結果
| 問題 | No.840 ほむほむほむら |
| ユーザー |
 Pachicobue
|
| 提出日時 | 2019-06-14 23:15:00 |
| 言語 | C++17 (gcc 13.3.0 + boost 1.87.0) |
| 結果 |
AC
|
| 実行時間 | 252 ms / 4,000 ms |
| コード長 | 17,947 bytes |
| コンパイル時間 | 2,396 ms |
| コンパイル使用メモリ | 204,636 KB |
| 最終ジャッジ日時 | 2025-01-07 04:37:34 |
|
ジャッジサーバーID （参考情報） |
judge2 / judge3 |
（要ログイン）
| ファイルパターン | 結果 |
|---|---|
| sample | AC * 3 |
| other | AC * 25 |
ソースコード
#include <bits/stdc++.h>
#pragma GCC diagnostic ignored "-Wsign-compare"
#pragma GCC diagnostic ignored "-Wsign-conversion"
#define NDEBUG
#define SHOW(...) static_cast<void>(0)
//!===========================================================!//
//! dP dP dP !//
//! 88 88 88 !//
//! 88aaaaa88a .d8888b. .d8888b. .d888b88 .d8888b. 88d888b. !//
//! 88 88 88ooood8 88' '88 88' '88 88ooood8 88' '88 !//
//! 88 88 88. ... 88. .88 88. .88 88. ... 88 !//
//! dP dP '88888P' '88888P8 '88888P8 '88888P' dP !//
//!===========================================================!//
template <typename T, typename A>
std::istream& operator>>(std::istream& is, std::vector<T, A>& v)
{
for (auto& e : v) { is >> e; }
return is;
}
template <typename T>
T read()
{
T v;
return std::cin >> v, v;
}
template <typename T>
std::vector<T> readVec(const std::size_t l)
{
std::vector<T> v(l);
for (auto& e : v) { std::cin >> e; }
return v;
}
using ld = long double;
using uint = unsigned int;
using ll = long long;
using ull = unsigned long long;
constexpr unsigned int MOD = 1000000007;
template <typename T>
constexpr T INF = std::numeric_limits<T>::max() / 4;
template <typename F>
constexpr F PI = static_cast<F>(3.1415926535897932385);
std::mt19937 mt{std::random_device{}()};
template <typename T>
bool chmin(T& a, const T& b) { return (a > b ? a = b, true : false); }
template <typename T>
bool chmax(T& a, const T& b) { return (a < b ? a = b, true : false); }
template <typename T>
std::vector<T> Vec(const std::size_t n, T v) { return std::vector<T>(n, v); }
template <class... Args>
auto Vec(const std::size_t n, Args... args) { return std::vector<decltype(Vec(args...))>(n, Vec(args...)); }
template <typename T>
constexpr T popCount(const T u)
{
#ifdef __has_builtin
return u == 0 ? T(0) : (T)__builtin_popcountll(u);
#else
unsigned long long v = static_cast<unsigned long long>(u);
return v = (v & 0x5555555555555555ULL) + (v >> 1 & 0x5555555555555555ULL), v = (v & 0x3333333333333333ULL) + (v >> 2 & 0x3333333333333333ULL), v = (v + (v >> 4)) & 0x0F0F0F0F0F0F0F0FULL, static_cast<T>(v * 0x0101010101010101ULL >> 56 & 0x7f);
#endif
}
template <typename T>
constexpr T log2p1(const T u)
{
#ifdef __has_builtin
return u == 0 ? T(0) : T(64 - __builtin_clzll(u));
#else
unsigned long long v = static_cast<unsigned long long>(u);
return v = static_cast<unsigned long long>(v), v |= (v >> 1), v |= (v >> 2), v |= (v >> 4), v |= (v >> 8), v |= (v >> 16), v |= (v >> 32), popCount(v);
#endif
}
template <typename T>
constexpr T clog(const T v) { return v == 0 ? T(0) : log2p1(v - 1); }
template <typename T>
constexpr T msbp1(const T v) { return log2p1(v); }
template <typename T>
constexpr T lsbp1(const T v)
{
#ifdef __has_builtin
return __builtin_ffsll(v);
#else
return v == 0 ? T(0) : popCount((v & (-v)) - T(1)) + T(1);
#endif
}
template <typename T>
constexpr bool ispow2(const T v) { return popCount(v) == 1; }
template <typename T>
constexpr T ceil2(const T v) { return v == 0 ? T(1) : T(1) << log2p1(v - 1); }
template <typename T>
constexpr T floor2(const T v) { return v == 0 ? T(0) : T(1) << (log2p1(v) - 1); }
//!===============================================================!//
//! 88888888b dP .88888. a88888b. 888888ba !//
//! 88 88 d8' '88 d8' '88 88 '8b !//
//! a88aaaa dP. .dP d8888P 88 88 88 88 !//
//! 88 '8bd8' 88 88 YP88 88 88 88 !//
//! 88 .d88b. 88 Y8. .88 Y8. .88 88 .8P !//
//! 88888888P dP' 'dP dP '88888' Y88888P' 8888888P !//
//!===============================================================!//
template <typename T>
constexpr std::pair<T, T> extgcd(const T a, const T b)
{
if (b == 0) { return std::pair<T, T>{1, 0}; }
const auto p = extgcd(b, a % b);
return {p.second, p.first - p.second * (a / b)};
}
template <typename T>
constexpr T inverse(const T a, const T mod) { return (mod + extgcd((mod + a % mod) % mod, mod).first % mod) % mod; }
//!========================================================!//
//! 8888ba.88ba dP dP dP !//
//! 88 '8b '8b 88 88 88 !//
//! 88 88 88 .d8888b. .d888b88 88 88d888b. d8888P !//
//! 88 88 88 88' '88 88' '88 88 88' '88 88 !//
//! 88 88 88 88. .88 88. .88 88 88 88 88 !//
//! dP dP dP '88888P' '88888P8 dP dP dP dP !//
//!========================================================!//
template <uint mod>
class ModInt
{
private:
uint v;
static uint norm(const uint& x) { return x < mod ? x : x - mod; }
static ModInt make(const uint& x)
{
ModInt m;
return m.v = x, m;
}
static ModInt power(ModInt x, ll n)
{
ModInt ans = 1;
for (; n; n >>= 1, x *= x) {
if (n & 1) { ans *= x; }
}
return ans;
}
static ModInt inv(const ModInt& x) { return ModInt{inverse((ll)x.v, (ll)mod)}; }
public:
ModInt() : v{0} {}
ModInt(const ll val) : v{norm(uint(val % (ll)mod + (ll)mod))} {}
ModInt(const ModInt<mod>& n) : v{n()} {}
explicit operator bool() const { return v != 0; }
ModInt<mod>& operator=(const ModInt<mod>& n) { return v = n(), (*this); }
ModInt<mod>& operator=(const ll val) { return v = norm(uint(val % (ll)mod + (ll)mod)), (*this); }
ModInt<mod> operator+() const { return *this; }
ModInt<mod> operator-() const { return make(norm(mod - v)); }
ModInt<mod> operator+(const ModInt<mod>& val) const { return make(norm(v + val())); }
ModInt<mod> operator-(const ModInt<mod>& val) const { return make(norm(v + mod - val())); }
ModInt<mod> operator*(const ModInt<mod>& val) const { return make((uint)((ll)v * val() % (ll)mod)); }
ModInt<mod> operator/(const ModInt<mod>& val) const { return *this * inv(val()); }
ModInt<mod>& operator+=(const ModInt<mod>& val) { return *this = *this + val; }
ModInt<mod>& operator-=(const ModInt<mod>& val) { return *this = *this - val; }
ModInt<mod>& operator*=(const ModInt<mod>& val) { return *this = *this * val; }
ModInt<mod>& operator/=(const ModInt<mod>& val) { return *this = *this / val; }
ModInt<mod> operator+(const ll val) const { return ModInt{v + val}; }
ModInt<mod> operator-(const ll val) const { return ModInt{v - val}; }
ModInt<mod> operator*(const ll val) const { return ModInt{(ll)v * (val % mod)}; }
ModInt<mod> operator/(const ll val) const { return ModInt{(ll)v * inv(val)}; }
template <typename I>
ModInt<mod> operator^(const I n) const { return power(v, n); }
ModInt<mod>& operator+=(const ll val) { return *this = *this + val; }
ModInt<mod>& operator-=(const ll val) { return *this = *this - val; }
ModInt<mod>& operator*=(const ll val) { return *this = *this * val; }
ModInt<mod>& operator/=(const ll val) { return *this = *this / val; }
template <typename I>
ModInt<mod>& operator^=(const I n) { return (*this) = ((*this) ^ n); }
bool operator==(const ModInt<mod>& val) const { return v == val.v; }
bool operator!=(const ModInt<mod>& val) const { return not(*this == val); }
bool operator==(const ll val) const { return v == norm(uint((ll)mod + val % (ll)mod)); }
bool operator!=(const ll val) const { return not(*this == val); }
uint operator()() const { return v; }
};
template <uint mod>
inline ModInt<mod> operator+(const ll val, const ModInt<mod>& n) { return n + val; }
template <uint mod>
inline ModInt<mod> operator-(const ll val, const ModInt<mod>& n) { return ModInt<mod>{val - (ll)n()}; }
template <uint mod>
inline ModInt<mod> operator*(const ll val, const ModInt<mod>& n) { return n * val; }
template <uint mod>
inline ModInt<mod> operator/(const ll val, const ModInt<mod>& n) { return ModInt<mod>(val) / n; }
template <uint mod>
inline bool operator==(const ll val, const ModInt<mod>& n) { return n == val; }
template <uint mod>
inline bool operator!=(const ll val, const ModInt<mod>& n) { return not(val == n); }
template <uint mod>
inline std::istream& operator>>(std::istream& is, ModInt<mod>& n)
{
uint v;
return is >> v, n = v, is;
}
template <uint mod>
std::ostream& operator<<(std::ostream& os, const ModInt<mod>& n) { return (os << n()); }
//!=====================================================!//
//! 8888ba.88ba dP oo !//
//! 88 '8b '8b 88 !//
//! 88 88 88 .d8888b. d8888P 88d888b. dP dP. .dP !//
//! 88 88 88 88' '88 88 88' '88 88 '8bd8' !//
//! 88 88 88 88. .88 88 88 88 .d88b. !//
//! dP dP dP '88888P8 dP dP dP dP' 'dP !//
//!=====================================================!//
template <typename T>
struct Matrix
{
Matrix(const std::size_t R, const std::size_t C) : R{R}, C{C}, table(R, std::vector<T>(C, T(0))) {}
const std::vector<T>& operator[](const std::size_t r) const { return table[r]; }
std::vector<T>& operator[](const std::size_t r) { return table[r]; }
Matrix<T> operator-() const
{
Matrix<T> ans(R, C);
for (std::size_t i = 0; i < R; i++) {
for (std::size_t j = 0; j < C; j++) { ans[i][j] = -table[i][j]; }
}
return ans;
}
Matrix<T> operator+(const Matrix<T>& m) const
{
assert(R == m.R);
assert(C == m.C);
Matrix<T> ans(R, C);
for (std::size_t i = 0; i < R; i++) {
for (std::size_t j = 0; j < C; j++) { ans[i][j] = table[i][j] + m[i][j]; }
}
return ans;
}
Matrix<T> operator-(const Matrix<T>& m) const
{
assert(R == m.R);
assert(C == m.C);
Matrix<T> ans(R, C);
for (std::size_t i = 0; i < R; i++) {
for (std::size_t j = 0; j < C; j++) { ans[i][j] = table[i][j] - m[i][j]; }
}
return ans;
}
Matrix<T> operator*(const Matrix<T>& m) const
{
assert(C == m.R);
Matrix<T> ans(R, m.C);
for (std::size_t i = 0; i < R; i++) {
for (std::size_t j = 0; j < m.C; j++) {
for (std::size_t k = 0; k < C; k++) { ans[i][j] += table[i][k] * m[k][j]; }
}
}
return ans;
}
Matrix<T> operator*(const T& t) const
{
Matrix<T> ans(R, C);
for (std::size_t i = 0; i < R; i++) {
for (std::size_t j = 0; j < C; j++) { ans[i][j] = table[i][j] * t; }
}
return ans;
}
template <typename C>
Matrix<T> operator^(const C n) const { return assert(n > 0), n == 1 ? *this : n % 2 == 1 ? (*this) * ((*this) ^ (n - 1)) : (((*this) * (*this)) ^ (n / 2)); }
Matrix<T>& operator=(const Matrix<T>& m)
{
assert(R == m.R);
assert(C == m.C);
for (std::size_t i = 0; i < R; i++) {
for (std::size_t j = 0; j < C; j++) { table[i][j] = m[i][j]; }
}
return *this;
}
Matrix<T>& operator+=(const Matrix<T>& m)
{
assert(R == m.R);
assert(C == m.C);
for (std::size_t i = 0; i < R; i++) {
for (std::size_t j = 0; j < C; j++) { table[i][j] += m[i][j]; }
}
}
Matrix<T>& operator-=(const Matrix<T>& m)
{
assert(R == m.R);
assert(C == m.C);
for (std::size_t i = 0; i < R; i++) {
for (std::size_t j = 0; j < C; j++) { table[i][j] -= m[i][j]; }
}
return *this;
}
Matrix<T>& operator*=(const Matrix<T>& m) { return *this = (*this) * m; }
Matrix<T>& operator*=(const T& t)
{
for (std::size_t i = 0; i < R; i++) {
for (std::size_t j = 0; j < C; j++) { table[i][j] *= t; }
}
return *this;
}
template <typename C>
Matrix<T>& operator^=(const C n) { return (*this) = ((*this) ^ n); }
const std::size_t R, C;
std::vector<std::vector<T>> table;
};
template <typename T>
Matrix<T> operator*(const T& t, const Matrix<T>& m) { return m * t; }
template <typename T>
std::ostream& operator<<(std::ostream& os, const Matrix<T>& m)
{
os << "[\n";
for (std::size_t i = 0; i < m.R; i++) {
os << "[";
for (std::size_t j = 0; j < m.C; j++) { os << m[i][j] << " "; }
os << "]\n";
}
return (os << "]\n");
}
template <typename T>
struct Vector
{
Vector(const std::size_t R) : R{R}, table(R, T(0)) {}
const T& operator[](const std::size_t r) const { return table[r]; }
T& operator[](const std::size_t r) { return table[r]; }
Vector<T> operator+(const Vector<T>& v) const
{
assert(R == v.R);
Vector<T> ans(R);
for (std::size_t i = 0; i < R; i++) { ans[i] = table[i] + v[i]; }
return ans;
}
Vector<T> operator-(const Vector<T>& v) const
{
assert(R == v.R);
Vector<T> ans(R);
for (std::size_t i = 0; i < R; i++) { ans[i] = table[i] - v[i]; }
return ans;
}
Vector<T> operator*(const T& t) const
{
Vector<T> ans(R);
for (std::size_t i = 0; i < R; i++) { ans[i] = table[i] * t; }
return ans;
}
Vector<T>& operator=(const Vector<T>& v)
{
assert(R == v.R);
for (std::size_t i = 0; i < R; i++) { table[i] = v[i]; }
return *this;
}
Vector<T>& operator+=(const Vector<T>& v)
{
assert(R == v.R);
for (std::size_t i = 0; i < R; i++) { table[i] += v[i]; }
return *this;
}
Vector<T>& operator-=(const Vector<T>& v)
{
assert(R == v.R);
for (std::size_t i = 0; i < R; i++) { table[i] -= v[i]; }
return *this;
}
Vector<T>& operator*=(const T& t)
{
Vector<T> ans(R);
for (std::size_t i = 0; i < R; i++) { table[i] *= t; }
return *this;
}
const std::size_t R;
std::vector<T> table;
};
template <typename T>
Vector<T> operator*(const T& t, const Vector<T>& v) { return v * t; }
template <typename T>
Vector<T> operator*(const Matrix<T>& m, const Vector<T>& v)
{
assert(m.C == v.R);
Vector<T> ans(m.R);
for (std::size_t i = 0; i < m.R; i++) {
for (std::size_t j = 0; j < m.C; j++) { ans[i] += m[i][j] * v[j]; }
}
return ans;
}
template <typename T>
std::ostream& operator<<(std::ostream& os, const Vector<T>& v)
{
os << "[\n";
for (std::size_t i = 0; i < v.R; i++) { os << v[i] << "\n"; }
return (os << "]\n");
}
template <typename T>
struct TVector
{
TVector(const std::size_t C) : C{C}, table(C, T(0)) {}
const T& operator[](const std::size_t c) const { return table[c]; }
T& operator[](const std::size_t c) { return table[c]; }
TVector<T> operator+(const TVector<T>& v) const
{
assert(C == v.C);
TVector<T> ans(C);
for (std::size_t i = 0; i < C; i++) { ans[i] = table[i] + v[i]; }
return ans;
}
TVector<T> operator-(const TVector<T>& v) const
{
assert(C == v.C);
TVector<T> ans(C);
for (std::size_t i = 0; i < C; i++) { ans[i] = table[i] - v[i]; }
return ans;
}
TVector<T> operator*(const T& t) const
{
TVector<T> ans(C);
for (std::size_t i = 0; i < C; i++) { ans[i] = table[i] * t; }
return ans;
}
TVector<T>& operator=(const TVector<T>& v)
{
assert(C == v.C);
for (std::size_t i = 0; i < C; i++) { table[i] = v[i]; }
return *this;
}
TVector<T>& operator+=(const TVector<T>& v)
{
assert(C == v.C);
for (std::size_t i = 0; i < C; i++) { table[i] += v[i]; }
return *this;
}
TVector<T>& operator-=(const TVector<T>& v)
{
assert(C == v.C);
for (std::size_t i = 0; i < C; i++) { table[i] -= v[i]; }
return *this;
}
TVector<T>& operator*=(const T& t)
{
TVector<T> ans(C);
for (std::size_t i = 0; i < C; i++) { table[i] *= t; }
return *this;
}
const std::size_t C;
std::vector<T> table;
};
template <typename T>
TVector<T> operator*(const T& t, const TVector<T>& v) { return v * t; }
template <typename T>
TVector<T> operator*(const TVector<T>& v, const Matrix<T>& m)
{
assert(v.C == m.R);
TVector<T> ans(m.C);
for (std::size_t i = 0; i < m.C; i++) {
for (std::size_t j = 0; j < m.R; j++) { ans[i] += v[j] * m[j][i]; }
}
return ans;
}
template <typename T>
std::ostream& operator<<(std::ostream& os, const TVector<T>& v)
{
os << "[ ";
for (std::size_t i = 0; i < v.C; i++) { os << v[i] << " "; }
return (os << "]\n");
}
//!============================================!//
//! 8888ba.88ba oo !//
//! 88 '8b '8b !//
//! 88 88 88 .d8888b. dP 88d888b. !//
//! 88 88 88 88' '88 88 88' '88 !//
//! 88 88 88 88. .88 88 88 88 !//
//! dP dP dP '88888P8 dP dP dP !//
//!============================================!//
int main()
{
constexpr uint MOD = 998244353;
using mint = ModInt<MOD>;
using Mat = Matrix<mint>;
const int N = read<int>(), K = read<int>();
Mat m(K * K * K, K * K * K);
auto encode = [&](const int i, const int j, const int k) { return i * K * K + j * K + k; };
for (int i = 0; i < K; i++) {
for (int j = 0; j < K; j++) {
for (int k = 0; k < K; k++) {
m[encode((i + 1) % K, j, k)][encode(i, j, k)] += 1;
m[encode(i, (i + j) % K, k)][encode(i, j, k)] += 1;
m[encode(i, j, (j + k) % K)][encode(i, j, k)] += 1;
}
}
}
m ^= N;
mint ans = 0;
for (int i = 0; i < K * K * K; i++) {
if (i % K == 0) { ans += m[i][0]; }
}
std::cout << ans << std::endl;
return 0;
}