#pragma GCC optimize ("O3") #include using namespace std; using ll = long long int; #define all(v) (v).begin(),(v).end() #define repeat(cnt,l) for(typename remove_const::type>::type cnt={};(cnt)<(l);++(cnt)) #define rrepeat(cnt,l) for(auto cnt=(l)-1;0<=(cnt);--(cnt)) #define iterate(cnt,b,e) for(auto cnt=(b);(cnt)!=(e);++(cnt)) #define diterate(cnt,b,e) for(auto cnt=(b);(cnt)!=(e);--(cnt)) const long long MD = 998244353ll; const long double PI = 3.1415926535897932384626433832795L; template inline ostream& operator <<(ostream &o, const pair p) { o << '(' << p.first << ':' << p.second << ')'; return o; } template inline T& chmax(T& to, const T& val) { return to = max(to, val); } template inline T& chmin(T& to, const T& val) { return to = min(to, val); } void bye(string s, int code = 0) { cout << s << endl; exit(code); } mt19937_64 randdev(8901016); template::value>::type* = nullptr> inline T rand(T l, T h, Random& rand = randdev) { return uniform_int_distribution(l, h)(rand); } template::value>::type* = nullptr> inline T rand(T l, T h, Random& rand = randdev) { return uniform_real_distribution(l, h)(rand); }template static ostream& operator<<(ostream& o, const std::vector& v) { o << "[ "; for(const auto& e : v) o< struct MyRangeFormat{ I b,e; MyRangeFormat(I _b, I _e):b(_b),e(_e){} }; template static ostream& operator<<(ostream& o, const MyRangeFormat& f) { o << "[ "; iterate(i,f.b,f.e) o<<*i<<' '; return o << ']'; } template struct MyMatrixFormat{ const I& p; long long n, m; MyMatrixFormat(const I& _p, long long _n, long long _m):p(_p),n(_n),m(_m){} }; template static ostream& operator<<(ostream& o, const MyMatrixFormat& f) { o<<'\n'; repeat(i,(f.n)) { repeat(j,f.m) o<(m,m+w)) #define FMTR(b,e) (MyRangeFormat(b,e)) #define FMTV(v) FMTR(v.begin(),v.end()) #define FMTM(m,h,w) (MyMatrixFormat(m,h,w)) #if defined(_WIN32) || defined(_WIN64) #define getc_x _getc_nolock #define putc_x _putc_nolock #elif defined(__GNUC__) #define getc_x getc_unlocked #define putc_x putc_unlocked #else #define getc_x getc #define putc_x putc #endif class MaiScanner { FILE* fp_; constexpr bool isvisiblechar(char c) noexcept { return (0x21<=(c)&&(c)<=0x7E); } public: inline MaiScanner(FILE* fp):fp_(fp){} template void input_integer(T& var) noexcept { var = 0; T sign = 1; int cc = getc_x(fp_); for (; cc < '0' || '9' < cc; cc = getc_x(fp_)) if (cc == '-') sign = -1; for (; '0' <= cc && cc <= '9'; cc = getc_x(fp_)) var = (var << 3) + (var << 1) + cc - '0'; var = var * sign; } inline int c() noexcept { return getc_x(fp_); } template::value, nullptr_t>::type = nullptr> inline MaiScanner& operator>>(T& var) noexcept { input_integer(var); return *this; } inline MaiScanner& operator>>(string& var) { int cc = getc_x(fp_); for (; !isvisiblechar(cc); cc = getc_x(fp_)); for (; isvisiblechar(cc); cc = getc_x(fp_)) var.push_back(cc); return *this; } template inline void in(IT begin, IT end) { for (auto it = begin; it != end; ++it) *this >> *it; } }; class MaiPrinter { FILE* fp_; public: inline MaiPrinter(FILE* fp):fp_(fp){} template void output_integer(T var) noexcept { if (var == 0) { putc_x('0', fp_); return; } if (var < 0) putc_x('-', fp_), var = -var; char stack[32]; int stack_p = 0; while (var) stack[stack_p++] = '0' + (var % 10), var /= 10; while (stack_p) putc_x(stack[--stack_p], fp_); } inline MaiPrinter& operator<<(char c) noexcept { putc_x(c, fp_); return *this; } template::value, nullptr_t>::type = nullptr> inline MaiPrinter& operator<<(T var) noexcept { output_integer(var); return *this; } inline MaiPrinter& operator<<(char* str_p) noexcept { while (*str_p) putc_x(*(str_p++), fp_); return *this; } inline MaiPrinter& operator<<(const string& str) { const char* p = str.c_str(); const char* l = p + str.size(); while (p < l) putc_x(*p++, fp_); return *this; } template void join(IT begin, IT end, char sep = ' ') { for (bool b = 0; begin != end; ++begin, b = 1) b ? *this << sep << *begin : *this << *begin; } }; MaiScanner scanner(stdin); MaiPrinter printer(stdout); class llmod { private: using value_type = long long; value_type val_; // inline ll cut(ll v) const { return ((v%MOD) + MOD) % MOD; } // safe public: static const value_type MOD = MD; // <= llmod() : val_(0) {} llmod(value_type num) : val_(((num % MOD) + MOD) % MOD) {} inline operator value_type() const { return val_; } inline value_type operator*() const { return val_; } inline llmod& operator=(const llmod& lm) { val_ = lm.val_; return *this; } inline llmod& operator=(value_type v) { val_ = (v) % MOD; return *this; } inline llmod& operator+=(value_type v) { val_ = (val_ + v) % MOD; return *this; } inline llmod& operator+=(const llmod& l) { val_ = (val_ + l.val_) % MOD; return *this; } inline llmod& operator-=(value_type v) { val_ = (val_ - v + MOD) % MOD; return *this; } inline llmod& operator-=(const llmod& l) { val_ = (val_ - l.val_ + MOD) % MOD; return *this; } inline llmod& operator*=(value_type v) { val_ = (val_ * v) % MOD; return *this; } inline llmod& operator*=(const llmod& l) { val_ = (val_ * l.val_) % MOD; return *this; } inline llmod& operator++() { val_ = (val_ + 1) % MOD; return *this; } inline llmod operator++(int) { llmod t = *this; val_ = (val_ + 1) % MOD; return t; } inline llmod& justify() { val_ = ((val_ % MOD) + MOD) % MOD; return *this; } friend llmod pow(llmod, long long); }; inline std::ostream& operator<<(std::ostream& os, const llmod& l) { os << *l; return os; } inline llmod operator+(llmod t, const llmod& r) { return t += r; } inline llmod operator-(llmod t, const llmod& r) { return t -= r; } inline llmod operator*(llmod t, const llmod& r) { return t *= r; } // MEMO : 逆元...pow(n,MD-2) llmod pow(llmod x, long long p) { llmod::value_type y = 1; llmod::value_type xval = x.justify(); while (0 < p) { if (p & 1) y = (xval * y) % llmod::MOD; xval = (xval * xval) % llmod::MOD; p >>= 1; } return llmod(y); } inline llmod& operator/=(llmod& l, const llmod& r) { return l *= pow(r, llmod::MOD - 2); } template > // using T = double; class Matrix { public: size_t height_, width_; Container data_; Matrix(size_t height = 1, size_t width = 1) : height_(height), width_(width), data_(height * width) {} template Matrix(size_t height, size_t width, const V& data) : height_(height), width_(width), data_(data) {} Matrix(size_t height, size_t width, initializer_list init) : height_(height), width_(width), data_(init) {} static Matrix makeDiag(size_t n, T val) { Matrix mat(n, n); for (size_t i = 0; i < n; ++i) mat(i, i) = val; return mat; } inline T& operator()(size_t y, size_t x) { return data_[y * width_ + x]; } inline T operator()(size_t y, size_t x) const { return data_[y * width_ + x]; } inline T& operator[](size_t i) { return data_[i]; } inline T operator[](size_t i) const { return data_[i]; } inline void resize(size_t h, size_t w) { height_ = h; width_ = w; data_.resize(h * w); } inline void resize(size_t h, size_t w, T val) { height_ = h; width_ = w; data_.resize(h * w, val); } inline void fill(T val) { data_ = val; } void transpose() { for (size_t y = 0; y < height_; ++y) for (size_t x = y + 1; x < width_; ++x) swap(operator()(y, x), operator()(x, y)); } Matrix transposed() const { auto m = *this; m.transpose(); return m; } void print(ostream& os) { os << "- - -" << endl; // << setprecision(3) for (size_t y = 0; y < height_; ++y) { for (size_t x = 0; x < width_; ++x) { os << setw(7) << operator()(y, x) << ' '; } os << endl; } } }; template inline ostream& operator<<(ostream& os, Matrix mat) { mat.print(os); return os; } template Matrix multiply(const Matrix& mat1, const Matrix& mat2) { assert(mat1.width_ == mat2.height_); Matrix result(mat1.height_, mat2.width_); for (size_t i = 0; i < mat1.height_; ++i) for (size_t j = 0; j < mat2.width_; ++j) for (size_t k = 0; k < mat1.width_; ++k) result(i, j) += mat1(i, k) * mat2(k, j); return result; } template V multiply(const Matrix& mat1, const V& vec2) { assert(mat1.width_ == vec2.size()); V result(mat1.height_); for (size_t i = 0, j; i < mat1.height_; ++i) for (j = 0; j < mat1.width_; ++j) result[i] += mat1(i, j) * vec2[j]; return result; } template inline Matrix& operator+=(Matrix& mat, T val) { mat.data_ += val; return mat; } template inline Matrix& operator-=(Matrix& mat, T val) { mat.data_ -= val; return mat; } template inline Matrix& operator*=(Matrix& mat, T val) { mat.data_ *= val; return mat; } template inline Matrix& operator/=(Matrix& mat, T val) { mat.data_ /= val; return mat; } template inline Matrix& operator^=(Matrix& mat, T val) { mat.data_ ^= val; return mat; } template inline Matrix& operator+=(Matrix& mat1, const Matrix& mat2) { mat1.data_ += mat2.data_; return mat1; } template inline Matrix operator+(Matrix& mat1, const Matrix& mat2) { return Matrix(mat1.height_, mat1.width_, mat1.data_ + mat2.data_); } template inline Matrix& operator-=(Matrix& mat1, const Matrix& mat2) { mat1.data_ -= mat2.data_; return mat1; } template inline Matrix operator-(Matrix& mat1, const Matrix& mat2) { return Matrix(mat1.height_, mat1.width_, mat1.data_ - mat2.data_); } template inline Matrix& operator*=(Matrix& mat1, const Matrix& mat2) { mat1 = multiply(mat1, mat2); return mat1; } template inline Matrix operator*(const Matrix& mat1, const Matrix& mat2) { return multiply(mat1, mat2); } template inline V operator*(const Matrix& mat1, const V& vec2) { return multiply(mat1, vec2); } template Matrix pow(Matrix a, long long p) { assert(a.height_ == a.width_); auto b = Matrix::makeDiag(a.height_, 1); while (0 < p) { if (p & 1) b *= a; a *= a; p >>= 1; } return b; } // ll N, K; // bool kado(int x, int y, int z) { return (x!=z)&&((xz)||(x>y&&y> idx; { int i = 0; repeat(a1, K) { repeat(a2, K) { if (a1 == a2) continue; idx[a1][a2] = i++; } } } int KK = K*K-K; Matrix mat(KK+KK, KK+KK); Matrix vec(KK+KK, 1); vec.fill(1); repeat(a1, K) { repeat(a2, K) { vec[KK+idx[a1][a2]] = a1+a2; repeat(b, K) { if (kado(a1,a2,b)) { mat(idx[a2][b], idx[a1][a2]) = 1; mat(KK+idx[a2][b], idx[a1][a2]) = b; mat(KK+idx[a2][b], KK+idx[a1][a2]) = 1; } } } } auto m2 = pow(mat, N-2); auto v2 = m2*vec; ll total1 = 0, total2 = 0; repeat(i, KK) { total1 += v2[i]; total1 %= MD; } repeat(i, KK) { total2 += v2[KK+i]; total2 %= MD; } cout << total1 << " " << total2 << endl; } int main() { cin >> N >> K; solve1(); return 0; }