / (1LL << k));
    y[k - 1] = w[k - 1].inverse();
    for (int i = k - 2; i > 0; --i)
      w[i] = w[i + 1] * w[i + 1], y[i] = y[i + 1] * y[i + 1];
    dw[1] = w[1], dy[1] = y[1], dw[2] = w[2], dy[2] = y[2];
    for (int i = 3; i < k; ++i) {
      dw[i] = dw[i - 1] * y[i - 2] * w[i];
      dy[i] = dy[i - 1] * w[i - 2] * y[i];
    }
  }

  NTT18446744069414584321() { setwy(level); }

  void fft(vector<mint>& a, int k) {
    if ((int)a.size() <= 1) return;
    if (k == 1) {
      mint a1 = a[1];
      a[1] = a[0] - a[1];
      a[0] = a[0] + a1;
      return;
    }
    if (k & 1) {
      int v = 1 << (k - 1);
      for (int j = 0; j < v; ++j) {
        mint ajv = a[j + v];
        a[j + v] = a[j] - ajv;
        a[j] += ajv;
      }
    }
    int u = 1 << (2 + (k & 1));
    int v = 1 << (k - 2 - (k & 1));
    mint one = mint(1);
    mint imag = dw[1];
    while (v) {
      {
        int j0 = 0;
        int j1 = v;
        int j2 = j1 + v;
        int j3 = j2 + v;
        for (; j0 < v; ++j0, ++j1, ++j2, ++j3) {
          mint t0 = a[j0], t1 = a[j1], t2 = a[j2], t3 = a[j3];
          mint t0p2 = t0 + t2, t1p3 = t1 + t3;
          mint t0m2 = t0 - t2, t1m3 = (t1 - t3) * imag;
          a[j0] = t0p2 + t1p3, a[j1] = t0p2 - t1p3;
          a[j2] = t0m2 + t1m3, a[j3] = t0m2 - t1m3;
        }
      }
      mint ww = one, xx = one * dw[2], wx = one;
      for (int jh = 4; jh < u;) {
        ww = xx * xx, wx = ww * xx;
        int j0 = jh * v;
        int je = j0 + v;
        int j2 = je + v;
        for (; j0 < je; ++j0, ++j2) {
          mint t0 = a[j0], t1 = a[j0 + v] * xx, t2 = a[j2] * ww,
               t3 = a[j2 + v] * wx;
          mint t0p2 = t0 + t2, t1p3 = t1 + t3;
          mint t0m2 = t0 - t2, t1m3 = (t1 - t3) * imag;
          a[j0] = t0p2 + t1p3, a[j0 + v] = t0p2 - t1p3;
          a[j2] = t0m2 + t1m3, a[j2 + v] = t0m2 - t1m3;
        }
        xx *= dw[__builtin_ctzll((jh += 4))];
      }
      u <<= 2;
      v >>= 2;
    }
  }

  void ifft(vector<mint>& a, int k) {
    if ((int)a.size() <= 1) return;
    if (k == 1) {
      mint a1 = a[1];
      a[1] = a[0] - a[1];
      a[0] = a[0] + a1;
      return;
    }
    int u = 1 << (k - 2);
    int v = 1;
    mint one = mint(1);
    mint imag = dy[1];
    while (u) {
      {
        int j0 = 0;
        int j1 = v;
        int j2 = v + v;
        int j3 = j2 + v;
        for (; j0 < v; ++j0, ++j1, ++j2, ++j3) {
          mint t0 = a[j0], t1 = a[j1], t2 = a[j2], t3 = a[j3];
          mint t0p1 = t0 + t1, t2p3 = t2 + t3;
          mint t0m1 = t0 - t1, t2m3 = (t2 - t3) * imag;
          a[j0] = t0p1 + t2p3, a[j2] = t0p1 - t2p3;
          a[j1] = t0m1 + t2m3, a[j3] = t0m1 - t2m3;
        }
      }
      mint ww = one, xx = one * dy[2], yy = one;
      u <<= 2;
      for (int jh = 4; jh < u;) {
        ww = xx * xx, yy = xx * imag;
        int j0 = jh * v;
        int je = j0 + v;
        int j2 = je + v;
        for (; j0 < je; ++j0, ++j2) {
          mint t0 = a[j0], t1 = a[j0 + v], t2 = a[j2], t3 = a[j2 + v];
          mint t0p1 = t0 + t1, t2p3 = t2 + t3;
          mint t0m1 = (t0 - t1) * xx, t2m3 = (t2 - t3) * yy;
          a[j0] = t0p1 + t2p3, a[j2] = (t0p1 - t2p3) * ww;
          a[j0 + v] = t0m1 + t2m3, a[j2 + v] = (t0m1 - t2m3) * ww;
        }
        xx *= dy[__builtin_ctzll(jh += 4)];
      }
      u >>= 4;
      v <<= 2;
    }
    if (k & 1) {
      u = 1 << (k - 1);
      for (int j = 0; j < u; ++j) {
        mint ajv = a[j] - a[j + u];
        a[j] += a[j + u];
        a[j + u] = ajv;
      }
    }
  }

  void ntt(vector<mint>& a) {
    if ((int)a.size() <= 1) return;
    fft(a, __builtin_ctz(a.size()));
  }

  void intt(vector<mint>& a) {
    if ((int)a.size() <= 1) return;
    ifft(a, __builtin_ctz(a.size()));
    mint iv = mint(a.size()).inverse();
    for (auto& x : a) x *= iv;
  }

  vector<mint> multiply(const vector<mint>& a, const vector<mint>& b) {
    int l = a.size() + b.size() - 1;
    if (min<int>(a.size(), b.size()) <= 40) {
      vector<mint> s(l);
      for (int i = 0; i < (int)a.size(); ++i)
        for (int j = 0; j < (int)b.size(); ++j) s[i + j] += a[i] * b[j];
      return s;
    }
    int k = 2, M = 4;
    while (M < l) M <<= 1, ++k;
    setwy(k);
    vector<mint> s(M);
    for (int i = 0; i < (int)a.size(); ++i) s[i] = a[i];
    if (a == b) {
      fft(s, k);
      for (int i = 0; i < M; i++) s[i] *= s[i];
    } else {
      vector<mint> t(M);
      for (int i = 0; i < (int)b.size(); ++i) t[i] = b[i];
      fft(s, k), fft(t, k);
      for (int i = 0; i < M; ++i) s[i] *= t[i];
    }
    ifft(s, k);
    s.resize(l);
    mint invm = mint(M).inverse();
    for (int i = 0; i < l; ++i) s[i] *= invm;
    return s;
  }

  // すべての要素が正, かつ答えの各成分が mod 以下である必要がある
  template <typename I, enable_if_t<is_integral_v<I>>* = nullptr>
  vector<unsigned long long> multiply(const vector<I>& a, const vector<I>& b) {
    if (min<int>(a.size(), b.size()) <= 40) {
      vector<U> c(a.size() + b.size() - 1);
      for (int i = 0; i < (int)a.size(); ++i) {
        for (int j = 0; j < (int)b.size(); ++j) c[i + j] += U(a[i]) * U(b[j]);
      }
      return c;
    }
    vector<mint> s(a.size()), t(b.size());
    for (int i = 0; i < (int)a.size(); i++) s[i] = a[i];
    for (int i = 0; i < (int)b.size(); i++) t[i] = b[i];
    auto u = multiply(s, t);
    vector<U> c(u.size());
    for (int i = 0; i < (int)c.size(); i++) c[i] = u[i].x;
    return c;
  }

  vector<int> bigint_mul_base_10_9(const vector<int>& a, const vector<int>& b) {
    constexpr int D = 1000000000;
    constexpr int B = 1000000;
    constexpr int C = 1000;
    auto convert = [&](const vector<int>& v) -> vector<mint> {
      vector<mint> c((v.size() * 3 + 1) / 2);
      int i = 0;
      for (; i * 2 + 1 < (int)v.size(); i++) {
        c[i * 3 + 0].x = v[i * 2 + 0] % B;
        c[i * 3 + 1].x = v[i * 2 + 0] / B + v[i * 2 + 1] % C * C;
        c[i * 3 + 2].x = v[i * 2 + 1] / C;
      }
      if (i * 2 + 1 == (int)v.size()) {
        c[i * 3 + 0].x = v[i * 2 + 0] % B;
        c[i * 3 + 1].x = v[i * 2 + 0] / B;
      }
      return c;
    };
    auto revert = [&](const vector<mint>& v) -> vector<int> {
      vector<int> c(v.size() + 4);
      int i = 0;
      U s = 0;
      for (; i < (int)v.size(); i++) s += v[i].x, c[i] = s % B, s /= B;
      while (s) c[i] = s % B, s /= B, i++;
      while (!c.empty() && c.back() == 0) c.pop_back();
      i = 0;
      for (; i * 3 + 0 < (int)c.size(); i++) {
        long long x = c[i * 3 + 0];
        c[i * 3 + 0] = 0;
        if (i * 3 + 1 < (int)c.size()) {
          x += 1LL * c[i * 3 + 1] * B;
          c[i * 3 + 1] = 0;
        }
        if (i * 3 + 2 < (int)c.size()) {
          x += 1LL * c[i * 3 + 2] * (1LL * B * B);
          c[i * 3 + 2] = 0;
        }
        c[i * 2 + 0] = x % D;
        if (i * 2 + 1 < (int)c.size()) c[i * 2 + 1] = x / D;
      }
      while (!c.empty() && c.back() == 0) c.pop_back();
      return c;
    };
    return revert(multiply(convert(a), convert(b)));
  }
};

NTT18446744069414584321 ntt18446744069414584321;

/**
 *  mod 18446744069414584321 (= 2^64 - 2^32 + 1) 上の数論変換
 */
#line 2 "ntt/arbitrary-ntt.hpp"

#line 2 "modint/montgomery-modint.hpp"

template <uint32_t mod>
struct LazyMontgomeryModInt {
  using mint = LazyMontgomeryModInt;
  using i32 = int32_t;
  using u32 = uint32_t;
  using u64 = uint64_t;

  static constexpr u32 get_r() {
    u32 ret = mod;
    for (i32 i = 0; i < 4; ++i) ret *= 2 - mod * ret;
    return ret;
  }

  static constexpr u32 r = get_r();
  static constexpr u32 n2 = -u64(mod) % mod;
  static_assert(mod < (1 << 30), "invalid, mod >= 2 ^ 30");
  static_assert((mod & 1) == 1, "invalid, mod % 2 == 0");
  static_assert(r * mod == 1, "this code has bugs.");

  u32 a;

  constexpr LazyMontgomeryModInt() : a(0) {}
  constexpr LazyMontgomeryModInt(const int64_t &b)
      : a(reduce(u64(b % mod + mod) * n2)){};

  static constexpr u32 reduce(const u64 &b) {
    return (b + u64(u32(b) * u32(-r)) * mod) >> 32;
  }

  constexpr mint &operator+=(const mint &b) {
    if (i32(a += b.a - 2 * mod) < 0) a += 2 * mod;
    return *this;
  }

  constexpr mint &operator-=(const mint &b) {
    if (i32(a -= b.a) < 0) a += 2 * mod;
    return *this;
  }

  constexpr mint &operator*=(const mint &b) {
    a = reduce(u64(a) * b.a);
    return *this;
  }

  constexpr mint &operator/=(const mint &b) {
    *this *= b.inverse();
    return *this;
  }

  constexpr mint operator+(const mint &b) const { return mint(*this) += b; }
  constexpr mint operator-(const mint &b) const { return mint(*this) -= b; }
  constexpr mint operator*(const mint &b) const { return mint(*this) *= b; }
  constexpr mint operator/(const mint &b) const { return mint(*this) /= b; }
  constexpr bool operator==(const mint &b) const {
    return (a >= mod ? a - mod : a) == (b.a >= mod ? b.a - mod : b.a);
  }
  constexpr bool operator!=(const mint &b) const {
    return (a >= mod ? a - mod : a) != (b.a >= mod ? b.a - mod : b.a);
  }
  constexpr mint operator-() const { return mint() - mint(*this); }
  constexpr mint operator+() const { return mint(*this); }

  constexpr mint pow(u64 n) const {
    mint ret(1), mul(*this);
    while (n > 0) {
      if (n & 1) ret *= mul;
      mul *= mul;
      n >>= 1;
    }
    return ret;
  }

  constexpr mint inverse() const {
    int x = get(), y = mod, u = 1, v = 0, t = 0, tmp = 0;
    while (y > 0) {
      t = x / y;
      x -= t * y, u -= t * v;
      tmp = x, x = y, y = tmp;
      tmp = u, u = v, v = tmp;
    }
    return mint{u};
  }

  friend ostream &operator<<(ostream &os, const mint &b) {
    return os << b.get();
  }

  friend istream &operator>>(istream &is, mint &b) {
    int64_t t;
    is >> t;
    b = LazyMontgomeryModInt<mod>(t);
    return (is);
  }

  constexpr u32 get() const {
    u32 ret = reduce(a);
    return ret >= mod ? ret - mod : ret;
  }

  static constexpr u32 get_mod() { return mod; }
};
#line 2 "ntt/ntt.hpp"

template <typename mint>
struct NTT {
  static constexpr uint32_t get_pr() {
    uint32_t _mod = mint::get_mod();
    using u64 = uint64_t;
    u64 ds[32] = {};
    int idx = 0;
    u64 m = _mod - 1;
    for (u64 i = 2; i * i <= m; ++i) {
      if (m % i == 0) {
        ds[idx++] = i;
        while (m % i == 0) m /= i;
      }
    }
    if (m != 1) ds[idx++] = m;

    uint32_t _pr = 2;
    while (1) {
      int flg = 1;
      for (int i = 0; i < idx; ++i) {
        u64 a = _pr, b = (_mod - 1) / ds[i], r = 1;
        while (b) {
          if (b & 1) r = r * a % _mod;
          a = a * a % _mod;
          b >>= 1;
        }
        if (r == 1) {
          flg = 0;
          break;
        }
      }
      if (flg == 1) break;
      ++_pr;
    }
    return _pr;
  };

  static constexpr uint32_t mod = mint::get_mod();
  static constexpr uint32_t pr = get_pr();
  static constexpr int level = __builtin_ctzll(mod - 1);
  mint dw[level], dy[level];

  void setwy(int k) {
    mint w[level], y[level];
    w[k - 1] = mint(pr).pow((mod - 1) / (1 << k));
    y[k - 1] = w[k - 1].inverse();
    for (int i = k - 2; i > 0; --i)
      w[i] = w[i + 1] * w[i + 1], y[i] = y[i + 1] * y[i + 1];
    dw[1] = w[1], dy[1] = y[1], dw[2] = w[2], dy[2] = y[2];
    for (int i = 3; i < k; ++i) {
      dw[i] = dw[i - 1] * y[i - 2] * w[i];
      dy[i] = dy[i - 1] * w[i - 2] * y[i];
    }
  }

  NTT() { setwy(level); }

  void fft4(vector<mint> &a, int k) {
    if ((int)a.size() <= 1) return;
    if (k == 1) {
      mint a1 = a[1];
      a[1] = a[0] - a[1];
      a[0] = a[0] + a1;
      return;
    }
    if (k & 1) {
      int v = 1 << (k - 1);
      for (int j = 0; j < v; ++j) {
        mint ajv = a[j + v];
        a[j + v] = a[j] - ajv;
        a[j] += ajv;
      }
    }
    int u = 1 << (2 + (k & 1));
    int v = 1 << (k - 2 - (k & 1));
    mint one = mint(1);
    mint imag = dw[1];
    while (v) {
      // jh = 0
      {
        int j0 = 0;
        int j1 = v;
        int j2 = j1 + v;
        int j3 = j2 + v;
        for (; j0 < v; ++j0, ++j1, ++j2, ++j3) {
          mint t0 = a[j0], t1 = a[j1], t2 = a[j2], t3 = a[j3];
          mint t0p2 = t0 + t2, t1p3 = t1 + t3;
          mint t0m2 = t0 - t2, t1m3 = (t1 - t3) * imag;
          a[j0] = t0p2 + t1p3, a[j1] = t0p2 - t1p3;
          a[j2] = t0m2 + t1m3, a[j3] = t0m2 - t1m3;
        }
      }
      // jh >= 1
      mint ww = one, xx = one * dw[2], wx = one;
      for (int jh = 4; jh < u;) {
        ww = xx * xx, wx = ww * xx;
        int j0 = jh * v;
        int je = j0 + v;
        int j2 = je + v;
        for (; j0 < je; ++j0, ++j2) {
          mint t0 = a[j0], t1 = a[j0 + v] * xx, t2 = a[j2] * ww,
               t3 = a[j2 + v] * wx;
          mint t0p2 = t0 + t2, t1p3 = t1 + t3;
          mint t0m2 = t0 - t2, t1m3 = (t1 - t3) * imag;
          a[j0] = t0p2 + t1p3, a[j0 + v] = t0p2 - t1p3;
          a[j2] = t0m2 + t1m3, a[j2 + v] = t0m2 - t1m3;
        }
        xx *= dw[__builtin_ctzll((jh += 4))];
      }
      u <<= 2;
      v >>= 2;
    }
  }

  void ifft4(vector<mint> &a, int k) {
    if ((int)a.size() <= 1) return;
    if (k == 1) {
      mint a1 = a[1];
      a[1] = a[0] - a[1];
      a[0] = a[0] + a1;
      return;
    }
    int u = 1 << (k - 2);
    int v = 1;
    mint one = mint(1);
    mint imag = dy[1];
    while (u) {
      // jh = 0
      {
        int j0 = 0;
        int j1 = v;
        int j2 = v + v;
        int j3 = j2 + v;
        for (; j0 < v; ++j0, ++j1, ++j2, ++j3) {
          mint t0 = a[j0], t1 = a[j1], t2 = a[j2], t3 = a[j3];
          mint t0p1 = t0 + t1, t2p3 = t2 + t3;
          mint t0m1 = t0 - t1, t2m3 = (t2 - t3) * imag;
          a[j0] = t0p1 + t2p3, a[j2] = t0p1 - t2p3;
          a[j1] = t0m1 + t2m3, a[j3] = t0m1 - t2m3;
        }
      }
      // jh >= 1
      mint ww = one, xx = one * dy[2], yy = one;
      u <<= 2;
      for (int jh = 4; jh < u;) {
        ww = xx * xx, yy = xx * imag;
        int j0 = jh * v;
        int je = j0 + v;
        int j2 = je + v;
        for (; j0 < je; ++j0, ++j2) {
          mint t0 = a[j0], t1 = a[j0 + v], t2 = a[j2], t3 = a[j2 + v];
          mint t0p1 = t0 + t1, t2p3 = t2 + t3;
          mint t0m1 = (t0 - t1) * xx, t2m3 = (t2 - t3) * yy;
          a[j0] = t0p1 + t2p3, a[j2] = (t0p1 - t2p3) * ww;
          a[j0 + v] = t0m1 + t2m3, a[j2 + v] = (t0m1 - t2m3) * ww;
        }
        xx *= dy[__builtin_ctzll(jh += 4)];
      }
      u >>= 4;
      v <<= 2;
    }
    if (k & 1) {
      u = 1 << (k - 1);
      for (int j = 0; j < u; ++j) {
        mint ajv = a[j] - a[j + u];
        a[j] += a[j + u];
        a[j + u] = ajv;
      }
    }
  }

  void ntt(vector<mint> &a) {
    if ((int)a.size() <= 1) return;
    fft4(a, __builtin_ctz(a.size()));
  }

  void intt(vector<mint> &a) {
    if ((int)a.size() <= 1) return;
    ifft4(a, __builtin_ctz(a.size()));
    mint iv = mint(a.size()).inverse();
    for (auto &x : a) x *= iv;
  }

  vector<mint> multiply(const vector<mint> &a, const vector<mint> &b) {
    int l = a.size() + b.size() - 1;
    if (min<int>(a.size(), b.size()) <= 40) {
      vector<mint> s(l);
      for (int i = 0; i < (int)a.size(); ++i)
        for (int j = 0; j < (int)b.size(); ++j) s[i + j] += a[i] * b[j];
      return s;
    }
    int k = 2, M = 4;
    while (M < l) M <<= 1, ++k;
    setwy(k);
    vector<mint> s(M);
    for (int i = 0; i < (int)a.size(); ++i) s[i] = a[i];
    fft4(s, k);
    if (a.size() == b.size() && a == b) {
      for (int i = 0; i < M; ++i) s[i] *= s[i];
    } else {
      vector<mint> t(M);
      for (int i = 0; i < (int)b.size(); ++i) t[i] = b[i];
      fft4(t, k);
      for (int i = 0; i < M; ++i) s[i] *= t[i];
    }
    ifft4(s, k);
    s.resize(l);
    mint invm = mint(M).inverse();
    for (int i = 0; i < l; ++i) s[i] *= invm;
    return s;
  }

  void ntt_doubling(vector<mint> &a) {
    int M = (int)a.size();
    auto b = a;
    intt(b);
    mint r = 1, zeta = mint(pr).pow((mint::get_mod() - 1) / (M << 1));
    for (int i = 0; i < M; i++) b[i] *= r, r *= zeta;
    ntt(b);
    copy(begin(b), end(b), back_inserter(a));
  }
};
#line 5 "ntt/arbitrary-ntt.hpp"

namespace ArbitraryNTT {
using i64 = int64_t;
using u128 = __uint128_t;
constexpr int32_t m0 = 167772161;
constexpr int32_t m1 = 469762049;
constexpr int32_t m2 = 754974721;
using mint0 = LazyMontgomeryModInt<m0>;
using mint1 = LazyMontgomeryModInt<m1>;
using mint2 = LazyMontgomeryModInt<m2>;
constexpr int r01 = mint1(m0).inverse().get();
constexpr int r02 = mint2(m0).inverse().get();
constexpr int r12 = mint2(m1).inverse().get();
constexpr int r02r12 = i64(r02) * r12 % m2;
constexpr i64 w1 = m0;
constexpr i64 w2 = i64(m0) * m1;

template <typename T, typename submint>
vector<submint> mul(const vector<T> &a, const vector<T> &b) {
  static NTT<submint> ntt;
  vector<submint> s(a.size()), t(b.size());
  for (int i = 0; i < (int)a.size(); ++i) s[i] = i64(a[i] % submint::get_mod());
  for (int i = 0; i < (int)b.size(); ++i) t[i] = i64(b[i] % submint::get_mod());
  return ntt.multiply(s, t);
}

template <typename T>
vector<int> multiply(const vector<T> &s, const vector<T> &t, int mod) {
  auto d0 = mul<T, mint0>(s, t);
  auto d1 = mul<T, mint1>(s, t);
  auto d2 = mul<T, mint2>(s, t);
  int n = d0.size();
  vector<int> ret(n);
  const int W1 = w1 % mod;
  const int W2 = w2 % mod;
  for (int i = 0; i < n; i++) {
    int n1 = d1[i].get(), n2 = d2[i].get(), a = d0[i].get();
    int b = i64(n1 + m1 - a) * r01 % m1;
    int c = (i64(n2 + m2 - a) * r02r12 + i64(m2 - b) * r12) % m2;
    ret[i] = (i64(a) + i64(b) * W1 + i64(c) * W2) % mod;
  }
  return ret;
}

template <typename mint>
vector<mint> multiply(const vector<mint> &a, const vector<mint> &b) {
  if (a.size() == 0 && b.size() == 0) return {};
  if (min<int>(a.size(), b.size()) < 128) {
    vector<mint> ret(a.size() + b.size() - 1);
    for (int i = 0; i < (int)a.size(); ++i)
      for (int j = 0; j < (int)b.size(); ++j) ret[i + j] += a[i] * b[j];
    return ret;
  }
  vector<int> s(a.size()), t(b.size());
  for (int i = 0; i < (int)a.size(); ++i) s[i] = a[i].get();
  for (int i = 0; i < (int)b.size(); ++i) t[i] = b[i].get();
  vector<int> u = multiply<int>(s, t, mint::get_mod());
  vector<mint> ret(u.size());
  for (int i = 0; i < (int)u.size(); ++i) ret[i] = mint(u[i]);
  return ret;
}

template <typename T>
vector<u128> multiply_u128(const vector<T> &s, const vector<T> &t) {
  if (s.size() == 0 && t.size() == 0) return {};
  if (min<int>(s.size(), t.size()) < 128) {
    vector<u128> ret(s.size() + t.size() - 1);
    for (int i = 0; i < (int)s.size(); ++i)
      for (int j = 0; j < (int)t.size(); ++j) ret[i + j] += i64(s[i]) * t[j];
    return ret;
  }
  auto d0 = mul<T, mint0>(s, t);
  auto d1 = mul<T, mint1>(s, t);
  auto d2 = mul<T, mint2>(s, t);
  int n = d0.size();
  vector<u128> ret(n);
  for (int i = 0; i < n; i++) {
    i64 n1 = d1[i].get(), n2 = d2[i].get();
    i64 a = d0[i].get();
    i64 b = (n1 + m1 - a) * r01 % m1;
    i64 c = ((n2 + m2 - a) * r02r12 + (m2 - b) * r12) % m2;
    ret[i] = a + b * w1 + u128(c) * w2;
  }
  return ret;
}
}  // namespace ArbitraryNTT
#line 2 "tree/centroid-decomposition.hpp"



template <typename G>
struct CentroidDecomposition {
  const G &g;
  vector<int> sub;
  vector<bool> v;
  vector<vector<int>> tree;
  int root;

  CentroidDecomposition(const G &g_, int isbuild = true) : g(g_) {
    sub.resize(g.size(), 0);
    v.resize(g.size(), false);
    if (isbuild) build();
  }

  void build() {
    tree.resize(g.size());
    root = build_dfs(0);
  }

  int get_size(int cur, int par) {
    sub[cur] = 1;
    for (auto &dst : g[cur]) {
      if (dst == par || v[dst]) continue;
      sub[cur] += get_size(dst, cur);
    }
    return sub[cur];
  }

  int get_centroid(int cur, int par, int mid) {
    for (auto &dst : g[cur]) {
      if (dst == par || v[dst]) continue;
      if (sub[dst] > mid) return get_centroid(dst, cur, mid);
    }
    return cur;
  }

  int build_dfs(int cur) {
    int centroid = get_centroid(cur, -1, get_size(cur, -1) / 2);
    v[centroid] = true;
    for (auto &dst : g[centroid]) {
      if (!v[dst]) {
        int nxt = build_dfs(dst);
        if (centroid != nxt) tree[centroid].emplace_back(nxt);
      }
    }
    v[centroid] = false;
    return centroid;
  }
};

/**
 * @brief Centroid Decomposition
 * @docs docs/tree/centroid-decomposition.md
 */
#line 6 "tree/frequency-table-of-tree-distance.hpp"

template <typename G>
struct FrequencyTableOfTreeDistance : CentroidDecomposition<G> {
  using CentroidDecomposition<G>::g;
  using CentroidDecomposition<G>::v;
  using CentroidDecomposition<G>::get_size;
  using CentroidDecomposition<G>::get_centroid;

  FrequencyTableOfTreeDistance(const G &_g)
      : CentroidDecomposition<G>(_g, false) {}

  vector<long long> count, self;

  void dfs_depth(int cur, int par, int d) {
    while ((int)count.size() <= d) count.emplace_back(0);
    while ((int)self.size() <= d) self.emplace_back(0);
    ++count[d];
    ++self[d];
    for (int dst : g[cur]) {
      if (par == dst || v[dst]) continue;
      dfs_depth(dst, cur, d + 1);
    }
  };

  vector<long long> get(int start = 0) {
    queue<int> Q;
    Q.push(get_centroid(start, -1, get_size(start, -1) / 2));
    vector<long long> ans;
    ans.reserve(g.size());
    count.reserve(g.size());
    self.reserve(g.size());

    while (!Q.empty()) {
      int r = Q.front();
      Q.pop();
      count.clear();
      v[r] = 1;
      for (auto &c : g[r]) {
        if (v[c]) continue;
        self.clear();
        Q.emplace(get_centroid(c, -1, get_size(c, -1) / 2));
        dfs_depth(c, r, 1);
        auto self2 = ntt18446744069414584321.multiply(self, self);
        while (self2.size() > ans.size()) ans.emplace_back(0);
        for (int i = 0; i < (int)self2.size(); i++) ans[i] -= self2[i];
      }
      if (count.empty()) continue;
      ++count[0];
      auto count2 = ntt18446744069414584321.multiply(count, count);
      while (count2.size() > ans.size()) ans.emplace_back(0);
      for (int i = 0; i < (int)count2.size(); i++) ans[i] += count2[i];
    }

    for (auto &x : ans) x >>= 1;
    return ans;
  }
};

/**
 * @brief 頂点間の距離の度数分布
 * @docs docs/tree/frequency-table-of-tree-distance.md
 */
#line 10 "verify/verify-yosupo-graph/yosupo-frequency-table-of-tree-distance.test.cpp"

using namespace Nyaan; void Nyaan::solve() {
  int N;
  rd(N);
  vvi g(N);
  rep(_, N - 1) {
    int u, v;
    rd(u, v);
    g[u].push_back(v);
    g[v].push_back(u);
  }
  FrequencyTableOfTreeDistance<vvi> ft(g);
  auto d = ft.get();
  d.resize(N);
  rep1(i, N - 1) {
    if (i != 1) wt(' ');
    wt(d[i]);
  }
  wt('\n');
}

Nyaan's Library

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verify/verify-yosupo-graph/yosupo-frequency-table-of-tree-distance.test.cpp

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