typedef long long ll; typedef long double ld; #include <bits/stdc++.h> using namespace std; // #define int long long #include <ext/pb_ds/assoc_container.hpp> using namespace __gnu_pbds; template<typename T> using ordered_set = tree<T, null_type, std::less<T>, rb_tree_tag, tree_order_statistics_node_update>; // std::cout << *s.find_by_order(1) << std::endl; // 2 // modint template<int MOD> struct Fp { // inner value long long val; // constructor constexpr Fp() : val(0) { } constexpr Fp(long long v) : val(v % MOD) { if (val < 0) val += MOD; } constexpr long long get() const { return val; } constexpr int get_mod() const { return MOD; } // arithmetic operators constexpr Fp operator + () const { return Fp(*this); } constexpr Fp operator - () const { return Fp(0) - Fp(*this); } constexpr Fp operator + (const Fp &r) const { return Fp(*this) += r; } constexpr Fp operator - (const Fp &r) const { return Fp(*this) -= r; } constexpr Fp operator * (const Fp &r) const { return Fp(*this) *= r; } constexpr Fp operator / (const Fp &r) const { return Fp(*this) /= r; } constexpr Fp& operator += (const Fp &r) { val += r.val; if (val >= MOD) val -= MOD; return *this; } constexpr Fp& operator -= (const Fp &r) { val -= r.val; if (val < 0) val += MOD; return *this; } constexpr Fp& operator *= (const Fp &r) { val = val * r.val % MOD; return *this; } constexpr Fp& operator /= (const Fp &r) { long long a = r.val, b = MOD, u = 1, v = 0; while (b) { long long t = a / b; a -= t * b, swap(a, b); u -= t * v, swap(u, v); } val = val * u % MOD; if (val < 0) val += MOD; return *this; } constexpr Fp pow(long long n) const { Fp res(1), mul(*this); while (n > 0) { if (n & 1) res *= mul; mul *= mul; n >>= 1; } return res; } constexpr Fp inv() const { Fp res(1), div(*this); return res / div; } // other operators constexpr bool operator == (const Fp &r) const { return this->val == r.val; } constexpr bool operator != (const Fp &r) const { return this->val != r.val; } constexpr Fp& operator ++ () { ++val; if (val >= MOD) val -= MOD; return *this; } constexpr Fp& operator -- () { if (val == 0) val += MOD; --val; return *this; } constexpr Fp operator ++ (int) const { Fp res = *this; ++*this; return res; } constexpr Fp operator -- (int) const { Fp res = *this; --*this; return res; } friend constexpr istream& operator >> (istream &is, Fp<MOD> &x) { is >> x.val; x.val %= MOD; if (x.val < 0) x.val += MOD; return is; } friend constexpr ostream& operator << (ostream &os, const Fp<MOD> &x) { return os << x.val; } friend constexpr Fp<MOD> pow(const Fp<MOD> &r, long long n) { return r.pow(n); } friend constexpr Fp<MOD> inv(const Fp<MOD> &r) { return r.inv(); } }; namespace NTT { long long modpow(long long a, long long n, int mod) { long long res = 1; while (n > 0) { if (n & 1) res = res * a % mod; a = a * a % mod; n >>= 1; } return res; } long long modinv(long long a, int mod) { long long b = mod, u = 1, v = 0; while (b) { long long t = a / b; a -= t * b, swap(a, b); u -= t * v, swap(u, v); } u %= mod; if (u < 0) u += mod; return u; } int calc_primitive_root(int mod) { if (mod == 2) return 1; if (mod == 167772161) return 3; if (mod == 469762049) return 3; if (mod == 754974721) return 11; if (mod == 998244353) return 3; int divs[20] = {}; divs[0] = 2; int cnt = 1; long long x = (mod - 1) / 2; while (x % 2 == 0) x /= 2; for (long long i = 3; i * i <= x; i += 2) { if (x % i == 0) { divs[cnt++] = i; while (x % i == 0) x /= i; } } if (x > 1) divs[cnt++] = x; for (int g = 2;; g++) { bool ok = true; for (int i = 0; i < cnt; i++) { if (modpow(g, (mod - 1) / divs[i], mod) == 1) { ok = false; break; } } if (ok) return g; } } int get_fft_size(int N, int M) { int size_a = 1, size_b = 1; while (size_a < N) size_a <<= 1; while (size_b < M) size_b <<= 1; return max(size_a, size_b) << 1; } // number-theoretic transform template<class mint> void trans(vector<mint> &v, bool inv = false) { if (v.empty()) return; int N = (int)v.size(); int MOD = v[0].get_mod(); int PR = calc_primitive_root(MOD); static bool first = true; static vector<long long> vbw(30), vibw(30); if (first) { first = false; for (int k = 0; k < 30; ++k) { vbw[k] = modpow(PR, (MOD - 1) >> (k + 1), MOD); vibw[k] = modinv(vbw[k], MOD); } } for (int i = 0, j = 1; j < N - 1; j++) { for (int k = N >> 1; k > (i ^= k); k >>= 1); if (i > j) swap(v[i], v[j]); } for (int k = 0, t = 2; t <= N; ++k, t <<= 1) { long long bw = vbw[k]; if (inv) bw = vibw[k]; for (int i = 0; i < N; i += t) { mint w = 1; for (int j = 0; j < t/2; ++j) { int j1 = i + j, j2 = i + j + t/2; mint c1 = v[j1], c2 = v[j2] * w; v[j1] = c1 + c2; v[j2] = c1 - c2; w *= bw; } } } if (inv) { long long invN = modinv(N, MOD); for (int i = 0; i < N; ++i) v[i] = v[i] * invN; } } // for garner static constexpr int MOD0 = 754974721; static constexpr int MOD1 = 167772161; static constexpr int MOD2 = 469762049; using mint0 = Fp<MOD0>; using mint1 = Fp<MOD1>; using mint2 = Fp<MOD2>; static const mint1 imod0 = 95869806; // modinv(MOD0, MOD1); static const mint2 imod1 = 104391568; // modinv(MOD1, MOD2); static const mint2 imod01 = 187290749; // imod1 / MOD0; // small case (T = mint, long long) template<class T> vector<T> naive_mul(const vector<T> &A, const vector<T> &B) { if (A.empty() || B.empty()) return {}; int N = (int)A.size(), M = (int)B.size(); vector<T> res(N + M - 1); for (int i = 0; i < N; ++i) for (int j = 0; j < M; ++j) res[i + j] += A[i] * B[j]; return res; } // mul by convolution template<class mint> vector<mint> mul(const vector<mint> &A, const vector<mint> &B) { if (A.empty() || B.empty()) return {}; int N = (int)A.size(), M = (int)B.size(); if (min(N, M) < 30) return naive_mul(A, B); int MOD = A[0].get_mod(); int size_fft = get_fft_size(N, M); if (MOD == 998244353) { vector<mint> a(size_fft), b(size_fft), c(size_fft); for (int i = 0; i < N; ++i) a[i] = A[i]; for (int i = 0; i < M; ++i) b[i] = B[i]; trans(a), trans(b); vector<mint> res(size_fft); for (int i = 0; i < size_fft; ++i) res[i] = a[i] * b[i]; trans(res, true); res.resize(N + M - 1); return res; } vector<mint0> a0(size_fft, 0), b0(size_fft, 0), c0(size_fft, 0); vector<mint1> a1(size_fft, 0), b1(size_fft, 0), c1(size_fft, 0); vector<mint2> a2(size_fft, 0), b2(size_fft, 0), c2(size_fft, 0); for (int i = 0; i < N; ++i) a0[i] = A[i].val, a1[i] = A[i].val, a2[i] = A[i].val; for (int i = 0; i < M; ++i) b0[i] = B[i].val, b1[i] = B[i].val, b2[i] = B[i].val; trans(a0), trans(a1), trans(a2), trans(b0), trans(b1), trans(b2); for (int i = 0; i < size_fft; ++i) { c0[i] = a0[i] * b0[i]; c1[i] = a1[i] * b1[i]; c2[i] = a2[i] * b2[i]; } trans(c0, true), trans(c1, true), trans(c2, true); mint mod0 = MOD0, mod01 = mod0 * MOD1; vector<mint> res(N + M - 1); for (int i = 0; i < N + M - 1; ++i) { int y0 = c0[i].val; int y1 = (imod0 * (c1[i] - y0)).val; int y2 = (imod01 * (c2[i] - y0) - imod1 * y1).val; res[i] = mod01 * y2 + mod0 * y1 + y0; } return res; } }; // Polynomial template<typename mint> struct Poly : vector<mint> { using vector<mint>::vector; // constructor constexpr Poly(const vector<mint> &r) : vector<mint>(r) {} // core operator constexpr mint eval(const mint &v) { mint res = 0; for (int i = (int)this->size()-1; i >= 0; --i) { res *= v; res += (*this)[i]; } return res; } constexpr Poly& normalize() { while (!this->empty() && this->back() == 0) this->pop_back(); return *this; } // basic operator constexpr Poly operator - () const noexcept { Poly res = (*this); for (int i = 0; i < (int)res.size(); ++i) res[i] = -res[i]; return res; } constexpr Poly operator + (const mint &v) const { return Poly(*this) += v; } constexpr Poly operator + (const Poly &r) const { return Poly(*this) += r; } constexpr Poly operator - (const mint &v) const { return Poly(*this) -= v; } constexpr Poly operator - (const Poly &r) const { return Poly(*this) -= r; } constexpr Poly operator * (const mint &v) const { return Poly(*this) *= v; } constexpr Poly operator * (const Poly &r) const { return Poly(*this) *= r; } constexpr Poly operator / (const mint &v) const { return Poly(*this) /= v; } constexpr Poly operator / (const Poly &r) const { return Poly(*this) /= r; } constexpr Poly operator % (const Poly &r) const { return Poly(*this) %= r; } constexpr Poly operator << (int x) const { return Poly(*this) <<= x; } constexpr Poly operator >> (int x) const { return Poly(*this) >>= x; } constexpr Poly& operator += (const mint &v) { if (this->empty()) this->resize(1); (*this)[0] += v; return *this; } constexpr Poly& operator += (const Poly &r) { if (r.size() > this->size()) this->resize(r.size()); for (int i = 0; i < (int)r.size(); ++i) (*this)[i] += r[i]; return this->normalize(); } constexpr Poly& operator -= (const mint &v) { if (this->empty()) this->resize(1); (*this)[0] -= v; return *this; } constexpr Poly& operator -= (const Poly &r) { if (r.size() > this->size()) this->resize(r.size()); for (int i = 0; i < (int)r.size(); ++i) (*this)[i] -= r[i]; return this->normalize(); } constexpr Poly& operator *= (const mint &v) { for (int i = 0; i < (int)this->size(); ++i) (*this)[i] *= v; return *this; } constexpr Poly& operator *= (const Poly &r) { return *this = NTT::mul((*this), r); } constexpr Poly& operator <<= (int x) { Poly res(x, 0); res.insert(res.end(), begin(*this), end(*this)); return *this = res; } constexpr Poly& operator >>= (int x) { Poly res; res.insert(res.end(), begin(*this) + x, end(*this)); return *this = res; } // division, pow constexpr Poly& operator /= (const mint &v) { assert(v != 0); mint iv = modinv(v); for (int i = 0; i < (int)this->size(); ++i) (*this)[i] *= iv; return *this; } constexpr Poly& operator /= (const Poly &r) { assert(!r.empty()); assert(r.back() != 0); this->normalize(); if (this->size() < r.size()) { this->clear(); return *this; } int need = (int)this->size() - (int)r.size() + 1; *this = (rev().pre(need) * r.rev().inner_inv(need)).pre(need).rev(); return *this; } constexpr Poly& operator %= (const Poly &r) { assert(!r.empty()); assert(r.back() != 0); this->normalize(); Poly q = (*this) / r; return *this -= q * r; } // FPS functions constexpr Poly pre(int siz) const { return Poly(begin(*this), begin(*this) + min((int)this->size(), siz)); } constexpr Poly rev() const { Poly res = *this; reverse(begin(res), end(res)); return res; } // df/dx constexpr Poly diff() const { int n = (int)this->size(); Poly res(n-1); for (int i = 1; i < n; ++i) res[i-1] = (*this)[i] * i; return res; } // \int f dx constexpr Poly integral() const { int n = (int)this->size(); Poly res(n+1, 0); for (int i = 0; i < n; ++i) res[i+1] = (*this)[i] / (i+1); return res; } // inv(f), f[0] must not be 0 constexpr Poly inner_inv(int deg) const { assert((*this)[0] != 0); if (deg < 0) deg = (int)this->size(); Poly res({mint(1) / (*this)[0]}); for (int i = 1; i < deg; i <<= 1) { res = (res + res - res * res * pre(i << 1)).pre(i << 1); } res.resize(deg); return res; } constexpr Poly inner_inv() const { return inner_inv((int)this->size()); } // log(f) = \int f'/f dx, f[0] must be 1 constexpr Poly inner_log(int deg) const { assert((*this)[0] == 1); Poly res = (diff() * inner_inv(deg)).integral(); res.resize(deg); return res; } constexpr Poly inner_log() const { return inner_log((int)this->size()); } // exp(f), f[0] must be 0 constexpr Poly inner_exp(int deg) const { assert((*this)[0] == 0); Poly res(1, 1); for (int i = 1; i < deg; i <<= 1) { res = res * (pre(i << 1) - res.inner_log(i << 1) + 1).pre(i << 1); } res.resize(deg); return res; } constexpr Poly inner_exp() const { return inner_exp((int)this->size()); } // pow(f) = exp(e * log f) constexpr Poly inner_pow(long long e, int deg) const { if (e == 0) { Poly res(deg, 0); res[0] = 1; return res; } long long i = 0; while (i < (int)this->size() && (*this)[i] == 0) ++i; if (i == (int)this->size() || i > (deg - 1) / e) return Poly(deg, 0); mint k = (*this)[i]; Poly res = ((((*this) >> i) / k).inner_log(deg) * e).inner_exp(deg) * mint(k).inner_pow(e) << (e * i); res.resize(deg); return res; } constexpr Poly inner_pow(long long e) const { return inner_pow(e, (int)this->size()); } }; //------------------------------// // Polynomial Algorithms //------------------------------// // Binomial coefficient template<class T> struct BiCoef { vector<T> fact_, inv_, finv_; constexpr BiCoef() {} constexpr BiCoef(int n) : fact_(n, 1), inv_(n, 1), finv_(n, 1) { init(n); } constexpr void init(int n) { fact_.assign(n, 1), inv_.assign(n, 1), finv_.assign(n, 1); int MOD = fact_[0].get_mod(); for(int i = 2; i < n; i++){ fact_[i] = fact_[i-1] * i; inv_[i] = -inv_[MOD%i] * (MOD/i); finv_[i] = finv_[i-1] * inv_[i]; } } constexpr T com(int n, int k) const { if (n < k || n < 0 || k < 0) return 0; return fact_[n] * finv_[k] * finv_[n-k]; } constexpr T fact(int n) const { if (n < 0) return 0; return fact_[n]; } constexpr T inv(int n) const { if (n < 0) return 0; return inv_[n]; } constexpr T finv(int n) const { if (n < 0) return 0; return finv_[n]; } }; // Polynomial Taylor Shift // given: f(x), c // find: coefficients of f(x + c) template<class mint> Poly<mint> PolynomialTaylorShift(const Poly<mint> &f, long long c) { int N = (int)f.size() - 1; BiCoef<mint> bc(N + 1); // convolution Poly<mint> p(N + 1), q(N + 1); for (int i = 0; i <= N; ++i) { p[i] = f[i] * bc.fact(i); q[N - i] = mint(c).pow(i) * bc.finv(i); } Poly<mint> pq = p * q; // result Poly<mint> res(N + 1); for (int i = 0; i <= N; ++i) res[i] = pq[i + N] * bc.finv(i); return res; } //------------------------------// // for any mod //------------------------------// // dynamic modint struct DynamicModint { using mint = DynamicModint; // static menber static int MOD; // inner value long long val; // constructor DynamicModint() : val(0) { } DynamicModint(long long v) : val(v % MOD) { if (val < 0) val += MOD; } long long get() const { return val; } static int get_mod() { return MOD; } static void set_mod(int mod) { MOD = mod; } // arithmetic operators mint operator + () const { return mint(*this); } mint operator - () const { return mint(0) - mint(*this); } mint operator + (const mint &r) const { return mint(*this) += r; } mint operator - (const mint &r) const { return mint(*this) -= r; } mint operator * (const mint &r) const { return mint(*this) *= r; } mint operator / (const mint &r) const { return mint(*this) /= r; } mint& operator += (const mint &r) { val += r.val; if (val >= MOD) val -= MOD; return *this; } mint& operator -= (const mint &r) { val -= r.val; if (val < 0) val += MOD; return *this; } mint& operator *= (const mint &r) { val = val * r.val % MOD; return *this; } mint& operator /= (const mint &r) { long long a = r.val, b = MOD, u = 1, v = 0; while (b) { long long t = a / b; a -= t * b, swap(a, b); u -= t * v, swap(u, v); } val = val * u % MOD; if (val < 0) val += MOD; return *this; } mint pow(long long n) const { mint res(1), mul(*this); while (n > 0) { if (n & 1) res *= mul; mul *= mul; n >>= 1; } return res; } mint inv() const { mint res(1), div(*this); return res / div; } // other operators bool operator == (const mint &r) const { return this->val == r.val; } bool operator != (const mint &r) const { return this->val != r.val; } mint& operator ++ () { ++val; if (val >= MOD) val -= MOD; return *this; } mint& operator -- () { if (val == 0) val += MOD; --val; return *this; } mint operator ++ (int) { mint res = *this; ++*this; return res; } mint operator -- (int) { mint res = *this; --*this; return res; } friend istream& operator >> (istream &is, mint &x) { is >> x.val; x.val %= x.get_mod(); if (x.val < 0) x.val += x.get_mod(); return is; } friend ostream& operator << (ostream &os, const mint &x) { return os << x.val; } friend mint pow(const mint &r, long long n) { return r.pow(n); } friend mint inv(const mint &r) { return r.inv(); } }; signed main(){ // これがないと落ちることがある ios_base::sync_with_stdio(false); cin.tie(0); const int MOD = 924844033; using mint = Fp<MOD>; ll a,b; cin >> a>>b; Poly<mint> f(b+1); f[b] = a; Poly<mint> g(3); g[2] = 1; g[1] = 1; g[0] = 1; auto r = f%g; cout << r[1]<<" "<<r[0] << endl; }