#include "tree/frequency-table-of-tree-distance.hpp"
頂点間の距離の度数分布を$\mathrm{O}(n \log^2 n)$で計算するライブラリ。
FrequencyTableOfTreeDistance(const G &g)
get(start = 0)
#pragma once #include "../ntt/arbitrary-ntt-mod18446744069414584321.hpp" #include "../ntt/arbitrary-ntt.hpp" #include "./centroid-decomposition.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 2 "tree/frequency-table-of-tree-distance.hpp" #line 2 "ntt/arbitrary-ntt-mod18446744069414584321.hpp" #include <cassert> #include <iostream> #include <type_traits> #include <vector> 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 */