結果
問題 | No.1100 Boxes |
ユーザー |
![]() |
提出日時 | 2023-04-07 21:58:55 |
言語 | C++17(gcc12) (gcc 12.3.0 + boost 1.87.0) |
結果 |
CE
(最新)
AC
(最初)
|
実行時間 | - |
コード長 | 20,194 bytes |
コンパイル時間 | 3,861 ms |
コンパイル使用メモリ | 161,792 KB |
最終ジャッジ日時 | 2025-02-12 01:19:06 |
ジャッジサーバーID (参考情報) |
judge1 / judge2 |
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コンパイルエラー時のメッセージ・ソースコードは、提出者また管理者しか表示できないようにしております。(リジャッジ後のコンパイルエラーは公開されます)
ただし、clay言語の場合は開発者のデバッグのため、公開されます。
ただし、clay言語の場合は開発者のデバッグのため、公開されます。
コンパイルメッセージ
main.cpp: In function 'FPS<mint> log(const FPS<mint>&, int)': main.cpp:553:19: error: expected 'auto' or 'decltype(auto)' after 'integral' 553 | FPS res = integral(diff(f) * inv(f, deg)); | ^~~~~~~~ main.cpp:553:19: error: 'auto(x)' cannot be constrained 553 | FPS res = integral(diff(f) * inv(f, deg)); | ^~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
ソースコード
#include<iostream>#include<string>#include<vector>#include<algorithm>#include<numeric>#include<cmath>#include<utility>#include<tuple>#include<cstdint>#include<cstdio>#include<iomanip>#include<map>#include<queue>#include<set>#include<stack>#include<deque>#include<unordered_map>#include<unordered_set>#include<bitset>#include<cctype>#include<chrono>#include<random>#include<cassert>#include<cstddef>#include<iterator>#include<string_view>#include<type_traits>#ifdef LOCAL# include "debug_print.hpp"# define debug(...) debug_print::multi_print(#__VA_ARGS__, __VA_ARGS__)#else# define debug(...) (static_cast<void>(0))#endifusing namespace std;#define rep(i,n) for(int i=0; i<(n); i++)#define rrep(i,n) for(int i=(n)-1; i>=0; i--)#define FOR(i,a,b) for(int i=(a); i<(b); i++)#define RFOR(i,a,b) for(int i=(b-1); i>=(a); i--)#define ALL(v) v.begin(), v.end()#define RALL(v) v.rbegin(), v.rend()#define UNIQUE(v) v.erase( unique(v.begin(), v.end()), v.end() );#define pb push_backusing ll = long long;using D = double;using LD = long double;using P = pair<int, int>;template<typename T> using PQ = priority_queue<T,vector<T>>;template<typename T> using minPQ = priority_queue<T, vector<T>, greater<T>>;template<class T>bool chmax(T &a, const T &b) { if (a<b) { a=b; return 1; } return 0; }template<class T>bool chmin(T &a, const T &b) { if (b<a) { a=b; return 1; } return 0; }void yesno(bool flag) {cout << (flag?"Yes":"No") << "\n";}template<typename T, typename U>ostream &operator<<(ostream &os, const pair<T, U> &p) {os << p.first << " " << p.second;return os;}template<typename T, typename U>istream &operator>>(istream &is, pair<T, U> &p) {is >> p.first >> p.second;return is;}template<typename T>ostream &operator<<(ostream &os, const vector<T> &v) {int s = (int)v.size();for (int i = 0; i < s; i++) os << (i ? " " : "") << v[i];return os;}template<typename T>istream &operator>>(istream &is, vector<T> &v) {for (auto &x : v) is >> x;return is;}void in() {}template<typename T, class... U>void in(T &t, U &...u) {cin >> t;in(u...);}void out() { cout << "\n"; }template<typename T, class... U, char sep = ' '>void out(const T &t, const U &...u) {cout << t;if (sizeof...(u)) cout << sep;out(u...);}void outr() {}template<typename T, class... U, char sep = ' '>void outr(const T &t, const U &...u) {cout << t;outr(u...);}// modinttemplate<int MOD> struct Fp {long long val;constexpr Fp(long long v = 0) noexcept : val(v % MOD) {if (val < 0) val += MOD;}constexpr int getmod() const { return MOD; }constexpr Fp operator - () const noexcept {return val ? MOD - val : 0;}constexpr Fp operator + (const Fp& r) const noexcept { return Fp(*this) += r; }constexpr Fp operator - (const Fp& r) const noexcept { return Fp(*this) -= r; }constexpr Fp operator * (const Fp& r) const noexcept { return Fp(*this) *= r; }constexpr Fp operator / (const Fp& r) const noexcept { return Fp(*this) /= r; }constexpr Fp& operator += (const Fp& r) noexcept {val += r.val;if (val >= MOD) val -= MOD;return *this;}constexpr Fp& operator -= (const Fp& r) noexcept {val -= r.val;if (val < 0) val += MOD;return *this;}constexpr Fp& operator *= (const Fp& r) noexcept {val = val * r.val % MOD;return *this;}constexpr Fp& operator /= (const Fp& r) noexcept {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 bool operator == (const Fp& r) const noexcept {return this->val == r.val;}constexpr bool operator != (const Fp& r) const noexcept {return this->val != r.val;}friend constexpr istream& operator >> (istream& is, Fp<MOD>& x) noexcept {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) noexcept {return os << x.val;}friend constexpr Fp<MOD> modpow(const Fp<MOD>& r, long long n) noexcept {if (n == 0) return 1;if (n < 0) return modpow(modinv(r), -n);auto t = modpow(r, n / 2);t = t * t;if (n & 1) t = t * r;return t;}friend constexpr Fp<MOD> modinv(const Fp<MOD>& r) noexcept {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);}return Fp<MOD>(u);}};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 transformtemplate<class mint> void trans(vector<mint>& v, bool inv = false) {if (v.empty()) return;int N = (int)v.size();int MOD = v[0].getmod();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 garnerstatic 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;}// minttemplate<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].getmod();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);static const 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;}// long longvector<long long> mul_ll(const vector<long long>& A, const vector<long long>& 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 size_fft = get_fft_size(N, M);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], a1[i] = A[i], a2[i] = A[i];for (int i = 0; i < M; ++i)b0[i] = B[i], b1[i] = B[i], b2[i] = B[i];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);static const long long mod0 = MOD0, mod01 = mod0 * MOD1;vector<long long> 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;}};// Binomial Coefficienttemplate<class T> struct BiCoef {vector<T> fact_, inv_, finv_;constexpr BiCoef() {}constexpr BiCoef(int n) noexcept : fact_(n, 1), inv_(n, 1), finv_(n, 1) {init(n);}constexpr void init(int n) noexcept {fact_.assign(n, 1), inv_.assign(n, 1), finv_.assign(n, 1);int MOD = fact_[0].getmod();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 noexcept {if (n < k || n < 0 || k < 0) return 0;return fact_[n] * finv_[k] * finv_[n-k];}constexpr T fact(int n) const noexcept {if (n < 0) return 0;return fact_[n];}constexpr T inv(int n) const noexcept {if (n < 0) return 0;return inv_[n];}constexpr T finv(int n) const noexcept {if (n < 0) return 0;return finv_[n];}};// Formal Power Seriestemplate <typename mint> struct FPS : vector<mint> {using vector<mint>::vector;// constructorFPS(const vector<mint>& r) : vector<mint>(r) {}// core operatorinline FPS pre(int siz) const {return FPS(begin(*this), begin(*this) + min((int)this->size(), siz));}inline FPS rev() const {FPS res = *this;reverse(begin(res), end(res));return res;}inline FPS& normalize() {while (!this->empty() && this->back() == 0) this->pop_back();return *this;}// basic operatorinline FPS operator - () const noexcept {FPS res = (*this);for (int i = 0; i < (int)res.size(); ++i) res[i] = -res[i];return res;}inline FPS operator + (const mint& v) const { return FPS(*this) += v; }inline FPS operator + (const FPS& r) const { return FPS(*this) += r; }inline FPS operator - (const mint& v) const { return FPS(*this) -= v; }inline FPS operator - (const FPS& r) const { return FPS(*this) -= r; }inline FPS operator * (const mint& v) const { return FPS(*this) *= v; }inline FPS operator * (const FPS& r) const { return FPS(*this) *= r; }inline FPS operator / (const mint& v) const { return FPS(*this) /= v; }inline FPS operator << (int x) const { return FPS(*this) <<= x; }inline FPS operator >> (int x) const { return FPS(*this) >>= x; }inline FPS& operator += (const mint& v) {if (this->empty()) this->resize(1);(*this)[0] += v;return *this;}inline FPS& operator += (const FPS& 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();}inline FPS& operator -= (const mint& v) {if (this->empty()) this->resize(1);(*this)[0] -= v;return *this;}inline FPS& operator -= (const FPS& 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();}inline FPS& operator *= (const mint& v) {for (int i = 0; i < (int)this->size(); ++i) (*this)[i] *= v;return *this;}inline FPS& operator *= (const FPS& r) {return *this = NTT::mul((*this), r);}inline FPS& 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;}inline FPS& operator <<= (int x) {FPS res(x, 0);res.insert(res.end(), begin(*this), end(*this));return *this = res;}inline FPS& operator >>= (int x) {FPS res;res.insert(res.end(), begin(*this) + x, end(*this));return *this = res;}inline 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;}inline friend FPS gcd(const FPS& f, const FPS& g) {if (g.empty()) return f;return gcd(g, f % g);}// advanced operation// df/dxinline friend FPS diff(const FPS& f) {int n = (int)f.size();FPS res(n-1);for (int i = 1; i < n; ++i) res[i-1] = f[i] * i;return res;}// \int f dxinline friend FPS integral(const FPS& f) {int n = (int)f.size();FPS res(n+1, 0);for (int i = 0; i < n; ++i) res[i+1] = f[i] / (i+1);return res;}// inv(f), f[0] must not be 0inline friend FPS inv(const FPS& f, int deg) {assert(f[0] != 0);if (deg < 0) deg = (int)f.size();FPS res({mint(1) / f[0]});for (int i = 1; i < deg; i <<= 1) {res = (res + res - res * res * f.pre(i << 1)).pre(i << 1);}res.resize(deg);return res;}inline friend FPS inv(const FPS& f) {return inv(f, f.size());}// division, r must be normalized (r.back() must not be 0)inline FPS& operator /= (const FPS& 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 = ((*this).rev().pre(need) * inv(r.rev(), need)).pre(need).rev();return *this;}inline FPS& operator %= (const FPS &r) {assert(!r.empty());assert(r.back() != 0);this->normalize();FPS q = (*this) / r;return *this -= q * r;}inline FPS operator / (const FPS& r) const { return FPS(*this) /= r; }inline FPS operator % (const FPS& r) const { return FPS(*this) %= r; }// log(f) = \int f'/f dx, f[0] must be 1inline friend FPS log(const FPS& f, int deg) {assert(f[0] == 1);FPS res = integral(diff(f) * inv(f, deg));res.resize(deg);return res;}inline friend FPS log(const FPS& f) {return log(f, f.size());}// exp(f), f[0] must be 0inline friend FPS exp(const FPS& f, int deg) {assert(f[0] == 0);FPS res(1, 1);for (int i = 1; i < deg; i <<= 1) {res = res * (f.pre(i<<1) - log(res, i<<1) + 1).pre(i<<1);}res.resize(deg);return res;}inline friend FPS exp(const FPS& f) {return exp(f, f.size());}// pow(f) = exp(e * log f)inline friend FPS pow(const FPS& f, long long e, int deg) {long long i = 0;while (i < (int)f.size() && f[i] == 0) ++i;if (i == (int)f.size()) return FPS(deg, 0);if (i * e >= deg) return FPS(deg, 0);mint k = f[i];FPS res = exp(log((f >> i) / k, deg) * e, deg) * modpow(k, e) << (e * i);res.resize(deg);return res;}inline friend FPS pow(const FPS& f, long long e) {return pow(f, e, f.size());}// sqrt(f), f[0] must be 1inline friend FPS sqrt_base(const FPS& f, int deg) {assert(f[0] == 1);mint inv2 = mint(1) / 2;FPS res(1, 1);for (int i = 1; i < deg; i <<= 1) {res = (res + f.pre(i << 1) * inv(res, i << 1)).pre(i << 1);for (mint& x : res) x *= inv2;}res.resize(deg);return res;}inline friend FPS sqrt_base(const FPS& f) {return sqrt_base(f, f.size());}};const int MOD = 998244353;using mint = Fp<MOD>;BiCoef<mint> bc;using fps = FPS<mint>;int main(){ios_base::sync_with_stdio(false);cin.tie(nullptr);int n,k; in(n,k);bc.init(k+1);fps f(k+1),g(k+1);rep(i,k+1){if(i&1) f[i] = bc.finv(i);else g[i] = bc.finv(i);}fps ff = f*f, fg = f*g;mint ans = 0;rep(t,k+1){mint tmp = modpow((mint)t,n) * bc.finv(t) * (t&1 ? -1:1);if((k-t)&1) ans += tmp * fg[k-t];else ans += tmp * ff[k-t];}ans *= bc.fact(k);if(!(k&1)) ans *= -1;out(ans);}