結果

問題 No.3006 ベイカーの問題
ユーザー 横山緑
提出日時 2025-01-18 00:12:26
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 9,703 bytes
コンパイル時間 4,772 ms
コンパイル使用メモリ 288,624 KB
実行使用メモリ 5,248 KB
最終ジャッジ日時 2025-01-18 00:12:45
合計ジャッジ時間 4,780 ms
ジャッジサーバーID
（参考情報） 		judge1 / judge4
このコードへのチャレンジ
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ファイルパターン 結果
sample AC * 3
other AC * 24
権限があれば一括ダウンロードができます

ソースコード

diff # 

#line 2 "template.hpp"
// #pragma GCC target("avx2")
// #pragma GCC optimize("O3")
// #pragma GCC optimize("unroll-loops")

#include <bits/stdc++.h>
using namespace std;
// https://xn--kst.jp/blog/2019/08/29/cpp-comp/
// debug methods
// usage: debug(x,y);
// vector 出力できるように修正
template <typename T> ostream &debug_print(ostream &os, const vector<T> &v) {
    os << "[";
    for(size_t i = 0; i < v.size(); ++i) {
        os << v[i];
        if(i < v.size() - 1)
            os << ", ";
    }
    os << "]";
    return os;
}
template <typename T> ostream &debug_print(ostream &os, const T &var) {
    os << var;
    return os;
}
#define CHOOSE(a) CHOOSE2 a
#define CHOOSE2(a0, a1, a2, a3, a4, x, ...) x
#define debug_1(x1)                                                            \
    {                                                                          \
        cout << #x1 << ": ";                                                   \
        debug_print(cout, x1) << endl;                                         \
    }
#define debug_2(x1, x2)                                                        \
    {                                                                          \
        cout << #x1 << ": ";                                                   \
        debug_print(cout, x1) << ", " << #x2 << ": ";                          \
        debug_print(cout, x2) << endl;                                         \
    }
#define debug_3(x1, x2, x3)                                                    \
    {                                                                          \
        cout << #x1 << ": ";                                                   \
        debug_print(cout, x1) << ", " << #x2 << ": ";                          \
        debug_print(cout, x2) << ", " << #x3 << ": ";                          \
        debug_print(cout, x3) << endl;                                         \
    }
#define debug_4(x1, x2, x3, x4)                                                \
    {                                                                          \
        cout << #x1 << ": ";                                                   \
        debug_print(cout, x1) << ", " << #x2 << ": ";                          \
        debug_print(cout, x2) << ", " << #x3 << ": ";                          \
        debug_print(cout, x3) << ", " << #x4 << ": ";                          \
        debug_print(cout, x4) << endl;                                         \
    }
#define debug_5(x1, x2, x3, x4, x5)                                            \
    {                                                                          \
        cout << #x1 << ": ";                                                   \
        debug_print(cout, x1) << ", " << #x2 << ": ";                          \
        debug_print(cout, x2) << ", " << #x3 << ": ";                          \
        debug_print(cout, x3) << ", " << #x4 << ": ";                          \
        debug_print(cout, x4) << ", " << #x5 << ": ";                          \
        debug_print(cout, x5) << endl;                                         \
    }

#ifdef LOCAL
#define debug(...)                                                             \
    CHOOSE((__VA_ARGS__, debug_5, debug_4, debug_3, debug_2, debug_1, ~))      \
    (__VA_ARGS__)
#else
#define debug(...)
#endif

using ll = long long;
using vl = vector<ll>;
using Graph = vector<vector<ll>>;
using P = pair<ll, ll>;
#define all(v) v.begin(), v.end()
template <typename T> inline bool chmax(T &a, T b) {
    return ((a < b) ? (a = b, true) : (false));
}
template <typename T> inline bool chmin(T &a, T b) {
    return ((a > b) ? (a = b, true) : (false));
}
#define rep1(i, n) for(ll i = 1; i <= ((ll)n); ++i)
// https://trap.jp/post/1224/
template <class... T> constexpr auto min(T... a) {
    return min(initializer_list<common_type_t<T...>>{a...});
}
template <class... T> constexpr auto max(T... a) {
    return max(initializer_list<common_type_t<T...>>{a...});
}
template <class... T> void input(T &...a) {
    (cin >> ... >> a);
}
template <class T> void input(vector<T> &a) {
    for(T &x : a)
        cin >> x;
}
void print() {
    cout << '\n';
}
template <class T, class... Ts> void print(const T &a, const Ts &...b) {
    cout << a;
    (cout << ... << (cout << ' ', b));
    cout << '\n';
}
void print(const string &s) {
    cout << s << '\n';
}
template <class Container, typename = void>
struct is_container : std::false_type {};
template <class Container>
struct is_container<Container,
                    std::void_t<decltype(std::declval<Container>().begin()),
                                decltype(std::declval<Container>().end())>>
    : std::true_type {};
template <class Container>
typename enable_if<is_container<Container>::value>::type
print(const Container &x) {
    if(!x.empty()) {
        auto it = x.begin();
        for(; it != prev(x.end()); ++it) {
            cout << *it << " ";
        }
        cout << *it << "\n"; // 最後の要素を出力して改行
    }
}
#define INT(...)                                                               \
    int __VA_ARGS__;                                                           \
    input(__VA_ARGS__)
#define LL(...)                                                                \
    long long __VA_ARGS__;                                                     \
    input(__VA_ARGS__)
#define STR(...)                                                               \
    string __VA_ARGS__;                                                        \
    input(__VA_ARGS__)
#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__)

ll inf = 3e18;
vl dx = {1, -1, 0, 0};
vl dy = {0, 0, 1, -1};
#line 3 "math/matrix.hpp"
template <class T> struct Matrix {
    vector<vector<T>> A;
    size_t height, width;
    Matrix() {
    }
    Matrix(size_t n, size_t m)
        : A(vector(n, vector<T>(m, 0))), height(n), width(m) {
    }
    Matrix(size_t n) : Matrix(n, n) {
    }
    Matrix(vector<vector<T>> A_)
        : A(A_), height(A_.size()), width(A_[0].size()) {
    }
    inline const vector<T> &operator[](size_t k) const {
        return A.at(k);
    };
    inline vector<T> &operator[](size_t k) {
        return A.at(k);
    };
    void show() {
        rep(i, height) {
            rep(j, width) {
                if constexpr(is_arithmetic<T>::value) {
                    cout << A[i][j] << " \n"[j + 1 == width];
                } else {
                    // atcoder::modint用
                    cout << A[i][j].val() << " \n"[j + 1 == width];
                }
            }
        }
    }

    Matrix &operator+=(const Matrix &B) {
        assert(height == B.height && width == B.width);
        rep(i, height) {
            rep(j, width) {
                A[i][j] += B[i][j];
            }
        }
        return *this;
    }
    Matrix &operator-=(const Matrix &B) {
        assert(height == B.height && width == B.width);
        rep(i, height) {
            rep(j, width) {
                A[i][j] -= B[i][j];
            }
        }
        return *this;
    }
    Matrix &operator*=(const Matrix &B) {
        assert(width == B.height);
        // (height,width)*(B.height,B.width) -> (height,B.width)
        Matrix<T> res(height, B.width);
        rep(i, height) {
            rep(j, width) {
                rep(k, B.width) {
                    res[i][k] += A[i][j] * B[j][k];
                }
            }
        }
        swap(*this, res);
        return *this;
    }
    Matrix &operator^=(size_t k) {
        assert(height == width);
        Matrix<T> res(height);
        rep(i, height) res[i][i] = 1;
        while(k) {
            if(k & 1) {
                res *= (*this);
            }
            (*this) *= (*this);
            k >>= 1;
        }
        swap(res, *this);
        return *this;
    }
    Matrix pow(size_t k) {
        auto res(*this);
        res ^= k;
        return res;
    }
    Matrix operator+(const Matrix &B) {
        return Matrix(*this) += B;
    }
    Matrix operator-(const Matrix &B) {
        return Matrix(*this) -= B;
    }
    Matrix operator*(const Matrix &B) {
        return Matrix(*this) *= B;
    }
};
#line 3 "/home/y_midori/cp/yukicoder/455/e.cpp"
#include <atcoder/modint>
// using namespace atcoder;
using mint = atcoder::modint998244353;
Matrix<mint> inv(Matrix<mint> a) {
    mint det = a[0][0] * a[1][1] - a[0][1] * a[1][0];
    mint idet = det.inv();
    // debug(det.val(), idet.val());
    Matrix<mint> res(2);
    res[0][0] = idet * a[1][1], res[1][1] = idet * a[0][0];
    res[0][1] = -idet * a[0][1];
    res[1][0] = -idet * a[1][0];
    return res;
}
void solve() {
    LL(x1, y1, n);
    mint x = x1, y = y1;
    if(x == 1 and y == 0) {
        print(n % mint::mod(), 0);
        return;
    }
    Matrix<mint> a(2), id(2);
    a[0][0] = a[1][1] = x;
    a[0][1] = -5 * y;
    a[1][0] = y;
    id[0][0] = id[1][1] = 1, id[0][1] = id[0][1] = 0;
    // a.pow(n).show();
    Matrix<mint> v = id - a.pow(n);
    // v.show();
    v = v * inv(id - a);
    // a.show();
    // id.show();
    // v.show();
    mint ax = v[0][0] * x + v[0][1] * y;
    mint ay = v[1][0] * x + v[1][1] * y;
    print(ax.val(), ay.val());
}
int main() {
    ios::sync_with_stdio(false);
    std::cin.tie(nullptr);
    cout << std::setprecision(16);
    int t = 1;
    rep(_, t) {
        solve();
    }
}
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