結果
問題 | No.931 Multiplicative Convolution |
ユーザー |
|
提出日時 | 2019-11-22 22:30:10 |
言語 | C++17 (gcc 13.3.0 + boost 1.87.0) |
結果 |
AC
|
実行時間 | 150 ms / 2,000 ms |
コード長 | 13,194 bytes |
コンパイル時間 | 2,588 ms |
コンパイル使用メモリ | 213,840 KB |
最終ジャッジ日時 | 2025-01-08 05:16:32 |
ジャッジサーバーID (参考情報) |
judge5 / judge2 |
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ファイルパターン | 結果 |
---|---|
sample | AC * 3 |
other | AC * 14 |
ソースコード
#include <bits/stdc++.h>// created [2019/11/22] 22:11:34#pragma GCC diagnostic ignored "-Wsign-compare"#pragma GCC diagnostic ignored "-Wsign-conversion"using i32 = int32_t;using i64 = int64_t;using u32 = uint32_t;using u64 = uint64_t;using uint = unsigned int;using usize = std::size_t;using ll = long long;using ull = unsigned long long;using ld = long double;template<typename T> constexpr T popcount(const T u) { return u ? static_cast<T>(__builtin_popcountll(static_cast<u64>(u))) : static_cast<T>(0); }template<typename T> constexpr T log2p1(const T u) { return u ? static_cast<T>(64 - __builtin_clzll(static_cast<u64>(u))) : static_cast<T>(0); }template<typename T> constexpr T msbp1(const T u) { return log2p1(u); }template<typename T> constexpr T lsbp1(const T u) { return __builtin_ffsll(u); }template<typename T> constexpr T clog(const T u) { return u ? log2p1(u - 1) : static_cast<T>(u); }template<typename T> constexpr bool ispow2(const T u) { return u and (static_cast<u64>(u) & static_cast<u64>(u - 1)) == 0; }template<typename T> constexpr T ceil2(const T u) { return static_cast<T>(1) << clog(u); }template<typename T> constexpr T floor2(const T u) { return u == 0 ? static_cast<T>(0) : static_cast<T>(1) << (log2p1(u) - 1); }template<typename T> constexpr bool btest(const T mask, const usize ind) { return static_cast<bool>((static_cast<u64>(mask) >> ind) & static_cast<u64>(1)); }template<typename T> void bset(T& mask, const usize ind) { mask |= (static_cast<T>(1) << ind); }template<typename T> void breset(T& mask, const usize ind) { mask &= ~(static_cast<T>(1) << ind); }template<typename T> void bflip(T& mask, const usize ind) { mask ^= (static_cast<T>(1) << ind); }template<typename T> void bset(T& mask, const usize ind, const bool b) { (b ? bset(mask, ind) : breset(mask, ind)); }template<typename T> constexpr T bcut(const T mask, const usize ind) { return ind == 0 ? static_cast<T>(0) : static_cast<T>((static_cast<u64>(mask)<< (64 - ind)) >> (64 - ind)); }template<typename T> bool chmin(T& a, const T& b) { return (a > b ? a = b, true : false); }template<typename T> bool chmax(T& a, const T& b) { return (a < b ? a = b, true : false); }constexpr unsigned int mod = 1000000007;template<typename T> constexpr T inf_v = std::numeric_limits<T>::max() / 4;template<typename Real> constexpr Real pi_v = Real{3.141592653589793238462643383279502884};template<typename T>T read(){T v;return std::cin >> v, v;}template<typename T, typename... Args>auto read(const usize size, Args... args){std::vector<decltype(read<T>(args...))> ans(size);for (usize i = 0; i < size; i++) { ans[i] = read<T>(args...); }return ans;}template<typename... Types>auto reads() { return std::tuple<std::decay_t<Types>...>{read<Types>()...}; }# define SHOW(...) static_cast<void>(0)template<typename T>std::vector<T> make_v(const usize size, const T v) { return std::vector<T>(size, v); }template<typename... Args>auto make_v(const usize size, Args... args) { return std::vector<decltype(make_v(args...))>(size, make_v(args...)); }template<typename T> T gcd(const T& a, const T& b) { return a < 0 ? gcd(-a, b) : b < 0 ? gcd(a, -b) : (a > b ? gcd(b, a) : a == 0 ? b : gcd(b % a, a)); }template<typename T> T lcm(const T& a, const T& b) { return a / gcd(a, b) * b; }template<typename T>constexpr std::pair<T, T> extgcd(const T a, const T b){if (b == 0) { return std::pair<T, T>{1, 0}; }const auto g = gcd(a, b), da = std::abs(b) / g;const auto p = extgcd(b, a % b);const auto x = (da + p.second % da) % da, y = (g - a * x) / b;return {x, y};}template<typename T>constexpr T inverse(const T a, const T mod) { return extgcd(a, mod).first; }template<uint mod_value, bool dynamic = false>class modint_base{public:template<typename UInt = uint>static std::enable_if_t<dynamic, const UInt> mod() { return mod_ref(); }template<typename UInt = uint>static constexpr std::enable_if_t<not dynamic, const UInt> mod() { return mod_value; }template<typename UInt = uint>static void set_mod(const std::enable_if_t<dynamic, const UInt> mod) { mod_ref() = mod, inv_ref() = {1, 1}; }modint_base() : v{0} {}modint_base(const ll val) : v{norm(static_cast<uint>(val % static_cast<ll>(mod()) + static_cast<ll>(mod())))} {}modint_base(const modint_base& n) : v{n()} {}explicit operator bool() const { return v != 0; }bool operator!() const { return not static_cast<bool>(*this); }modint_base& operator=(const modint_base& m) { return v = m(), (*this); }modint_base& operator=(const ll val) { return v = norm(uint(val % static_cast<ll>(mod()) + static_cast<ll>(mod()))), (*this); }friend modint_base operator+(const modint_base& m) { return m; }friend modint_base operator-(const modint_base& m) { return make(norm(mod() - m.v)); }friend modint_base operator+(const modint_base& m1, const modint_base& m2) { return make(norm(m1.v + m2.v)); }friend modint_base operator-(const modint_base& m1, const modint_base& m2) { return make(norm(m1.v + mod() - m2.v)); }friend modint_base operator*(const modint_base& m1, const modint_base& m2) { return make(static_cast<uint>(static_cast<ll>(m1.v) * static_cast<ll>(m2.v) % static_cast<ll>(mod()))); }friend modint_base operator/(const modint_base& m1, const modint_base& m2) { return m1 * inv(m2.v); }friend modint_base operator+(const modint_base& m, const ll val) { return modint_base{static_cast<ll>(m.v) + val}; }friend modint_base operator-(const modint_base& m, const ll val) { return modint_base{static_cast<ll>(m.v) - val}; }friend modint_base operator*(const modint_base& m, const ll val) { return modint_base{static_cast<ll>(m.v) * (val % static_cast<ll>(mod()))}; }friend modint_base operator/(const modint_base& m, const ll val) { return modint_base{static_cast<ll>(m.v) * inv(val)}; }friend modint_base operator+(const ll val, const modint_base& m) { return modint_base{static_cast<ll>(m.v) + val}; }friend modint_base operator-(const ll val, const modint_base& m) { return modint_base{-static_cast<ll>(m.v) + val}; }friend modint_base operator*(const ll val, const modint_base& m) { return modint_base{static_cast<ll>(m.v) * (val % static_cast<ll>(mod()))}; }friend modint_base operator/(const ll val, const modint_base& m) { return modint_base{val * inv(static_cast<ll>(m.v))}; }friend modint_base& operator+=(modint_base& m1, const modint_base& m2) { return m1 = m1 + m2; }friend modint_base& operator-=(modint_base& m1, const modint_base& m2) { return m1 = m1 - m2; }friend modint_base& operator*=(modint_base& m1, const modint_base& m2) { return m1 = m1 * m2; }friend modint_base& operator/=(modint_base& m1, const modint_base& m2) { return m1 = m1 / m2; }friend modint_base& operator+=(modint_base& m, const ll val) { return m = m + val; }friend modint_base& operator-=(modint_base& m, const ll val) { return m = m - val; }friend modint_base& operator*=(modint_base& m, const ll val) { return m = m * val; }friend modint_base& operator/=(modint_base& m, const ll val) { return m = m / val; }friend modint_base operator^(const modint_base& m, const ll n) { return power(m.v, n); }friend modint_base& operator^=(modint_base& m, const ll n) { return m = m ^ n; }friend bool operator==(const modint_base& m1, const modint_base& m2) { return m1.v == m2.v; }friend bool operator!=(const modint_base& m1, const modint_base& m2) { return not(m1 == m2); }friend bool operator==(const modint_base& m, const ll val) { return m.v == norm(static_cast<uint>(static_cast<ll>(mod()) + val % static_cast<ll>(mod()))); }friend bool operator!=(const modint_base& m, const ll val) { return not(m == val); }friend bool operator==(const ll val, const modint_base& m) { return m.v == norm(static_cast<uint>(static_cast<ll>(mod()) + val % static_cast<ll>(mod()))); }friend bool operator!=(const ll val, const modint_base& m) { return not(m == val); }friend std::istream& operator>>(std::istream& is, modint_base& m){ll v;return is >> v, m = v, is;}friend std::ostream& operator<<(std::ostream& os, const modint_base& m) { return os << m(); }uint operator()() const { return v; }static modint_base small_inv(const usize n){auto& in = inv_ref();if (n < in.size()) { return in[n]; }for (usize i = in.size(); i <= n; i++) { in.push_back(-in[modint_base::mod() % i] * (modint_base::mod() / i)); }return in.back();}private:template<typename UInt = uint>static std::enable_if_t<dynamic, UInt&> mod_ref(){static UInt mod = 0;return mod;}static uint norm(const uint x) { return x < mod() ? x : x - mod(); }static modint_base make(const uint x){modint_base m;return m.v = x, m;}static modint_base power(modint_base x, ull n){modint_base ans = 1;for (; n; n >>= 1, x *= x) {if (n & 1) { ans *= x; }}return ans;}static modint_base inv(const ll v) { return v < 1000000 ? small_inv(static_cast<usize>(v)) : modint_base{inverse(v, static_cast<ll>(mod()))}; }static std::vector<modint_base>& inv_ref(){static std::vector<modint_base> in{1, 1};return in;}uint v;};template<uint mod>using modint = modint_base<mod, false>;template<uint id>using dynamic_modint = modint_base<id, true>;template<typename T>std::vector<std::pair<T, usize>> prime_factors(T n){std::vector<std::pair<T, usize>> ans;for (T i = 2; i * i <= n; i++) {usize cnt = 0;for (; n % i == 0; n /= i, cnt++) {}if (cnt > 0) { ans.push_back({i, cnt}); }}if (n > 1) { ans.push_back({n, 1}); }return ans;}template<uint mod = 924844033, uint root = 5>class ntt{private:using value_type = modint<mod>;static constexpr usize depth = 30;static void transform(std::vector<value_type>& a, const usize lg, const bool rev){const usize N = a.size();assert(1UL << lg == N);static std::vector<value_type> R[depth];if (R[lg].empty()) {R[lg].reserve(N), R[lg].resize(N, value_type(1));const value_type r = value_type(root) ^ ((mod - 1) / N);for (usize i = 1; i < N; i++) { R[lg][i] = R[lg][i - 1] * r; }}std::vector<value_type> tmp(N);for (usize w = (N >> 1); w > 0; w >>= 1) {for (usize y = 0; y < (N >> 1); y += w) {const value_type r = rev ? R[lg][y == 0 ? 0 : N - y] : R[lg][y];for (usize x = 0; x < w; x++) {const auto u = a[y << 1 | x], v = a[y << 1 | x | w]() * r;tmp[y | x] = u + v, tmp[y | x | (N >> 1)] = u - v;}}std::swap(tmp, a);}if (rev) {for (usize i = 0; i < N; i++) { a[i] /= value_type(N); }}}public:ntt() = delete;static std::vector<value_type> convolute(const std::vector<value_type>& a, const std::vector<value_type>& b){const usize need = a.size() + b.size() - 1, lg = clog(need), sz = 1UL << lg;std::vector<value_type> A(sz, 0), B(sz, 0);for (usize i = 0; i < a.size(); i++) { A[i] = a[i](); }for (usize i = 0; i < b.size(); i++) { B[i] = b[i](); }transform(A, lg, false), transform(B, lg, false);for (usize i = 0; i < sz; i++) { A[i] *= B[i]; }transform(A, lg, true);std::vector<value_type> ans(need);for (usize i = 0; i < need; i++) { ans[i] = int(A[i]()); }return ans;}};int main(){using mint = dynamic_modint<0>;const auto P = read<uint>();mint::set_mod(P);std::vector<uint> A(P, 0), B(P, 0);for (int i = 1; i < P; i++) { std::cin >> A[i]; }for (int i = 1; i < P; i++) { std::cin >> B[i]; }uint g = 2;const auto fs = prime_factors(P - 1);for (; g < P; g++) {bool ok = true;for (const auto& p : fs) {const uint q = p.first;const uint per = (P - 1) / q;if ((mint(g) ^ per) == 1) {ok = false;break;}}if (ok) { break; }}SHOW(g);std::vector<mint> ps(P - 1, 1);for (int i = 1; i < P - 1; i++) { ps[i] = ps[i - 1] * g; }constexpr uint mod = 998244353;std::vector<modint<mod>> a(P), b(P);for (int i = 0; i < P - 1; i++) { a[i] = A[ps[i]()]; }for (int i = 0; i < P - 1; i++) { b[i] = B[ps[i]()]; }SHOW(a, b);auto c = ntt<mod>::convolute(a, b);SHOW(c);std::vector<modint<mod>> d(P - 1, 0);for (int i = 0; i < c.size(); i++) { d[i % (P - 1)] += c[i]; }SHOW(d);std::vector<modint<mod>> C(P, 0);for (int i = 0; i < P - 1; i++) { C[ps[i]()] = d[i]; }for (int i = 1; i < P; i++) { std::cout << C[i] << " "; }std::cout << std::endl;return 0;}