Submit Info #19046

Problem Lang User Status Time Memory
Polynomial Taylor Shift cpp Haar AC 251 ms 41.30 MiB

ケース詳細
Name Status Time Memory
example_00 AC 7 ms 5.24 MiB
example_01 AC 9 ms 5.25 MiB
fft_killer_00 AC 251 ms 41.30 MiB
fft_killer_01 AC 249 ms 41.30 MiB
max_random_00 AC 249 ms 41.30 MiB
max_random_01 AC 250 ms 41.30 MiB
medium_00 AC 10 ms 5.30 MiB
medium_01 AC 11 ms 5.67 MiB
medium_02 AC 11 ms 5.65 MiB
medium_all_zero_00 AC 10 ms 5.29 MiB
medium_c_zero_00 AC 9 ms 5.30 MiB
random_00 AC 228 ms 36.11 MiB
random_01 AC 241 ms 38.92 MiB
random_02 AC 36 ms 9.30 MiB
small_00 AC 8 ms 5.17 MiB
small_01 AC 8 ms 5.17 MiB
small_02 AC 9 ms 5.17 MiB
small_03 AC 9 ms 5.27 MiB
small_04 AC 8 ms 5.24 MiB
small_05 AC 8 ms 5.28 MiB
small_06 AC 12 ms 5.16 MiB
small_07 AC 8 ms 5.17 MiB
small_08 AC 9 ms 5.17 MiB
small_09 AC 9 ms 5.24 MiB
small_10 AC 8 ms 5.17 MiB
small_11 AC 9 ms 5.17 MiB
small_12 AC 10 ms 5.17 MiB
small_13 AC 9 ms 5.17 MiB
small_14 AC 8 ms 5.17 MiB
small_15 AC 8 ms 5.17 MiB

#include <bits/stdc++.h> #ifdef DEBUG #include <Mylib/Debug/debug.cpp> #else #define dump(...) #endif /** * @title Modint * @docs mint.md */ template <int32_t M> class ModInt{ public: constexpr static int32_t MOD = M; uint32_t val; constexpr ModInt(): val(0){} constexpr ModInt(int64_t n){ if(n >= M) val = n % M; else if(n < 0) val = n % M + M; else val = n; } constexpr auto& operator=(const ModInt &a){val = a.val; return *this;} constexpr auto& operator+=(const ModInt &a){ if(val + a.val >= M) val = (uint64_t)val + a.val - M; else val += a.val; return *this; } constexpr auto& operator-=(const ModInt &a){ if(val < a.val) val += M; val -= a.val; return *this; } constexpr auto& operator*=(const ModInt &a){ val = (uint64_t)val * a.val % M; return *this; } constexpr auto& operator/=(const ModInt &a){ val = (uint64_t)val * a.inv().val % M; return *this; } constexpr auto operator+(const ModInt &a) const {return ModInt(*this) += a;} constexpr auto operator-(const ModInt &a) const {return ModInt(*this) -= a;} constexpr auto operator*(const ModInt &a) const {return ModInt(*this) *= a;} constexpr auto operator/(const ModInt &a) const {return ModInt(*this) /= a;} constexpr bool operator==(const ModInt &a) const {return val == a.val;} constexpr bool operator!=(const ModInt &a) const {return val != a.val;} constexpr auto& operator++(){*this += 1; return *this;} constexpr auto& operator--(){*this -= 1; return *this;} constexpr auto operator++(int){auto t = *this; *this += 1; return t;} constexpr auto operator--(int){auto t = *this; *this -= 1; return t;} constexpr static ModInt power(int64_t n, int64_t p){ if(p < 0) return power(n, -p).inv(); int64_t ret = 1, e = n % M; for(; p; (e *= e) %= M, p >>= 1) if(p & 1) (ret *= e) %= M; return ret; } constexpr static ModInt inv(int64_t a){ int64_t b = M, u = 1, v = 0; while(b){ int64_t t = a / b; a -= t * b; std::swap(a,b); u -= t * v; std::swap(u,v); } u %= M; if(u < 0) u += M; return u; } constexpr static auto frac(int64_t a, int64_t b){return ModInt(a) / ModInt(b);} constexpr auto power(int64_t p) const {return power(val, p);} constexpr auto inv() const {return inv(val);} friend constexpr auto operator-(const ModInt &a){return ModInt(M-a.val);} friend constexpr auto operator+(int64_t a, const ModInt &b){return ModInt(a) + b;} friend constexpr auto operator-(int64_t a, const ModInt &b){return ModInt(a) - b;} friend constexpr auto operator*(int64_t a, const ModInt &b){return ModInt(a) * b;} friend constexpr auto operator/(int64_t a, const ModInt &b){return ModInt(a) / b;} friend std::istream& operator>>(std::istream &s, ModInt<M> &a){s >> a.val; return s;} friend std::ostream& operator<<(std::ostream &s, const ModInt<M> &a){s << a.val; return s;} template <int N> static auto div(){ static auto value = inv(N); return value; } explicit operator int32_t() const noexcept {return val;} explicit operator int64_t() const noexcept {return val;} }; /** * @title Number theoretic transform * @docs ntt_convolution.md */ template <typename T, int PRIM_ROOT, int MAX_SIZE> class NumberTheoreticTransform{ const int MAX_POWER; std::vector<T> BASE, INV_BASE; public: NumberTheoreticTransform(): MAX_POWER(__builtin_ctz(MAX_SIZE)), BASE(MAX_POWER + 1), INV_BASE(MAX_POWER + 1) { static_assert((MAX_SIZE & (MAX_SIZE - 1)) == 0, "MAX_SIZE must be power of 2."); T t = T::power(PRIM_ROOT, (T::MOD-1) >> (MAX_POWER + 2)); T s = t.inv(); for(int i = MAX_POWER - 1; i >= 0; --i){ t *= t; s *= s; BASE[i] = -t; INV_BASE[i] = -s; } } void run_ntt(std::vector<T> &f, bool INVERSE = false){ const int n = f.size(); assert((n & (n-1)) == 0 and n <= MAX_SIZE); // データ数は2の冪乗個 if(INVERSE){ for(int b = 1; b < n; b <<= 1){ T w = 1; for(int j = 0, k = 1; j < n; j += 2 * b, ++k){ for(int i = 0; i < b; ++i){ const auto s = f[i+j]; const auto t = f[i+j+b]; f[i+j] = s + t; f[i+j+b] = (s - t) * w; } w *= INV_BASE[__builtin_ctz(k)]; } } const T t = T::inv(n); for(auto &x : f) x *= t; }else{ for(int b = n >> 1; b; b >>= 1){ T w = 1; for(int j = 0, k = 1; j < n; j += 2 * b, ++k){ for(int i = 0; i < b; ++i){ const auto s = f[i+j]; const auto t = f[i+j+b] * w; f[i+j] = s + t; f[i+j+b] = s - t; } w *= BASE[__builtin_ctz(k)]; } } } } template <typename U> std::vector<T> run_convolution(std::vector<U> f, std::vector<U> g){ const int m = f.size() + g.size() - 1; int n = 1; while(n < m) n *= 2; std::vector<T> f2(n), g2(n); for(int i = 0; i < (int)f.size(); ++i) f2[i] = f[i]; for(int i = 0; i < (int)g.size(); ++i) g2[i] = g[i]; run_ntt(f2); run_ntt(g2); for(int i = 0; i < n; ++i) f2[i] *= g2[i]; run_ntt(f2, true); return f2; } }; template <typename T, typename U> std::vector<T> ntt_convolution(std::vector<U> f, std::vector<U> g){ static constexpr int M1 = 167772161, P1 = 3; static constexpr int M2 = 469762049, P2 = 3; static constexpr int M3 = 1224736769, P3 = 3; for(auto &x : f) x %= T::MOD; for(auto &x : g) x %= T::MOD; auto res1 = NumberTheoreticTransform<ModInt<M1>, P1, 1 << 20>().run_convolution(f, g); auto res2 = NumberTheoreticTransform<ModInt<M2>, P2, 1 << 20>().run_convolution(f, g); auto res3 = NumberTheoreticTransform<ModInt<M3>, P3, 1 << 20>().run_convolution(f, g); const int n = res1.size(); std::vector<T> ret(n); const int64_t M12 = ModInt<M2>::inv(M1).val; const int64_t M13 = ModInt<M3>::inv(M1).val; const int64_t M23 = ModInt<M3>::inv(M2).val; for(int i = 0; i < n; ++i){ const int64_t r[3] = {(int64_t)res1[i].val, (int64_t)res2[i].val, (int64_t)res3[i].val}; const int64_t t0 = r[0] % M1; const int64_t t1 = (r[1] - t0 + M2) * M12 % M2; const int64_t t2 = ((r[2] - t0 + M3) * M13 % M3 - t1 + M3) * M23 % M3; ret[i] = T(t0) + T(t1) * M1 + T(t2) * M1 * M2; } return ret; } /** * @docs input_vector.md */ template <typename T> std::vector<T> input_vector(int N){ std::vector<T> ret(N); for(int i = 0; i < N; ++i) std::cin >> ret[i]; return ret; } template <typename T> std::vector<std::vector<T>> input_vector(int N, int M){ std::vector<std::vector<T>> ret(N); for(int i = 0; i < N; ++i) ret[i] = input_vector<T>(M); return ret; } /** * @title Factorial table * @docs factorial_table.md */ template <typename T> class FactorialTable{ using value_type = T; std::vector<T> f_table; std::vector<T> if_table; public: FactorialTable(int N){ f_table.assign(N+1, 1); if_table.assign(N+1, 1); for(int i = 1; i <= N; ++i){ f_table[i] = f_table[i-1] * i; } if_table[N] = f_table[N].inv(); for(int i = N-1; i >= 0; --i){ if_table[i] = if_table[i+1] * (i+1); } } T factorial(int64_t i) const { assert(i < (int)f_table.size()); return f_table[i]; } T inv_factorial(int64_t i) const { assert(i < (int)if_table.size()); return if_table[i]; } T P(int64_t n, int64_t k) const { if(n < k or n < 0 or k < 0) return 0; return factorial(n) * inv_factorial(n-k); } T C(int64_t n, int64_t k) const { if(n < k or n < 0 or k < 0) return 0; return P(n,k) * inv_factorial(k); } T H(int64_t n, int64_t k) const { if(n == 0 and k == 0) return 1; return C(n+k-1, k); } }; /** * @docs join.md */ template <typename ITER> std::string join(ITER first, ITER last, std::string delim = " "){ std::stringstream s; for(auto it = first; it != last; ++it){ if(it != first) s << delim; s << *it; } return s.str(); } template <typename T, typename Ft, typename Conv> auto polynomial_taylor_shift(std::vector<T> a, T c, const Ft &ft, const Conv &convolve){ const int N = a.size(); std::vector<T> A(2 * N - 1); for(int i = 0; i < N; ++i){ A[i + N - 1] = a[i] * ft.factorial(i); } T d = 1; std::vector<T> B(2 * N - 1); for(int i = 0; i < N; ++i){ B[N - i - 1] = d * ft.inv_factorial(i); d *= c; } auto C = convolve(A, B); std::vector<T> ret(N); for(int i = 0; i < N; ++i) ret[i] = C[(N - 1) * 2 + i] * ft.inv_factorial(i); return ret; } using mint = ModInt<998244353>; int main(){ std::cin.tie(0); std::ios::sync_with_stdio(false); auto ntt = NumberTheoreticTransform<mint, 3, 1<<21>(); auto ft = FactorialTable<mint>(600000); int N, c; std::cin >> N >> c; auto a = input_vector<mint>(N); auto ans = polynomial_taylor_shift(a, mint(c), ft, [&](const auto &x, const auto &y){return ntt.run_convolution(x, y);} ); std::cout << join(ans.begin(), ans.end()) << "\n"; return 0; }