結果
| 問題 |
No.931 Multiplicative Convolution
|
| コンテスト | |
| ユーザー |
 AC2K
|
| 提出日時 | 2023-06-18 21:41:03 |
| 言語 | C++23 (gcc 13.3.0 + boost 1.87.0) |
| 結果 |
WA
|
| 実行時間 | - |
| コード長 | 21,546 bytes |
| コンパイル時間 | 6,648 ms |
| コンパイル使用メモリ | 330,832 KB |
| 実行使用メモリ | 8,196 KB |
| 最終ジャッジ日時 | 2024-06-26 08:55:59 |
| 合計ジャッジ時間 | 9,654 ms |
|
ジャッジサーバーID （参考情報） |
judge2 / judge1 |
（要ログイン）
| ファイルパターン | 結果 |
|---|---|
| sample | AC * 1 WA * 2 |
| other | WA * 5 RE * 9 |
ソースコード
#line 1 "main.cpp"
#include <atcoder/all>
#line 2 "library/src/internal/barrett.hpp"
#include <cstdint>
namespace kyopro {
namespace internal {
/**
* @brief Barrett Reduction
*/
class barrett {
using u32 = uint32_t;
using u64 = uint64_t;
u32 m;
u64 im;
public:
constexpr barrett() : m(0), im(0) {}
constexpr barrett(u32 m_)
: m(m_), im((u64) static_cast<u64>(-1) / m_ + 1) {}
constexpr u32 get_mod() const { return m; }
constexpr u32 reduce(int64_t a) const { return mul(a, 1); }
constexpr u32 mul(u32 a, u32 b) const {
if (!a || !b) {
return 0;
}
u64 z = (u64)a * b;
u64 x = (u64)(((__uint128_t)z * im) >> 64);
u64 y = x * m;
return (u32)(z - y + (z < y ? m : 0));
}
};
}; // namespace internal
}; // namespace kyopro
/**
* @ref
* https://github.com/atcoder/ac-library/blob/master/atcoder/internal_math.hpp
*/
#line 2 "library/src/math/dynamic_modint.hpp"
#include <cassert>
#include <iostream>
#line 3 "library/src/internal/montgomery.hpp"
#include <limits>
#include <numeric>
#line 5 "library/src/internal/type_traits.hpp"
#include <typeinfo>
namespace kyopro {
namespace internal {
/*
* @ref https://qiita.com/kazatsuyu/items/f8c3b304e7f8b35263d8
*/
template <typename... Args> struct first_enabled {};
template <typename T, typename... Args>
struct first_enabled<std::enable_if<true, T>, Args...> {
using type = T;
};
template <typename T, typename... Args>
struct first_enabled<std::enable_if<false, T>, Args...>
: first_enabled<Args...> {};
template <typename T, typename... Args> struct first_enabled<T, Args...> {
using type = T;
};
template <typename... Args>
using first_enabled_t = typename first_enabled<Args...>::type;
template <int dgt> struct int_least {
static_assert(dgt <= 128);
using type = first_enabled_t<std::enable_if<dgt <= 8, __int8_t>,
std::enable_if<dgt <= 16, __int16_t>,
std::enable_if<dgt <= 32, __int32_t>,
std::enable_if<dgt <= 64, __int64_t>,
std::enable_if<dgt <= 128, __int128_t> >;
};
template <int dgt> struct uint_least {
static_assert(dgt <= 128);
using type = first_enabled_t<std::enable_if<dgt <= 8, __uint8_t>,
std::enable_if<dgt <= 16, __uint16_t>,
std::enable_if<dgt <= 32, __uint32_t>,
std::enable_if<dgt <= 64, __uint64_t>,
std::enable_if<dgt <= 128, __uint128_t> >;
};
template <int dgt> using int_least_t = typename int_least<dgt>::type;
template <int dgt> using uint_least_t = typename uint_least<dgt>::type;
template <typename T>
using double_size_uint_t = uint_least_t<2 * std::numeric_limits<T>::digits>;
template <typename T>
using double_size_int_t = int_least_t<2 * std::numeric_limits<T>::digits>;
}; // namespace internal
}; // namespace kyopro
#line 6 "library/src/internal/montgomery.hpp"
namespace kyopro {
namespace internal {
using u32 = uint32_t;
using u64 = uint64_t;
using i32 = int32_t;
using i64 = int64_t;
using u128 = __uint128_t;
using i128 = __int128_t;
/**
* @brief Montgomery Reduction
*/
template <typename T> class Montgomery {
static constexpr int lg = std::numeric_limits<T>::digits;
using LargeT = internal::double_size_uint_t<T>;
T mod, r, r2, minv;
T inv() {
T t = 0, res = 0;
for (int i = 0; i < lg; ++i) {
if (~t & 1) {
t += mod;
res += static_cast<T>(1) << i;
}
t >>= 1;
}
return res;
}
public:
Montgomery() = default;
constexpr T get_mod() { return mod; }
void set_mod(T m) {
assert(m);
assert(m & 1);
mod = m;
r = (-static_cast<T>(mod)) % mod;
r2 = (-static_cast<LargeT>(mod)) % mod;
minv = inv();
}
T reduce(LargeT x) const {
u64 res =
(x + static_cast<LargeT>(static_cast<T>(x) * minv) * mod) >> lg;
if (res >= mod) res -= mod;
return res;
}
T generate(LargeT x) { return reduce(x * r2); }
T mul(T x, T y) { return reduce((LargeT)x * y); }
};
}; // namespace internal
}; // namespace kyopro
#line 6 "library/src/math/dynamic_modint.hpp"
namespace kyopro {
template <int id = -1> class barrett_modint {
using u32 = uint32_t;
using u64 = uint64_t;
using i32 = int32_t;
using i64 = int64_t;
using br = internal::barrett;
static br brt;
static u32 mod;
u32 v;
public:
static void set_mod(u32 mod_) {
brt = br(mod_);
mod = mod_;
}
public:
explicit constexpr barrett_modint() : v(0) { assert(mod); }
explicit constexpr barrett_modint(i64 v_) : v(brt.reduce(v_)) {
assert(mod);
}
u32 val() const { return v; }
static u32 get_mod() { return mod; }
using mint = barrett_modint<id>;
constexpr mint& operator=(i64 r) {
v = brt.reduce(r);
return (*this);
}
constexpr mint& operator+=(const mint& r) {
v += r.v;
if (v >= mod) {
v -= mod;
}
return (*this);
}
constexpr mint& operator-=(const mint& r) {
v += mod - r.v;
if (v >= mod) {
v -= mod;
}
return (*this);
}
constexpr mint& operator*=(const mint& r) {
v = brt.mul(v, r.v);
return (*this);
}
constexpr mint operator+(const mint& r) const { return mint(*this) += r; }
constexpr mint operator-(const mint& r) const { return mint(*this) -= r; }
constexpr mint operator*(const mint& r) const { return mint(*this) *= r; }
constexpr mint& operator+=(i64 r) { return (*this) += mint(r); }
constexpr mint& operator-=(i64 r) { return (*this) -= mint(r); }
constexpr mint& operator*=(i64 r) { return (*this) *= mint(r); }
friend mint operator+(i64 l, const mint& r) { return mint(l) += r; }
friend mint operator+(const mint& l, i64 r) { return mint(l) += r; }
friend mint operator-(i64 l, const mint& r) { return mint(l) -= r; }
friend mint operator-(const mint& l, i64 r) { return mint(l) -= r; }
friend mint operator*(i64 l, const mint& r) { return mint(l) *= r; }
friend mint operator*(const mint& l, i64 r) { return mint(l) += r; }
friend std::ostream& operator<<(std::ostream& os, const mint& mt) {
os << mt.val();
return os;
}
friend std::istream& operator>>(std::istream& is, mint& mt) {
i64 v_;
is >> v_;
mt = v_;
return is;
}
template <typename T> mint pow(T e) const {
mint res(1), base(*this);
while (e) {
if (e & 1) {
res *= base;
}
e >>= 1;
base *= base;
}
return res;
}
mint inv() const { return pow(mod - 2); }
mint& operator/=(const mint& r) { return (*this) *= r.inv(); }
mint operator/(const mint& r) const { return mint(*this) *= r.inv(); }
mint& operator/=(i64 r) { return (*this) /= mint(r); }
friend mint operator/(const mint& l, i64 r) { return mint(l) /= r; }
friend mint operator/(i64 l, const mint& r) { return mint(l) /= r; }
};
}; // namespace kyopro
template <int id>
typename kyopro::barrett_modint<id>::u32 kyopro::barrett_modint<id>::mod;
template <int id>
typename kyopro::barrett_modint<id>::br kyopro::barrett_modint<id>::brt;
namespace kyopro {
template <typename T, int id = -1> class dynamic_modint {
using LargeT = internal::double_size_uint_t<T>;
static T mod;
static internal::Montgomery<T> mr;
public:
static void set_mod(T mod_) {
mr.set_mod(mod_);
mod = mod_;
}
static T get_mod() { return mod; }
private:
T v;
public:
dynamic_modint(T v_ = 0) {
assert(mod);
v = mr.generate(v_);
}
T val() const { return mr.reduce(v); }
using mint = dynamic_modint<T, id>;
mint& operator+=(const mint& r) {
v += r.v;
if (v >= mr.get_mod()) {
v -= mr.get_mod();
}
return (*this);
}
mint& operator-=(const mint& r) {
v += mr.get_mod() - r.v;
if (v >= mr.get_mod) {
v -= mr.get_mod();
}
return (*this);
}
mint& operator*=(const mint& r) {
v = mr.mul(v, r.v);
return (*this);
}
mint operator+(const mint& r) { return mint(*this) += r; }
mint operator-(const mint& r) { return mint(*this) -= r; }
mint operator*(const mint& r) { return mint(*this) *= r; }
mint& operator=(const T& v_) {
(*this) = mint(v_);
return (*this);
}
friend std::ostream& operator<<(std::ostream& os, const mint& mt) {
os << mt.val();
return os;
}
friend std::istream& operator>>(std::istream& is, mint& mt) {
T v_;
is >> v_;
mt = v_;
return is;
}
template <typename P> mint pow(P e) const {
assert(e >= 0);
mint res(1), base(*this);
while (e) {
if (e & 1) {
res *= base;
}
e >>= 1;
base *= base;
}
return res;
}
mint inv() const { return pow(mod - 2); }
mint& operator/=(const mint& r) { return (*this) *= r.inv(); }
mint operator/(const mint& r) const { return mint(*this) *= r.inv(); }
mint& operator/=(T r) { return (*this) /= mint(r); }
friend mint operator/(const mint& l, T r) { return mint(l) /= r; }
friend mint operator/(T l, const mint& r) { return mint(l) /= r; }
};
}; // namespace kyopro
template <typename T, int id> T kyopro::dynamic_modint<T, id>::mod;
template <typename T, int id>
kyopro::internal::Montgomery<T> kyopro::dynamic_modint<T, id>::mr;
/**
* @brief 動的modint
* @docs docs/math/dynamic_modint.md
*/
#line 2 "library/src/math/rho.hpp"
#include <algorithm>
#include <vector>
#line 3 "library/src/math/gcd.hpp"
#include <tuple>
namespace kyopro {
template <typename T> constexpr T inline _gcd(T a, T b) {
assert(a >= 0 && b >= 0);
if (a == 0 || b == 0) return a + b;
int d = std::min<T>(__builtin_ctzll(a), __builtin_ctzll(b));
a >>= __builtin_ctzll(a), b >>= __builtin_ctzll(b);
while (a != b) {
if (!a || !b) {
return a + b;
}
if (a >= b) {
a -= b;
a >>= __builtin_ctzll(a);
} else {
b -= a;
b >>= __builtin_ctzll(b);
}
}
return a << d;
}
template <typename T> constexpr T ext_gcd(T a, T b, T& x, T& y) {
x = 1, y = 0;
T nx = 0, ny = 1;
while (b) {
T q = a / b;
std::tie(a, b) = std::pair<T, T>{b, a % b};
std::tie(x, nx) = std::pair<T, T>{nx, x - nx * q};
std::tie(y, ny) = std::pair<T, T>{ny, y - ny * q};
}
return a;
}
}; // namespace kyopro
#line 3 "library/src/math/miller.hpp"
namespace kyopro {
/**
* @brief MillerRabin素数判定法
*/
class miller {
using i128 = __int128_t;
using u128 = __uint128_t;
using u64 = uint64_t;
using u32 = uint32_t;
template <typename T, typename mint, const int bases[], int length>
static constexpr bool miller_rabin(T n) {
T d = n - 1;
while (~d & 1) {
d >>= 1;
}
const T rev = n - 1;
if (mint::get_mod() != n) {
mint::set_mod(n);
}
for (int i = 0; i < length; ++i) {
if (n <= bases[i]) {
return true;
}
T t = d;
mint y = mint(bases[i]).pow(t);
while (t != n - 1 && y.val() != 1 && y.val() != rev) {
y *= y;
t <<= 1;
}
if (y.val() != rev && (~t & 1)) return false;
}
return true;
}
// 底
static constexpr int bases_int[3] = {2, 7, 61};
static constexpr int bases_ll[7] = {2, 325, 9375, 28178,
450775, 9780504, 1795265022};
public:
template <typename T> static constexpr bool is_prime(T n) {
if (n < 2) {
return false;
} else if (n == 2) {
return true;
} else if (~n & 1) {
return false;
};
if (std::numeric_limits<T>::digits < 32 || n <= 1 << 30) {
return miller_rabin<T, dynamic_modint<std::make_unsigned_t<T>>,
bases_int, 3>(n);
} else {
return miller_rabin<T, dynamic_modint<std::make_unsigned_t<T>>,
bases_ll, 7>(n);
}
return false;
}
};
}; // namespace kyopro
/**
* @docs docs/math/miller.md
*/
#line 2 "library/src/random/xor_shift.hpp"
#include <chrono>
#line 4 "library/src/random/xor_shift.hpp"
#include <random>
namespace kyopro {
struct xor_shift32 {
uint32_t rng;
constexpr explicit xor_shift32(uint32_t seed) : rng(seed) {}
explicit xor_shift32()
: rng(std::chrono::steady_clock::now().time_since_epoch().count()) {}
constexpr uint32_t operator()() {
rng ^= rng << 13;
rng ^= rng >> 17;
rng ^= rng << 5;
return rng;
}
};
struct xor_shift {
uint64_t rng;
constexpr xor_shift(uint64_t seed) : rng(seed) {}
explicit xor_shift()
: rng(std::chrono::steady_clock::now().time_since_epoch().count()) {}
constexpr uint64_t operator()() {
rng ^= rng << 13;
rng ^= rng >> 7;
rng ^= rng << 17;
return rng;
}
};
}; // namespace kyopro
/**
* @brief xor shift
*/
#line 7 "library/src/math/rho.hpp"
namespace kyopro {
/**
* @brief Pollard Rho 素因数分解法
*/
class rho {
using i128 = __int128_t;
using u128 = __uint128_t;
using u64 = uint64_t;
using u32 = uint32_t;
template <typename mint> static u64 find_factor(u64 n) {
xor_shift32 rng(2023);
if (~n & 1uL) {
return 2;
}
if (kyopro::miller::is_prime(n)) {
return n;
}
if (mint::get_mod() != n) {
mint::set_mod(n);
}
while (1) {
u64 c = rng();
const auto f = [&](mint x) -> mint { return x * x + c; };
mint x = rng();
mint y = f(x);
u64 d = 1;
while (d == 1) {
d = _gcd<long long>(
std::abs((long long)x.val() - (long long)y.val()), n);
x = f(x);
y = f(f(y));
}
if (1 < d && d < n) {
return d;
}
}
exit(0);
}
template <typename mint> static std::vector<u64> rho_fact(u64 n) {
if (n < 2) {
return {};
}
if (kyopro::miller::is_prime(n)) {
return {n};
}
std::vector<u64> v;
std::vector<u64> st{n};
while (st.size()) {
u64& m = st.back();
if (kyopro::miller::is_prime(m)) {
v.emplace_back(m);
st.pop_back();
} else {
u64 d = find_factor<mint>(m);
m /= d;
st.emplace_back(d);
}
}
return v;
}
public:
static std::vector<u64> factorize(u64 n) {
if (n < 2) {
return {};
}
auto v = (n < (1uL << 31) ? rho_fact<dynamic_modint<u32>>(n)
: rho_fact<dynamic_modint<u64>>(n));
std::sort(v.begin(), v.end());
return v;
}
static std::vector<std::pair<u64, int>> exp_factorize(u64 n) {
std::vector<u64> pf = factorize(n);
if (pf.empty()) {
return {};
}
std::vector<std::pair<u64, int>> res;
res.emplace_back(pf.front(), 1);
for (int i = 1; i < (int)pf.size(); i++) {
if (res.back().first == pf[i]) {
res.back().second++;
} else {
res.emplace_back(pf[i], 1);
}
}
return res;
}
static std::vector<u64> enumerate_divisor(u64 n) {
std::vector<std::pair<u64, int>> pf = rho::exp_factorize(n);
std::vector<u64> divisor{1};
for (auto [p, e] : pf) {
u64 pow = p;
int sz = divisor.size();
for (int i = 0; i < e; ++i) {
for (int j = 0; j < sz; ++j)
divisor.emplace_back(divisor[j] * pow);
pow *= p;
}
}
return divisor;
}
};
}; // namespace kyopro
/**
* @docs docs/math/rho.md
*/
#line 5 "library/src/math/primitive_root.hpp"
namespace kyopro {
/**
* @brief 原始根
*/
inline uint64_t primitive_root(uint64_t p) {
if (p == 2) return 1;
auto pf = kyopro::rho::factorize(p - 1);
pf.erase(std::unique(pf.begin(), pf.end()), pf.end());
for (auto& q : pf) {
q = (p - 1) / q;
}
using ull = unsigned long long;
if (dynamic_modint<uint64_t>::get_mod() != p) {
dynamic_modint<uint64_t>::set_mod(p);
}
xor_shift rng(2023);
while (1) {
dynamic_modint<uint64_t> g(rng());
if (g.val() == 0) continue;
bool is_ok = true;
for (auto q : pf) {
if (dynamic_modint<uint64_t>(g).pow(q).val() == 1) {
is_ok = false;
break;
}
}
if (is_ok) {
return g.val();
}
}
}
}; // namespace kyopro
#line 2 "library/src/stream.hpp"
#include <ctype.h>
#include <stdio.h>
#include <string>
namespace kyopro {
/**
* 整数の入出力
*/
template <typename T> constexpr inline void readint(T& a) {
a = 0;
bool is_negative = false;
char c = getchar_unlocked();
while (isspace(c)) {
c = getchar_unlocked();
}
if (c == '-') is_negative = true, c = getchar_unlocked();
while (isdigit(c)) {
a = 10 * a + (c - '0');
c = getchar_unlocked();
}
if (is_negative) a *= -1;
}
template <typename Head, typename... Tail>
constexpr inline void readint(Head& head, Tail&... tail) {
readint(head);
readint(tail...);
}
template <typename T> void write_int(T a) {
if (!a) {
putchar_unlocked('0');
putchar_unlocked('\n');
return;
}
if (a < 0) putchar_unlocked('-'), a *= -1;
char s[37];
int now = 37;
while (a) {
s[--now] = (char)'0' + a % 10;
a /= 10;
}
while (now < 37) putchar_unlocked(s[now++]);
}
template <typename T> constexpr inline void putint(T a) {
if (!a) {
putchar_unlocked('0');
putchar_unlocked('\n');
return;
}
if (a < 0) putchar_unlocked('-'), a *= -1;
char s[37];
int now = 37;
while (a) {
s[--now] = (char)'0' + a % 10;
a /= 10;
}
while (now < 37) putchar_unlocked(s[now++]);
putchar_unlocked('\n');
}
template <typename Head, typename... Tail>
constexpr inline void putint(Head head, Tail... tail) {
putint(head);
putint(tail...);
}
/**
* 文字列の入出力
*/
void readstr(std::string& str) {
char c = getchar_unlocked();
while (isspace(c)) c = getchar_unlocked();
while (!isspace(c)) {
str += c;
c = getchar_unlocked();
}
}
void putstr(const std::string& str) {
for (auto c : str) {
putchar_unlocked(c);
}
putchar_unlocked('\n');
}
}; // namespace kyopro
/**
* @brief fastIO
*/
#line 2 "library/src/template.hpp"
#include <bits/stdc++.h>
#define rep(i, N) for (int i = 0; i < (N); i++)
#define all(x) (x).begin(), (x).end()
#define popcount(x) __builtin_popcountll(x)
using i128 = __int128_t;
using ll = long long;
using ld = long double;
using graph = std::vector<std::vector<int>>;
using P = std::pair<int, int>;
constexpr int inf = 1e9;
constexpr ll infl = 1e18;
constexpr ld eps = 1e-6;
const long double pi = acos(-1);
constexpr uint64_t MOD = 1e9 + 7;
constexpr uint64_t MOD2 = 998244353;
constexpr int dx[] = {1, 0, -1, 0};
constexpr int dy[] = {0, 1, 0, -1};
template <typename T1, typename T2> constexpr inline bool chmax(T1& a, T2 b) {
return a < b && (a = b, true);
}
template <typename T1, typename T2> constexpr inline bool chmin(T1& a, T2 b) {
return a > b && (a = b, true);
}
#line 6 "main.cpp"
#define debug(x) \
std::cout << #x << " : "; \
for (auto __ : x) std::cout << __.val() << ' '; \
std::cout << std::endl;
using namespace std;
using namespace atcoder;
using namespace kyopro;
using mint = atcoder::modint998244353;
int main() {
int p;
readint(p);
int g = primitive_root(p);
// putint(g);
vector<mint> a(p), b(p);
for (int i = 1; i < p; ++i) readint(a[i]);
for (int i = 1; i < p; ++i) readint(b[i]);
vector<mint> ap(p), bp(p);
vector<int> lg(p);
vector<int> pow(p);
{
for (int e = 0, pw = 1; e < p; ++e) {
lg[pw] = e;
pow[e] = pw;
(pw *= g) %= p;
}
}
for (int i = 1; i < p; ++i) {
ap[lg[i]] = a[i];
bp[lg[i]] = b[i];
}
// debug(ap) debug(bp);
vector<mint> cp = convolution(ap, bp);
// debug(cp);
vector<mint> c(p);
for (int i = 0; i < (int)cp.size(); ++i) {
c[pow[i > p - 1 ? i - p + 1 : i]] += cp[i];
}
// debug(c);
for (int i = 1; i < p; ++i) putint(c[i].val());
}