#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; using mat = Matrix<mint>; 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, n); 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; mat b(4); rep(i, 2) rep(j, 2) { b[i][j] = a[i][j]; b[i][j + 2] = id[i][j]; b[i + 2][j + 2] = id[i][j]; } b = b.pow(n); mat v(2); rep(i, 2) rep(j, 2) v[i][j] = b[i][j + 2]; // 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(); } }