結果
| 問題 |
No.3226 2×2行列累乗
|
| ユーザー |
 a01sa01to
|
| 提出日時 | 2025-08-11 08:41:44 |
| 言語 | C++23 (gcc 13.3.0 + boost 1.87.0) |
| 結果 |
AC
|
| 実行時間 | 2 ms / 2,000 ms |
| コード長 | 13,414 bytes |
| コンパイル時間 | 3,765 ms |
| コンパイル使用メモリ | 279,488 KB |
| 実行使用メモリ | 6,272 KB |
| 最終ジャッジ日時 | 2025-08-11 08:41:49 |
| 合計ジャッジ時間 | 4,405 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 * 3 |
| other | AC * 27 |
ソースコード
#line 1 "main.cpp"
#include <bits/stdc++.h>
using namespace std;
#define rep(i, n) for (int i = 0; i < (n); ++i)
using ll = long long;
using ull = unsigned long long;
#line 2 "my-library\\library\\data-structure\\matrix.hpp"
#line 4 "my-library\\library\\data-structure\\matrix.hpp"
#include <concepts>
#line 7 "my-library\\library\\data-structure\\matrix.hpp"
using namespace std;
#line 2 "my-library\\library\\_internal\\types.hpp"
#line 4 "my-library\\library\\_internal\\types.hpp"
using namespace std;
#line 2 "my-library\\library\\_internal\\modint-base.hpp"
#line 4 "my-library\\library\\_internal\\modint-base.hpp"
#include <type_traits>
using namespace std;
namespace asalib {
namespace _internal {
class modint_base {};
template<typename T>
concept is_modint = is_base_of_v<modint_base, T>;
}
}
#line 7 "my-library\\library\\_internal\\types.hpp"
namespace asalib {
namespace _internal {
template<class T>
concept integral_like = integral<T> || is_modint<T>;
template<class T>
concept floating_like = floating_point<T>;
template<class T>
concept numeric_like = integral_like<T> || floating_like<T>;
template<class T>
T plus(T a, T b) { return a + b; }
template<class T>
T minus(T a, T b) { return a - b; }
template<class T>
T zero() { return 0; }
}
}
#line 10 "my-library\\library\\data-structure\\matrix.hpp"
namespace asalib {
namespace matrix {
template<_internal::numeric_like T>
class Matrix {
public:
constexpr Matrix(): _n_row(0), _n_col(0) {};
constexpr Matrix(size_t n_row, size_t n_col): _n_row(n_row), _n_col(n_col) {
_data.resize(n_row, valarray<T>(n_col));
};
constexpr Matrix(size_t n_row, size_t n_col, T x): _n_row(n_row), _n_col(n_col) {
_data.resize(n_row, valarray<T>(n_col, x));
};
inline constexpr T& at(size_t i, size_t j) {
assert(i < _n_row);
assert(j < _n_col);
return _data[i][j];
}
inline constexpr T at(size_t i, size_t j) const {
assert(i < _n_row);
assert(j < _n_col);
return _data[i][j];
}
inline constexpr Matrix& operator+=(const T& x) {
_data += x;
return *this;
}
inline constexpr Matrix& operator-=(const T& x) {
_data -= x;
return *this;
}
inline constexpr Matrix& operator*=(const T& x) {
_data *= x;
return *this;
}
inline constexpr Matrix& operator/=(const T& x) {
_data /= x;
return *this;
}
inline constexpr Matrix& operator%=(const T& x) {
_data %= x;
return *this;
}
inline constexpr Matrix operator+(const T& x) const { return Matrix(*this) += x; }
inline constexpr Matrix operator-(const T& x) const { return Matrix(*this) -= x; }
inline constexpr Matrix operator*(const T& x) const { return Matrix(*this) *= x; }
inline constexpr Matrix operator/(const T& x) const { return Matrix(*this) /= x; }
inline constexpr Matrix operator%(const T& x) const { return Matrix(*this) %= x; }
inline constexpr Matrix& operator+=(const Matrix& x) {
assert(_n_row == x._n_row);
assert(_n_col == x._n_col);
_data += x._data;
return *this;
}
inline constexpr Matrix& operator-=(const Matrix& x) {
assert(_n_row == x._n_row);
assert(_n_col == x._n_col);
_data -= x._data;
return *this;
}
inline constexpr Matrix& operator*=(const Matrix& x) {
assert(_n_col == x._n_row);
Matrix res(_n_row, x._n_col);
for (size_t i = 0; i < _n_row; ++i) {
for (size_t k = 0; k < _n_col; ++k) {
for (size_t j = 0; j < x._n_col; ++j) {
res._data[i][j] += _data[i][k] * x._data[k][j];
}
}
}
return *this = res;
}
inline constexpr Matrix operator+(const Matrix& x) const { return Matrix(*this) += x; }
inline constexpr Matrix operator-(const Matrix& x) const { return Matrix(*this) -= x; }
inline constexpr Matrix operator*(const Matrix& x) const { return Matrix(*this) *= x; }
inline constexpr bool operator==(const Matrix& x) const { return _n_row == x._n_row && _n_col == x._n_col && _data == x._data; }
inline constexpr bool operator!=(const Matrix& x) const { return !(*this == x); }
inline constexpr bool operator<(const Matrix& x) const { return _data < x._data; }
inline constexpr Matrix transpose() const {
Matrix res(_n_col, _n_row);
for (size_t i = 0; i < _n_row; ++i) {
for (size_t j = 0; j < _n_col; ++j) {
res._data[j][i] = _data[i][j];
}
}
return res;
}
template<integral U>
inline constexpr Matrix pow(U x) const {
assert(_n_row == _n_col);
Matrix res = I(_n_row);
Matrix a(*this);
while (x) {
if (x & 1) res *= a;
a *= a;
x >>= 1;
}
return res;
}
inline static constexpr Matrix I(size_t n) {
Matrix res(n, n);
for (size_t i = 0; i < n; ++i) {
res._data[i][i] = 1;
}
return res;
}
inline constexpr size_t n_row() const { return _n_row; }
inline constexpr size_t n_col() const { return _n_col; }
private:
size_t _n_row, _n_col;
valarray<valarray<T>> _data;
public:
inline constexpr T determinant() const;
template<_internal::numeric_like U>
inline constexpr U determinant() const;
};
}
}
#line 2 "my-library\\library\\data-structure\\modint.hpp"
#line 8 "my-library\\library\\data-structure\\modint.hpp"
using namespace std;
#line 2 "my-library\\library\\math\\extgcd.hpp"
#line 4 "my-library\\library\\math\\extgcd.hpp"
#include <optional>
#line 6 "my-library\\library\\math\\extgcd.hpp"
using namespace std;
namespace asalib {
namespace math {
template<integral T>
constexpr optional<pair<T, T>> extgcd(T a, T b, T c) {
if (b == 0) {
if (c % a != 0) return nullopt;
return make_pair(c / a, 0);
}
auto res = extgcd(b, a % b, c);
if (!res) return nullopt;
auto [x, y] = *res;
return make_pair(y, x - (a / b) * y);
}
}
}
#line 12 "my-library\\library\\data-structure\\modint.hpp"
namespace asalib {
namespace ds {
template<unsigned int mod>
requires(mod >= 1)
class static_modint: private _internal::modint_base {
using mint = static_modint;
using uint = unsigned int;
using ll = long long;
using ull = unsigned long long;
public:
inline constexpr static_modint(): _val(0) {};
template<integral T>
inline constexpr static_modint(const T& x) {
if constexpr (is_signed_v<T>) {
ll y = x % (ll) mod;
if (y < 0) y += mod;
_val = y;
}
else {
_val = x % mod;
}
}
friend inline constexpr mint operator+(const mint& l, const mint& r) { return mint(l) += r; }
friend inline constexpr mint operator-(const mint& l, const mint& r) { return mint(l) -= r; }
friend inline constexpr mint operator*(const mint& l, const mint& r) { return mint(l) *= r; }
friend inline constexpr mint operator/(const mint& l, const mint& r) { return mint(l) /= r; }
inline constexpr mint operator+() const { return *this; }
inline constexpr mint operator-() const { return 0 - *this; }
inline constexpr mint& operator+=(const mint& other) {
_val += other._val;
if (_val >= mod) _val -= mod;
return *this;
}
inline constexpr mint& operator-=(const mint& other) {
_val -= other._val;
if (_val >= mod) _val += mod;
return *this;
}
inline constexpr mint& operator*=(const mint& other) {
ull z = _val;
z *= other._val;
_val = z % mod;
return *this;
}
inline constexpr mint& operator/=(const mint& other) { return *this = *this * other.inv(); }
inline constexpr mint& operator++() {
_val++;
if (_val == mod) _val = 0;
return *this;
}
inline constexpr mint& operator--() {
if (_val == 0) _val = mod;
_val--;
return *this;
}
inline constexpr mint operator++(int) {
mint res = *this;
++*this;
return res;
}
inline constexpr mint operator--(int) {
mint res = *this;
--*this;
return res;
}
inline constexpr bool operator==(const mint& r) const { return _val == r._val; }
inline constexpr bool operator!=(const mint& r) const { return _val != r._val; }
inline constexpr bool operator<(const mint& r) const { return _val < r._val; }
template<integral T>
inline constexpr mint pow(T x) const {
assert(x >= 0);
mint res = 1, base = *this;
while (x) {
if (x & 1) res *= base;
base *= base;
x >>= 1;
}
return res;
}
inline constexpr mint inv() const {
if constexpr (is_prime_mod) return pow(mod - 2);
else {
if (gcd(_val, mod) != 1) throw invalid_argument("Modular inverse does not exist");
return mint(math::extgcd<long long>(_val, mod, 1).value().first);
}
}
constexpr inline unsigned int val() const { return _val; }
private:
uint _val;
static inline constexpr bool is_prime_mod = []() {
for (unsigned int i = 2; i * i <= mod; ++i) {
if (mod % i == 0) return false;
}
return true;
}();
};
template<unsigned int id>
class dynamic_modint: private _internal::modint_base {
using mint = dynamic_modint;
using uint = unsigned int;
using ll = long long;
using ull = unsigned long long;
public:
inline constexpr dynamic_modint(): _val(0) {}
template<integral T>
inline constexpr dynamic_modint(const T& x) {
assert(_mod >= 1);
if constexpr (is_signed_v<T>) {
ll y = x % (ll) _mod;
if (y < 0) y += _mod;
_val = y;
}
else {
_val = x % _mod;
}
};
friend inline constexpr mint operator+(const mint& l, const mint& r) { return mint(l) += r; }
friend inline constexpr mint operator-(const mint& l, const mint& r) { return mint(l) -= r; }
friend inline constexpr mint operator*(const mint& l, const mint& r) { return mint(l) *= r; }
friend inline constexpr mint operator/(const mint& l, const mint& r) { return mint(l) /= r; }
inline constexpr mint operator+() const { return *this; }
inline constexpr mint operator-() const { return 0 - *this; }
inline constexpr mint& operator+=(const mint& other) {
_val += other._val;
if (_val >= _mod) _val -= _mod;
return *this;
}
inline constexpr mint& operator-=(const mint& other) {
_val -= other._val;
if (_val >= _mod) _val += _mod;
return *this;
}
inline constexpr mint& operator*=(const mint& other) {
ull z = _val;
z *= other._val;
_val = z % _mod;
return *this;
}
inline constexpr mint& operator/=(const mint& other) { return *this = *this * other.inv(); }
inline constexpr mint& operator++() {
_val++;
if (_val == _mod) _val = 0;
return *this;
}
inline constexpr mint& operator--() {
if (_val == 0) _val = _mod;
_val--;
return *this;
}
inline constexpr mint operator++(int) {
mint res = *this;
++*this;
return res;
}
inline constexpr mint operator--(int) {
mint res = *this;
--*this;
return res;
}
inline constexpr bool operator==(const mint& r) const { return _val == r._val; }
inline constexpr bool operator!=(const mint& r) const { return _val != r._val; }
inline constexpr bool operator<(const mint& r) const { return _val < r._val; }
template<integral T>
inline constexpr mint pow(T x) const {
assert(x >= 0);
mint res = 1, base = *this;
while (x) {
if (x & 1) res *= base;
base *= base;
x >>= 1;
}
return res;
}
inline constexpr mint inv() const {
if (gcd(_val, _mod) != 1) throw invalid_argument("Modular inverse does not exist");
return mint(math::extgcd<long long>(_val, _mod, 1).value().first);
}
inline constexpr uint val() const { return _val; }
inline constexpr static uint mod() { return _mod; }
inline constexpr static void set_mod(uint mod) {
assert(mod >= 1);
_mod = mod;
}
private:
uint _val;
static inline uint _mod;
};
}
}
#line 9 "main.cpp"
using mint = asalib::ds::dynamic_modint<0>;
int main() {
cin.tie(nullptr)->sync_with_stdio(false);
ll a, b, c, d, s, t, n, k;
cin >> a >> b >> c >> d >> s >> t >> n >> k;
mint::set_mod(k);
asalib::matrix::Matrix<mint> M(2, 2), st(2, 1);
M.at(0, 0) = a, M.at(0, 1) = b, M.at(1, 0) = c, M.at(1, 1) = d;
st.at(0, 0) = s, st.at(1, 0) = t;
auto res = M.pow(n) * st;
cout << res.at(0, 0).val() << ' ' << res.at(1, 0).val() << '\n';
return 0;
}