結果
| 問題 | No.3620 Compositional Power with Schröder Coordinate 2 |
| コンテスト | |
| ユーザー |
 apricity
|
| 提出日時 | 2026-08-10 23:38:46 |
| 言語 | C++23 (gcc 15.2.0 + boost 1.90.0) |
| 結果 |
AC
|
| 実行時間 | 1,170 ms / 10,000 ms |
| + 275µs | |
| コード長 | 30,426 bytes |
| 記録 | |
| コンパイル時間 | 3,512 ms |
| コンパイル使用メモリ | 336,604 KB |
| 実行使用メモリ | 33,400 KB |
| 最終ジャッジ日時 | 2026-08-11 00:01:28 |
| 合計ジャッジ時間 | 11,519 ms |
|
ジャッジサーバーID （参考情報） |
judge3_1 / judge2_0 |
（要ログイン）
| ファイルパターン | 結果 |
|---|---|
| sample | AC * 2 |
| other | AC * 7 |
ソースコード
#ifdef LOCAL
#include "template.hpp"
#else
#include<iostream>
#include<string>
#include<vector>
#include<algorithm>
#include<numeric>
#include<cmath>
#include<utility>
#include<tuple>
#include<array>
#include<cstdint>
#include<cstdio>
#include<iomanip>
#include<map>
#include<set>
#include<unordered_map>
#include<unordered_set>
#include<queue>
#include<stack>
#include<deque>
#include<bitset>
#include<cctype>
#include<chrono>
#include<random>
#include<cassert>
#include<cstddef>
#include<iterator>
#include<string_view>
#include<type_traits>
#include<functional>
using namespace std;
namespace io {
template <typename T, typename U>
istream &operator>>(istream &is, pair<T, U> &p) {
is >> p.first >> p.second;
return is;
}
template <size_t N = 0, typename T>
istream& cin_tuple_impl(istream &is, T &t) {
if constexpr (N < std::tuple_size<T>::value) {
auto &x = std::get<N>(t);
is >> x;
cin_tuple_impl<N + 1>(is, t);
}
return is;
}
template <class... T>
istream &operator>>(istream &is, tuple<T...> &t) {
return cin_tuple_impl(is, t);
}
template <typename T, size_t N = 0>
istream &operator>>(istream &is, array<T, N> &v) {
for (auto &x : v) is >> x;
return is;
}
template <typename T>
istream &operator>>(istream &is, vector<T> &v) {
for (auto &x : v) is >> x;
return is;
}
template<typename T, typename U>
ostream &operator<<(ostream &os, const pair<T, U> &p) {
os << p.first << " " << p.second;
return os;
}
template <size_t N = 0, typename T>
ostream& cout_tuple_impl(ostream &os, const T &t) {
if constexpr (N < std::tuple_size<T>::value) {
if constexpr (N > 0) os << " ";
const auto &x = std::get<N>(t);
os << x;
cout_tuple_impl<N + 1>(os, t);
}
return os;
}
template <class... T>
ostream &operator<<(ostream &os, const tuple<T...> &t) {
return cout_tuple_impl(os, t);
}
template<typename T, size_t N>
ostream &operator<<(ostream &os, const array<T, N> &v) {
size_t n = v.size();
for (size_t i = 0; i < n; i++) {
if (i) os << " ";
os << v[i];
}
return os;
}
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;
}
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...);
}
void outr() {}
template<typename T, class... U, char sep = ' '>
void outr(const T &t, const U &...u) {
cout << t;
outr(u...);
}
void __attribute__((constructor)) _c() {
ios_base::sync_with_stdio(false);
cin.tie(nullptr);
cout << fixed << setprecision(15);
}
} // namespace io
using io::in;
using io::out;
using io::outr;
#define SHOW(x) static_cast<void>(0)
using ll = long long;
using D = double;
using LD = long double;
using P = pair<ll, ll>;
using u8 = uint8_t;
using u16 = uint16_t;
using u32 = uint32_t;
using u64 = uint64_t;
using i128 = __int128;
using u128 = unsigned __int128;
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>>;
#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__))))
template<typename T> using PQ = priority_queue<T,vector<T>>;
template<typename T> using minPQ = priority_queue<T, vector<T>, greater<T>>;
#define rep1(a) for(ll i = 0; i < a; i++)
#define rep2(i, a) for(ll i = 0; i < a; i++)
#define rep3(i, a, b) for(ll i = a; i < b; i++)
#define rep4(i, a, b, c) for(ll i = a; i < b; i += c)
#define overload4(a, b, c, d, e, ...) e
#define rep(...) overload4(__VA_ARGS__, rep4, rep3, rep2, rep1)(__VA_ARGS__)
#define rrep1(a) for(ll i = (a)-1; i >= 0; i--)
#define rrep2(i, a) for(ll i = (a)-1; i >= 0; i--)
#define rrep3(i, a, b) for(ll i = (b)-1; i >= a; i--)
#define rrep4(i, a, b, c) for(ll i = (b)-1; i >= a; i -= c)
#define rrep(...) overload4(__VA_ARGS__, rrep4, rrep3, rrep2, rrep1)(__VA_ARGS__)
#define for_subset(t, s) for (ll t = (s); t >= 0; t = (t == 0 ? -1 : (t - 1) & (s)))
#define ALL(v) v.begin(), v.end()
#define RALL(v) v.rbegin(), v.rend()
#define UNIQUE(v) v.erase( unique(v.begin(), v.end()), v.end() )
#define SZ(v) ll(v.size())
#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)))
template <typename T, typename U>
T SUM(const vector<U> &v) {
T res = 0;
for(auto &&a : v) res += a;
return res;
}
template <typename T>
vector<pair<T,int>> RLE(const vector<T> &v) {
if (v.empty()) return {};
T cur = v.front();
int cnt = 1;
vector<pair<T,int>> res;
for (int i = 1; i < (int)v.size(); i++) {
if (cur == v[i]) cnt++;
else {
res.emplace_back(cur, cnt);
cnt = 1; cur = v[i];
}
}
res.emplace_back(cur, cnt);
return res;
}
template<class T, class S>
inline bool chmax(T &a, const S &b) { return (a < b ? a = b, true : false); }
template<class T, class S>
inline bool chmin(T &a, const S &b) { return (a > b ? a = b, true : false); }
void YESNO(bool flag) { out(flag ? "YES" : "NO"); }
void yesno(bool flag) { out(flag ? "Yes" : "No"); }
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_sgn(int x) { return (__builtin_parity(x) & 1 ? -1 : 1); }
int popcnt_sgn(u32 x) { return (__builtin_parity(x) & 1 ? -1 : 1); }
int popcnt_sgn(ll x) { return (__builtin_parityl(x) & 1 ? -1 : 1); }
int popcnt_sgn(u64 x) { return (__builtin_parityl(x) & 1 ? -1 : 1); }
int highbit(int x) { return (x == 0 ? -1 : 31 - __builtin_clz(x)); }
int highbit(u32 x) { return (x == 0 ? -1 : 31 - __builtin_clz(x)); }
int highbit(ll x) { return (x == 0 ? -1 : 63 - __builtin_clzll(x)); }
int highbit(u64 x) { return (x == 0 ? -1 : 63 - __builtin_clzll(x)); }
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 get_bit(T x, int k) { return x >> k & 1; }
template <typename T>
T set_bit(T x, int k) { return x | T(1) << k; }
template <typename T>
T reset_bit(T x, int k) { return x & ~(T(1) << k); }
template <typename T>
T flip_bit(T x, int k) { return x ^ T(1) << k; }
template <typename T>
T popf(deque<T> &que) { T a = que.front(); que.pop_front(); return a; }
template <typename T>
T popb(deque<T> &que) { T a = que.back(); que.pop_back(); return a; }
template <typename T>
T pop(queue<T> &que) { T a = que.front(); que.pop(); return a; }
template <typename T>
T pop(stack<T> &que) { T a = que.top(); que.pop(); return a; }
template <typename T>
T pop(PQ<T> &que) { T a = que.top(); que.pop(); return a; }
template <typename T>
T pop(minPQ<T> &que) { T a = que.top(); que.pop(); 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) {
ll mid = (ok + ng) / 2;
(check(mid) ? ok : ng) = mid;
}
return ok;
}
template <typename F>
double binary_search_real(F check, double ok, double ng, int iter = 60) {
for (int _ = 0; _ < iter; _++) {
double mid = (ok + ng) / 2;
(check(mid) ? ok : ng) = mid;
}
return (ok + ng) / 2;
}
// max x s.t. b*x <= a
ll div_floor(ll a, ll b) {
assert(b != 0);
if (b < 0) a = -a, b = -b;
return a / b - (a % b < 0);
}
// max x s.t. b*x < a
ll div_under(ll a, ll b) {
assert(b != 0);
if (b < 0) a = -a, b = -b;
return a / b - (a % b <= 0);
}
// min x s.t. b*x >= a
ll div_ceil(ll a, ll b) {
assert(b != 0);
if (b < 0) a = -a, b = -b;
return a / b + (a % b > 0);
}
// min x s.t. b*x > a
ll div_over(ll a, ll b) {
assert(b != 0);
if (b < 0) a = -a, b = -b;
return a / b + (a % b >= 0);
}
// x = a mod b (b > 0), 0 <= x < b
ll modulo(ll a, ll b) {
assert(b > 0);
ll c = a % b;
return c < 0 ? c + b : c;
}
// (q,r) s.t. a = b*q + r, 0 <= r < b (b > 0)
// div_floor(a,b), modulo(a,b)
pair<ll,ll> divmod(ll a, ll b) {
ll q = div_floor(a,b);
return {q, a - b*q};
}
#endif
#include "atcoder/modint.hpp"
#include "atcoder/convolution.hpp"
template <typename mint>
struct Polynomial : vector<mint> {
using vector<mint>::vector;
using poly = Polynomial<mint>;
void shrink() {
while(!this->empty() and this->back() == mint(0)) this->pop_back();
}
poly rev() const {
poly res(*this);
reverse(res.begin(), res.end());
return res;
}
poly pre(int sz) const {
poly res(this->begin(), this->begin() + min(this->size(), (size_t)sz));
if (res.size() < (size_t)sz) res.resize(sz);
return res;
}
poly &operator>>=(int sz) {
if (this->size() <= (size_t)sz) {
this->clear();
return *this;
}
this->erase(this->begin(), this->begin() + (size_t)sz);
return *this;
}
poly &operator<<=(int sz) {
this->insert(this->begin(), sz, mint::raw(0));
return *this;
}
poly &operator+=(const mint &s) {
if (this->empty()) this->resize(1);
(*this)[0] += s;
return *this;
}
poly &operator+=(const poly &p) {
if (this->size() < p.size()) this->resize(p.size());
for (size_t i = 0; i < p.size(); i++) (*this)[i] += p[i];
return *this;
}
poly &operator-=(const mint &s) {
if (this->empty()) this->resize(1);
(*this)[0] -= s;
return *this;
}
poly &operator-=(const poly &p) {
if (this->size() < p.size()) this->resize(p.size());
for (size_t i = 0; i < p.size(); i++) (*this)[i] -= p[i];
return *this;
}
poly &operator*=(const mint &s) {
for (size_t i = 0; i < this->size(); i++) (*this)[i] *= s;
return *this;
}
poly operator*=(const poly &p) {
if (this->empty() or p.empty()) {
this->clear();
return *this;
}
vector<mint> prod = atcoder::convolution(*this, p);
return *this = poly(prod.begin(), prod.end());
}
poly &operator/=(const mint &s) {
mint s_inv = s.inv();
for (size_t i = 0; i < this->size(); i++) (*this)[i] *= s_inv;
return *this;
}
poly operator/=(const poly &p) {
if (this->size() < p.size()) {
this->clear();
return *this;
}
size_t q_sz = this->size() - p.size() + 1;
return *this = (this->rev().pre(q_sz) * p.rev().inv(q_sz)).pre(q_sz).rev();
}
poly operator%=(const poly &p) {
*this -= (*this / p) * p;
shrink();
assert(this->size() < p.size());
return *this;
}
poly operator+(const mint &s) const { return poly(*this) += s; }
poly operator+(const poly &p) const { return poly(*this) += p; }
poly operator-(const mint &s) const { return poly(*this) -= s; }
poly operator-(const poly &p) const { return poly(*this) -= p; }
poly operator*(const mint &s) const { return poly(*this) *= s; }
poly operator*(const poly &p) const { return poly(*this) *= p; }
poly operator/(const mint &s) const { return poly(*this) /= s; }
poly operator/(const poly &p) const { return poly(*this) /= p; }
poly operator%(const poly &p) const { return poly(*this) %= p; }
poly operator>>(int s) const { return poly(*this) >>= s; }
poly operator<<(int s) const { return poly(*this) <<= s; }
poly operator-() const {
poly res(this->size());
for (size_t i = 0; i < this->size(); i++) res[i] = -(*this)[i];
return res;
}
poly dot(const poly &p) const {
poly res(min(this->size(), p.size()));
for (size_t i = 0; i < res.size(); i++) res[i] = (*this)[i] * p[i];
return res;
}
mint eval(mint x) const {
mint res = 0, pw = 1;
for (auto &c : *this) res += c * pw, pw *= x;
return res;
}
void ntt() {
atcoder::internal::butterfly(*this);
}
void intt() {
atcoder::internal::butterfly_inv(*this);
mint sz_inv = mint::raw(this->size()).inv();
for (auto &c : *this) c *= sz_inv;
}
poly inv(int deg = -1) const {
assert(!this->empty() and (*this)[0] != 0);
if (deg == -1) deg = (int)this->size();
poly res(deg);
res[0] = (*this)[0].inv();
for (int d = 1; d < deg; d <<= 1) {
poly f(2 * d), g(2 * d);
for (int j = 0; j < min((int)this->size(), 2 * d); j++) f[j] = (*this)[j];
for (int j = 0; j < d; j++) g[j] = res[j];
// atcoder::internal::butterfly(f);
f.ntt();
// atcoder::internal::butterfly(g);
g.ntt();
for (int j = 0; j < 2 * d; j++) f[j] *= g[j];
// atcoder::internal::butterfly_inv(f);
f.intt();
for (int j = 0; j < d; j++) f[j] = 0;
// atcoder::internal::butterfly(f);
f.ntt();
for (int j = 0; j < 2 * d; j++) f[j] *= g[j];
// atcoder::internal::butterfly_inv(f);
f.intt();
for (int j = d; j < min(2 * d, deg); j++) res[j] = -f[j];
}
return res.pre(deg);
}
poly differentiate() const {
const size_t n = this->size();
poly res(n == 0 ? 0 : n - 1);
mint coef = 1;
for (size_t i = 1; i < n; i++) {
res[i - 1] = (*this)[i] * coef;
coef += 1;
}
return res;
}
poly integrate() const {
const size_t n = this->size();
poly res(n + 1);
res[0] = mint::raw(0);
if (n > 0) res[1] = mint(1);
int mod = mint::mod();
for (size_t i = 2; i <= n; i++) res[i] = (-res[mod % i]) * (mod / i);
for (size_t i = 0; i < n; i++) res[i + 1] *= (*this)[i];
return res;
}
poly log(int deg = -1) const {
assert(!this->empty() and (*this)[0] == 1);
if (deg == -1) deg = (int)this->size();
return (this->differentiate() * this->inv(deg)).pre(deg - 1).integrate();
}
poly exp(int deg = -1) const {
assert(this->empty() or (*this)[0] == mint(0));
if (deg == -1) deg = (int)this->size();
vector<mint> inv;
inv.reserve(deg + 1);
inv.emplace_back(mint::raw(0));
inv.emplace_back(mint::raw(1));
poly b{1, 1 < (int)this->size() ? (*this)[1] : 0};
poly c{1}, z1, z2{1, 1};
int mod = mint::mod();
for (int d = 2; d < deg ; d <<= 1) {
poly y = b;
y.resize(2 * d);
// atcoder::internal::butterfly(y);
y.ntt();
z1 = z2;
poly z(d);
for (int i = 0; i < d; i++) z[i] = y[i] * z1[i];
// atcoder::internal::butterfly_inv(z);
z.intt();
fill(z.begin(), z.begin() + d / 2, mint::raw(0));
// atcoder::internal::butterfly(z);
z.ntt();
for (int i = 0; i < d; i++) z[i] *= -z1[i];
// atcoder::internal::butterfly_inv(z);
z.intt();
c.insert(c.end(), z.begin() + d / 2, z.end());
z2 = c;
z2.resize(2 * d);
// atcoder::internal::butterfly(z2);
z2.ntt();
poly x(this->begin(), this->begin() + min<int>(this->size(), d));
x.resize(d);
{
x.erase(x.begin());
mint coef = 1;
for (int i = 0; i < d-1; i++) x[i] *= coef, coef += 1;
}
x.emplace_back(mint::raw(0));
// atcoder::internal::butterfly(x);
x.ntt();
for (int i = 0; i < d; i++) x[i] *= y[i];
// atcoder::internal::butterfly_inv(x);
x.intt();
x -= b.differentiate();
x.resize(2 * d);
for (int i = 0; i < d - 1; i++) x[d + i] = x[i], x[i] = mint::raw(0);
// atcoder::internal::butterfly(x);
x.ntt();
for (int i = 0; i < 2 * d; i++) x[i] *= z2[i];
// atcoder::internal::butterfly_inv(x);
x.intt();
x.pop_back();
{
int sz;
while((sz = (int)inv.size()) <= (int)x.size()) {
inv.emplace_back((-inv[mod % sz]) * (mod / sz));
}
x.insert(x.begin(), mint::raw(0));
for (size_t i = 1; i < x.size(); i++) x[i] *= inv[i];
}
for (int i = d; i < min((int)this->size(), 2 * d); i++) x[i] += (*this)[i];
fill(x.begin(), x.begin() + d, mint::raw(0));
// atcoder::internal::butterfly(x);
x.ntt();
for (int i = 0; i < 2 * d; i++) x[i] *= y[i];
// atcoder::internal::butterfly_inv(x);
x.intt();
b.insert(b.end(), x.begin() + d, x.end());
}
return b.pre(deg);
}
poly pow(long long k, int deg = -1) const {
const int n = (int)this->size();
if (deg == -1) deg = n;
if (k == 0) {
poly res(deg);
if (deg > 0) res[0] = 1;
return res;
}
int l = 0;
while (l < n and (*this)[l] == 0){
l++;
if (l >= (deg + k - 1) / k) return poly(deg, mint::raw(0));
}
if (l == n) return poly(deg, mint::raw(0));
mint rev = (*this)[l].inv();
poly res = (((*this * rev) >> l).log(deg) * k).exp(deg);
res *= (*this)[l].pow(k);
res = (res << (k * l)).pre(deg);
if ((int)res.size() < deg) res.resize(deg, mint::raw(0));
return res;
}
};
template<typename T> struct Binomial {
vector<T> fact_, inv_, finv_;
constexpr Binomial() {}
constexpr Binomial(int n) noexcept : fact_(n, 1), inv_(n, 1), finv_(n, 1) {
init(n);
}
constexpr void init(int n) noexcept {
constexpr int mod = T::mod();
fact_.assign(n, 1), inv_.assign(n, 1), finv_.assign(n, 1);
for(int i = 2; i < n; i++){
fact_[i] = fact_[i-1] * i;
inv_[i] = -inv_[mod%i] * (mod/i);
finv_[i] = finv_[i-1] * inv_[i];
}
}
constexpr T com(int n, int k) const noexcept {
if (n < k || n < 0 || k < 0) return 0;
return fact_[n] * finv_[k] * finv_[n-k];
}
constexpr T perm(int n, int k) const noexcept {
if (n < k || n < 0 || k < 0) return 0;
return fact_[n] * finv_[n-k];
}
constexpr T fact(int n) const noexcept {
if (n < 0) return 0;
return fact_[n];
}
constexpr T inv(int n) const noexcept {
if (n < 0) return 0;
return inv_[n];
}
constexpr T finv(int n) const noexcept {
if (n < 0) return 0;
return finv_[n];
}
constexpr T com_naive(int n, int k) const noexcept {
if (n < 0 || k < 0 || n < k) return 0;
T res = T(1);
k = min(k, n-k);
for (int i = 1; i <= k; i++)res *= (n--) * inv(i);
return res;
}
template <typename I>
constexpr T multi(const vector<I> &v) const noexcept {
static_assert(is_integral<I>::value);
I n = 0;
for (auto& x : v) {
if (x < 0) return 0;
n += x;
}
T res = fact(n);
for (auto &x : v) res *= finv(x);
return res;
}
// [x^k] (1-x)^{-n} = com(n+k-1, k)
constexpr T neg(int n, int k) const noexcept {
if (n < 0 || k < 0) return 0;
return k == 0 ? 1 : com(n+k-1, k);
}
};
using mint = atcoder::modint998244353;
using poly = Polynomial<mint>;
Binomial<mint> bc(300000);
// deg(f) = n-1
// [x^{n-1}] g(x)f(x)^i for i=0,1,...,m
template <typename mint>
Polynomial<mint> power_projection(Polynomial<mint> f, Polynomial<mint> g = {1}, int m = -1) {
using poly = Polynomial<mint>;
if (f.empty()) return poly(m+1,0);
if (f[0] != 0) {
mint c = f[0];
f[0] = 0;
poly a = power_projection(f, g, m);
for (int i = 0; i <= m; i++) a[i] *= bc.finv(i);
poly b(m+1);
mint pc = 1;
for (int i = 0; i <= m; i++) b[i] = bc.finv(i) * pc, pc *= c;
a *= b; a.resize(m+1);
for (int i = 0; i <= m; i++) a[i] *= bc.fact(i);
return a;
}
int fn = f.size();
if(m == -1) m = fn - 1;
g.resize(fn);
int n = 1;
while (n < fn) n *= 2;
f.resize(n);
reverse(g.begin(), g.end());
g.resize(n);
reverse(g.begin(), g.end());
int k = 1;
poly p(n * 2), q(n * 2), r(n * 2);
for (int i = 0; i < n; i++) p[i] = g[i], q[i] = -f[i];
while (n > 1) {
for (int i = 0; i < 2 * n * k; i++) r[i] = (i % 2 == 0 ? q[i] : -q[i]);
poly pq = p * r;
poly qq = q * r;
pq.resize(4 * n * k);
qq.resize(4 * n * k);
for (int i = 0; i < 2 * n * k; i++) {
pq[2 * n * k + i] += p[i];
qq[2 * n * k + i] += q[i] + r[i];
}
fill(p.begin(), p.end(), 0);
fill(q.begin(), q.end(), 0);
for (int i = 0; i < 2 * k; i++) {
for (int j = 0; j < n / 2; j++) {
p[n * i + j] = pq[2 * n * i + 2 * j + 1];
q[n * i + j] = qq[2 * n * i + 2 * j + 0];
}
}
n /= 2; k *= 2;
}
poly pk(k),qk(k+1);
for (int i = 0; i < k; i++) pk[i] = p[2 * i];
for (int i = 0; i < k; i++) qk[i] = q[2 * i];
qk[k] = 1;
reverse(pk.begin(), pk.end());
reverse(qk.begin(), qk.end());
return (pk * qk.inv(m+1)).pre(m+1);
}
// g(f(x))
template <typename mint>
Polynomial<mint> composition(Polynomial<mint> f, Polynomial<mint> g, int deg = -1) {
using poly = Polynomial<mint>;
auto middle_product = [&] (poly x, poly y) -> poly {
int nm_1 = x.size(), m = y.size();
int l = bit_ceil(x.size());
reverse(y.begin(), y.end());
x.resize(l); y.resize(l);
x.ntt(); y.ntt();
for (int i = 0; i < l; i++) x[i] *= y[i];
x.intt();
return poly{x.begin() + m - 1, x.begin() + nm_1};
};
auto rec = [&] (this auto self, int n, int k, poly q) -> poly {
if (n == 1) {
reverse(g.begin(), g.end());
poly p(2 * k);
for (int i = 0; i < k; i++) p[2 * i] = g[i];
return p;
}
poly r(2 * n * k);
for (int i = 0; i < 2 * n * k; i++) r[i] = (i % 2 == 0 ? q[i] : -q[i]);
poly qq = q * r;
qq.resize(4 * n * k);
for (int i = 0; i < 2 * n * k; i++) qq[2 * n * k + i] += q[i] + r[i];
poly nq(2 * n * k);
for (int i = 0; i < k * 2; i++) {
for (int j = 0; j < n / 2; j++) {
nq[n * i + j] = qq[2 * n * i + 2 * j];
}
}
poly np = self(n / 2, k * 2, nq);
poly pq(4 * n * k);
for (int i = 0; i < k * 2; i++) {
for (int j = 0; j < n / 2; j++) {
pq[2 * n * i + 2 * j + 1] += np[n * i + j];
}
}
poly p(2 * n * k);
for (int i = 0; i < 2 * n * k; i++) p[i] += pq[2 * n * k + i];
pq.pop_back();
poly mp = middle_product(pq, r);
for (int i = 0; i < 2 * n * k; i++) p[i] += mp[i];
return p;
};
if (deg == -1) deg = max(f.size(), g.size());
int n = 1;
while (n < deg) n *= 2;
f.resize(n); g.resize(n);
poly q(n * 2);
for (int i = 0; i < n; i++) q[i] = -f[i];
poly p = rec(n, 1, q);
return p.pre(n).rev().pre(deg);
}
template <typename mint>
Polynomial<mint> power_projection_ntt(Polynomial<mint> f, Polynomial<mint> g = {1}, int m = -1) {
using poly = Polynomial<mint>;
if (f.empty()) return poly(m+1,0);
if (f[0] != 0) {
mint c = f[0];
f[0] = 0;
poly a = power_projection(f, g, m);
for (int i = 0; i <= m; i++) a[i] *= bc.finv(i);
poly b(m+1);
mint pc = 1;
for (int i = 0; i <= m; i++) b[i] = bc.finv(i) * pc, pc *= c;
a *= b; a.resize(m+1);
for (int i = 0; i <= m; i++) a[i] *= bc.fact(i);
return a;
}
int fn = f.size();
if(m == -1) m = fn - 1;
g.resize(fn);
int n = 1;
while (n < fn) n *= 2;
f.resize(n);
reverse(g.begin(), g.end());
g.resize(n);
reverse(g.begin(), g.end());
vector<int> br(2 * n);
const int log = 31 - countl_zero(static_cast<unsigned>(2 * n));
for (int i = 0; i < 2 * n; i++) br[i] = (br[i >> 1] >> 1) + ((i & 1) << (log - 1));
constexpr int mod = mint::mod();
constexpr int inv2 = atcoder::internal::pow_mod_constexpr(2, mod - 2, mod);
constexpr int pr = atcoder::internal::primitive_root_constexpr(mod);
constexpr int trz = countr_zero(static_cast<unsigned>(mod - 1));
constexpr int rt = atcoder::internal::pow_mod_constexpr(pr, (mod - 1) >> trz, mod);
constexpr int inv_rt = atcoder::internal::pow_mod_constexpr(rt, mod - 2, mod);
const int w = atcoder::internal::pow_mod_constexpr(inv_rt, (1 << trz) / (4 * n), mod);
vector<mint> wp(n * 2);
mint wi = 1;
for (int i : br) wp[i] = wi, wi *= w;
int k = 1;
poly p(n * 2), q(n * 2);
for (int i = 0; i < n; i++) p[i] = g[i], q[i] = -f[i];
while (n > 1) {
p.resize(4 * n * k);
q.resize(4 * n * k);
q[2 * n * k] = 1;
p.ntt(); q.ntt();
for (int i = 0; i < 2 * n * k; i++) {
p[i] = wp[i] * inv2 * (p[2*i] * q[2*i+1] - p[2*i+1] * q[2*i]);
q[i] = q[2*i] * q[2*i+1];
}
p.resize(2 * n * k);
q.resize(2 * n * k);
p.intt(); q.intt();
for (int i = 0; i < 2 * k; i++) {
for (int j = n / 2; j < n; j++) {
p[n * i + j] = q[n * i + j] = 0;
}
}
q[0] = 0;
n /= 2; k *= 2;
}
poly pk(k),qk(k+1);
for (int i = 0; i < k; i++) pk[i] = p[2 * i];
for (int i = 0; i < k; i++) qk[i] = q[2 * i];
qk[k] = 1;
reverse(pk.begin(), pk.end());
reverse(qk.begin(), qk.end());
return (pk * qk.inv(m+1)).pre(m+1);
}
// g(f(x))
template <typename mint>
Polynomial<mint> composition_ntt(Polynomial<mint> f, Polynomial<mint> g, int deg = -1) {
using poly = Polynomial<mint>;
if (deg == -1) deg = max(f.size(), g.size());
int n = 1;
while (n < deg) n *= 2;
f.resize(n); g.resize(n);
vector<int> br(2 * n);
const int log = countr_zero(static_cast<unsigned>(2 * n));
for (int i = 0; i < 2 * n; i++) br[i] = (br[i >> 1] >> 1) + ((i & 1) << (log - 1));
constexpr int mod = mint::mod();
constexpr int inv2 = atcoder::internal::pow_mod_constexpr(2, mod - 2, mod);
constexpr int pr = atcoder::internal::primitive_root_constexpr(mod);
constexpr int trz = countr_zero(static_cast<unsigned>(mod - 1));
constexpr int rt = atcoder::internal::pow_mod_constexpr(pr, (mod - 1) >> trz, mod);
constexpr int inv_rt = atcoder::internal::pow_mod_constexpr(rt, mod - 2, mod);
const int w = atcoder::internal::pow_mod_constexpr(inv_rt, (1 << trz) / (4 * n), mod);
vector<mint> wp(2 * n);
mint wi = 1;
for (int i : br) wp[i] = wi, wi *= w;
auto transposed_ntt = [&] (poly &p) -> void {
int sz = p.size();
p.intt();
reverse(p.begin() + 1, p.end());
for (mint &x : p) x *= sz;
};
auto transposed_intt = [&] (poly &p) -> void {
mint sz_inv = mint::raw(p.size()).inv();
reverse(p.begin() + 1, p.end());
p.ntt();
for (mint &x : p) x *= sz_inv;
};
auto rec = [&] (this auto self, int n, int k, poly q) -> poly {
if (n == 1) {
reverse(g.begin(), g.end());
poly p(2 * k);
for (int i = 0; i < k; i++) p[2 * i] = g[i];
return p;
}
q.resize(4 * n * k);
q[2 * n * k] = 1;
q.ntt();
poly nq(2 * n * k);
for (int i = 0; i < 2 * n * k; i++) nq[i] = q[2*i] * q[2*i+1];
nq.intt();
for (int i = 0; i < 2 * k; i++) {
for (int j = n / 2; j < n; j++) {
nq[i * n + j] = 0;
}
}
nq[0] = 0;
poly p = self(n / 2, k * 2, nq);
for (int i = 0; i < 2 * k; i++) {
for (int j = n / 2; j < n; j++) {
p[i * n + j] = 0;
}
}
transposed_intt(p);
p.resize(4 * n * k);
for (int i = 2 * n * k - 1; i >= 0; i--) {
p[2 * i + 1] = wp[i] * -inv2 * q[2 * i] * p[i];
p[2 * i] = wp[i] * inv2 * q[2 * i + 1] * p[i];
}
transposed_ntt(p);
p.resize(2 * n * k);
return p;
};
poly q(n * 2);
for (int i = 0; i < n; i++) q[i] = -f[i];
poly p = rec(n, 1, q);
return p.pre(n).rev().pre(deg);
}
void solve() {
int n,m; in(n,m);
poly a(n),b(n),c(n);
rep(i,n){
int x; in(x);
a[i] = x;
}
rep(i,n){
int x; in(x);
b[i] = x;
}
rep(i,n){
int x; in(x);
c[i] = x;
}
auto p = power_projection_ntt(b);
rep(i,n) p[i] *= c[i];
rep(i,n) p[i] *= a[1].inv().pow(i*(i-1)/2);
poly q(n+m);
rep(i,n+m) q[i] = a[1].pow(i*(i-1)/2);
reverse(ALL(p));
p *= q;
rep(i,m){
mint ans = p[n-1+i] * a[1].inv().pow(i*(i-1)/2);
outr(ans.val(), " \n"[i==m-1]);
}
}
int main() {
int tc = 1;
// in(tc);
while(tc--){
solve();
}
}