結果
問題 | No.1962 Not Divide |
ユーザー |
|
提出日時 | 2022-08-07 10:54:21 |
言語 | C++17 (gcc 13.3.0 + boost 1.87.0) |
結果 |
AC
|
実行時間 | 129 ms / 2,000 ms |
コード長 | 18,453 bytes |
コンパイル時間 | 2,587 ms |
コンパイル使用メモリ | 212,252 KB |
最終ジャッジ日時 | 2025-01-30 19:11:04 |
ジャッジサーバーID (参考情報) |
judge4 / judge4 |
(要ログイン)
ファイルパターン | 結果 |
---|---|
sample | AC * 3 |
other | AC * 21 |
ソースコード
#include <bits/stdc++.h>using namespace std;#define rep(i, n) for (int i = 0; i < n; i++)#define rep2(i, x, n) for (int i = x; i <= n; i++)#define rep3(i, x, n) for (int i = x; i >= n; i--)#define each(e, v) for (auto &e : v)#define pb push_back#define eb emplace_back#define all(x) x.begin(), x.end()#define rall(x) x.rbegin(), x.rend()#define sz(x) (int)x.size()using ll = long long;using pii = pair<int, int>;using pil = pair<int, ll>;using pli = pair<ll, int>;using pll = pair<ll, ll>;template <typename T>bool chmax(T &x, const T &y) {return (x < y) ? (x = y, true) : false;}template <typename T>bool chmin(T &x, const T &y) {return (x > y) ? (x = y, true) : false;}template <typename T>int flg(T x, int i) {return (x >> i) & 1;}template <typename T>void print(const vector<T> &v, T x = 0) {int n = v.size();for (int i = 0; i < n; i++) cout << v[i] + x << (i == n - 1 ? '\n' : ' ');if (v.empty()) cout << '\n';}template <typename T>void printn(const vector<T> &v, T x = 0) {int n = v.size();for (int i = 0; i < n; i++) cout << v[i] + x << '\n';}template <typename T>int lb(const vector<T> &v, T x) {return lower_bound(begin(v), end(v), x) - begin(v);}template <typename T>int ub(const vector<T> &v, T x) {return upper_bound(begin(v), end(v), x) - begin(v);}template <typename T>void rearrange(vector<T> &v) {sort(begin(v), end(v));v.erase(unique(begin(v), end(v)), end(v));}template <typename T>vector<int> id_sort(const vector<T> &v, bool greater = false) {int n = v.size();vector<int> ret(n);iota(begin(ret), end(ret), 0);sort(begin(ret), end(ret), [&](int i, int j) { return greater ? v[i] > v[j] : v[i] < v[j]; });return ret;}template <typename S, typename T>pair<S, T> operator+(const pair<S, T> &p, const pair<S, T> &q) {return make_pair(p.first + q.first, p.second + q.second);}template <typename S, typename T>pair<S, T> operator-(const pair<S, T> &p, const pair<S, T> &q) {return make_pair(p.first - q.first, p.second - q.second);}template <typename S, typename T>istream &operator>>(istream &is, pair<S, T> &p) {S a;T b;is >> a >> b;p = make_pair(a, b);return is;}template <typename S, typename T>ostream &operator<<(ostream &os, const pair<S, T> &p) {return os << p.first << ' ' << p.second;}struct io_setup {io_setup() {ios_base::sync_with_stdio(false);cin.tie(NULL);cout << fixed << setprecision(15);}} io_setup;const int inf = (1 << 30) - 1;const ll INF = (1LL << 60) - 1;// const int MOD = 1000000007;const int MOD = 998244353;template <int mod>struct Mod_Int {int x;Mod_Int() : x(0) {}Mod_Int(long long y) : x(y >= 0 ? y % mod : (mod - (-y) % mod) % mod) {}static int get_mod() { return mod; }Mod_Int &operator+=(const Mod_Int &p) {if ((x += p.x) >= mod) x -= mod;return *this;}Mod_Int &operator-=(const Mod_Int &p) {if ((x += mod - p.x) >= mod) x -= mod;return *this;}Mod_Int &operator*=(const Mod_Int &p) {x = (int)(1LL * x * p.x % mod);return *this;}Mod_Int &operator/=(const Mod_Int &p) {*this *= p.inverse();return *this;}Mod_Int &operator++() { return *this += Mod_Int(1); }Mod_Int operator++(int) {Mod_Int tmp = *this;++*this;return tmp;}Mod_Int &operator--() { return *this -= Mod_Int(1); }Mod_Int operator--(int) {Mod_Int tmp = *this;--*this;return tmp;}Mod_Int operator-() const { return Mod_Int(-x); }Mod_Int operator+(const Mod_Int &p) const { return Mod_Int(*this) += p; }Mod_Int operator-(const Mod_Int &p) const { return Mod_Int(*this) -= p; }Mod_Int operator*(const Mod_Int &p) const { return Mod_Int(*this) *= p; }Mod_Int operator/(const Mod_Int &p) const { return Mod_Int(*this) /= p; }bool operator==(const Mod_Int &p) const { return x == p.x; }bool operator!=(const Mod_Int &p) const { return x != p.x; }Mod_Int inverse() const {assert(*this != Mod_Int(0));return pow(mod - 2);}Mod_Int pow(long long k) const {Mod_Int now = *this, ret = 1;for (; k > 0; k >>= 1, now *= now) {if (k & 1) ret *= now;}return ret;}friend ostream &operator<<(ostream &os, const Mod_Int &p) { return os << p.x; }friend istream &operator>>(istream &is, Mod_Int &p) {long long a;is >> a;p = Mod_Int<mod>(a);return is;}};using mint = Mod_Int<MOD>;template <typename T>struct Number_Theoretic_Transform {static int max_base;static T root;static vector<T> r, ir;Number_Theoretic_Transform() {}static void init() {if (!r.empty()) return;int mod = T::get_mod();int tmp = mod - 1;root = 2;while (root.pow(tmp >> 1) == 1) root++;max_base = 0;while (tmp % 2 == 0) tmp >>= 1, max_base++;r.resize(max_base), ir.resize(max_base);for (int i = 0; i < max_base; i++) {r[i] = -root.pow((mod - 1) >> (i + 2)); // r[i] := 1 の 2^(i+2) 乗根ir[i] = r[i].inverse(); // ir[i] := 1/r[i]}}static void ntt(vector<T> &a) {init();int n = a.size();assert((n & (n - 1)) == 0);assert(n <= (1 << max_base));for (int k = n; k >>= 1;) {T w = 1;for (int s = 0, t = 0; s < n; s += 2 * k) {for (int i = s, j = s + k; i < s + k; i++, j++) {T x = a[i], y = w * a[j];a[i] = x + y, a[j] = x - y;}w *= r[__builtin_ctz(++t)];}}}static void intt(vector<T> &a) {init();int n = a.size();assert((n & (n - 1)) == 0);assert(n <= (1 << max_base));for (int k = 1; k < n; k <<= 1) {T w = 1;for (int s = 0, t = 0; s < n; s += 2 * k) {for (int i = s, j = s + k; i < s + k; i++, j++) {T x = a[i], y = a[j];a[i] = x + y, a[j] = w * (x - y);}w *= ir[__builtin_ctz(++t)];}}T inv = T(n).inverse();for (auto &e : a) e *= inv;}static vector<T> convolve(vector<T> a, vector<T> b) {if (a.empty() || b.empty()) return {};int k = (int)a.size() + (int)b.size() - 1, n = 1;while (n < k) n <<= 1;a.resize(n), b.resize(n);ntt(a), ntt(b);for (int i = 0; i < n; i++) a[i] *= b[i];intt(a), a.resize(k);return a;}};template <typename T>int Number_Theoretic_Transform<T>::max_base = 0;template <typename T>T Number_Theoretic_Transform<T>::root = T();template <typename T>vector<T> Number_Theoretic_Transform<T>::r = vector<T>();template <typename T>vector<T> Number_Theoretic_Transform<T>::ir = vector<T>();using NTT = Number_Theoretic_Transform<mint>;template <typename T>struct Formal_Power_Series : vector<T> {using NTT_ = Number_Theoretic_Transform<T>;using vector<T>::vector;Formal_Power_Series(const vector<T> &v) : vector<T>(v) {}Formal_Power_Series pre(int n) const { return Formal_Power_Series(begin(*this), begin(*this) + min((int)this->size(), n)); }Formal_Power_Series rev(int deg = -1) const {Formal_Power_Series ret = *this;if (deg != -1) ret.resize(deg, T(0));reverse(begin(ret), end(ret));return ret;}void normalize() {while (!this->empty() && this->back() == 0) this->pop_back();}Formal_Power_Series operator-() const {Formal_Power_Series ret = *this;for (int i = 0; i < (int)ret.size(); i++) ret[i] = -ret[i];return ret;}Formal_Power_Series &operator+=(const T &x) {if (this->empty()) this->resize(1);(*this)[0] += x;return *this;}Formal_Power_Series &operator+=(const Formal_Power_Series &v) {if (v.size() > this->size()) this->resize(v.size());for (int i = 0; i < (int)v.size(); i++) (*this)[i] += v[i];this->normalize();return *this;}Formal_Power_Series &operator-=(const T &x) {if (this->empty()) this->resize(1);*this[0] -= x;return *this;}Formal_Power_Series &operator-=(const Formal_Power_Series &v) {if (v.size() > this->size()) this->resize(v.size());for (int i = 0; i < (int)v.size(); i++) (*this)[i] -= v[i];this->normalize();return *this;}Formal_Power_Series &operator*=(const T &x) {for (int i = 0; i < (int)this->size(); i++) (*this)[i] *= x;return *this;}Formal_Power_Series &operator*=(const Formal_Power_Series &v) {if (this->empty() || empty(v)) {this->clear();return *this;}return *this = NTT_::convolve(*this, v);}Formal_Power_Series &operator/=(const T &x) {assert(x != 0);T inv = x.inverse();for (int i = 0; i < (int)this->size(); i++) (*this)[i] *= inv;return *this;}Formal_Power_Series &operator/=(const Formal_Power_Series &v) {if (v.size() > this->size()) {this->clear();return *this;}int n = this->size() - (int)v.size() + 1;return *this = (rev().pre(n) * v.rev().inv(n)).pre(n).rev(n);}Formal_Power_Series &operator%=(const Formal_Power_Series &v) { return *this -= (*this / v) * v; }Formal_Power_Series &operator<<=(int x) {Formal_Power_Series ret(x, 0);ret.insert(end(ret), begin(*this), end(*this));return *this = ret;}Formal_Power_Series &operator>>=(int x) {Formal_Power_Series ret;ret.insert(end(ret), begin(*this) + x, end(*this));return *this = ret;}Formal_Power_Series operator+(const T &x) const { return Formal_Power_Series(*this) += x; }Formal_Power_Series operator+(const Formal_Power_Series &v) const { return Formal_Power_Series(*this) += v; }Formal_Power_Series operator-(const T &x) const { return Formal_Power_Series(*this) -= x; }Formal_Power_Series operator-(const Formal_Power_Series &v) const { return Formal_Power_Series(*this) -= v; }Formal_Power_Series operator*(const T &x) const { return Formal_Power_Series(*this) *= x; }Formal_Power_Series operator*(const Formal_Power_Series &v) const { return Formal_Power_Series(*this) *= v; }Formal_Power_Series operator/(const T &x) const { return Formal_Power_Series(*this) /= x; }Formal_Power_Series operator/(const Formal_Power_Series &v) const { return Formal_Power_Series(*this) /= v; }Formal_Power_Series operator%(const Formal_Power_Series &v) const { return Formal_Power_Series(*this) %= v; }Formal_Power_Series operator<<(int x) const { return Formal_Power_Series(*this) <<= x; }Formal_Power_Series operator>>(int x) const { return Formal_Power_Series(*this) >>= x; }T val(const T &x) const {T ret = 0;for (int i = (int)this->size() - 1; i >= 0; i--) ret *= x, ret += (*this)[i];return ret;}Formal_Power_Series diff() const { // df/dxint n = this->size();Formal_Power_Series ret(n - 1);for (int i = 1; i < n; i++) ret[i - 1] = (*this)[i] * i;return ret;}Formal_Power_Series integral() const { // ∫f(x)dxint n = this->size();Formal_Power_Series ret(n + 1);for (int i = 0; i < n; i++) ret[i + 1] = (*this)[i] / (i + 1);return ret;}Formal_Power_Series inv(int deg) const { // 1/f(x) (f[0] != 0)assert((*this)[0] != T(0));Formal_Power_Series ret(1, (*this)[0].inverse());for (int i = 1; i < deg; i <<= 1) {Formal_Power_Series f = pre(2 * i), g = ret;f.resize(2 * i), g.resize(2 * i);NTT_::ntt(f), NTT_::ntt(g);Formal_Power_Series h(2 * i);for (int j = 0; j < 2 * i; j++) h[j] = f[j] * g[j];NTT_::intt(h);for (int j = 0; j < i; j++) h[j] = 0;NTT_::ntt(h);for (int j = 0; j < 2 * i; j++) h[j] *= g[j];NTT_::intt(h);for (int j = 0; j < i; j++) h[j] = 0;ret -= h;}ret.resize(deg);return ret;}Formal_Power_Series inv() const { return inv(this->size()); }Formal_Power_Series log(int deg) const { // log(f(x)) (f[0] = 1)assert((*this)[0] == 1);Formal_Power_Series ret = (diff() * inv(deg)).pre(deg - 1).integral();ret.resize(deg);return ret;}Formal_Power_Series log() const { return log(this->size()); }Formal_Power_Series exp(int deg) const { // exp(f(x)) (f[0] = 0)assert((*this)[0] == 0);Formal_Power_Series inv;inv.reserve(deg + 1);inv.push_back(0), inv.push_back(1);auto inplace_integral = [&](Formal_Power_Series &F) -> void {int n = F.size();int mod = T::get_mod();while ((int)inv.size() <= n) {int i = inv.size();inv.push_back((-inv[mod % i]) * (mod / i));}F.insert(begin(F), 0);for (int i = 1; i <= n; i++) F[i] *= inv[i];};auto inplace_diff = [](Formal_Power_Series &F) -> void {if (F.empty()) return;F.erase(begin(F));T coeff = 1, one = 1;for (int i = 0; i < (int)F.size(); i++) {F[i] *= coeff;coeff += one;}};Formal_Power_Series ret{1, this->size() > 1 ? (*this)[1] : 0}, c{1}, z1, z2{1, 1};for (int m = 2; m < deg; m *= 2) {auto y = ret;y.resize(2 * m);NTT_::ntt(y);z1 = z2;Formal_Power_Series z(m);for (int i = 0; i < m; i++) z[i] = y[i] * z1[i];NTT_::intt(z);fill(begin(z), begin(z) + m / 2, 0);NTT_::ntt(z);for (int i = 0; i < m; i++) z[i] *= -z1[i];NTT_::intt(z);c.insert(end(c), begin(z) + m / 2, end(z));z2 = c, z2.resize(2 * m);NTT_::ntt(z2);Formal_Power_Series x(begin(*this), begin(*this) + min((int)this->size(), m));inplace_diff(x);x.push_back(0);NTT_::ntt(x);for (int i = 0; i < m; i++) x[i] *= y[i];NTT_::intt(x);x -= ret.diff(), x.resize(2 * m);for (int i = 0; i < m - 1; i++) x[m + i] = x[i], x[i] = 0;NTT_::ntt(x);for (int i = 0; i < 2 * m; i++) x[i] *= z2[i];NTT_::intt(x);x.pop_back();inplace_integral(x);for (int i = m; i < min((int)this->size(), 2 * m); i++) x[i] += (*this)[i];fill(begin(x), begin(x) + m, 0);NTT_::ntt(x);for (int i = 0; i < 2 * m; i++) x[i] *= y[i];NTT_::intt(x);ret.insert(end(ret), begin(x) + m, end(x));}ret.resize(deg);return ret;}Formal_Power_Series exp() const { return exp(this->size()); }Formal_Power_Series pow(long long k, int deg) const { // f(x)^kint n = this->size();for (int i = 0; i < n; i++) {if ((*this)[i] == 0) continue;T rev = (*this)[i].inverse();Formal_Power_Series C(*this * rev), D(n - i, 0);for (int j = i; j < n; j++) D[j - i] = C[j];D = (D.log() * k).exp() * ((*this)[i].pow(k));Formal_Power_Series E(deg, 0);if (i > 0 && k > deg / i) return E;long long S = i * k;for (int j = 0; j + S < deg && j < D.size(); j++) E[j + S] = D[j];E.resize(deg);return E;}return Formal_Power_Series(deg, 0);}Formal_Power_Series pow(long long k) const { return pow(k, this->size()); }Formal_Power_Series Taylor_shift(T c) const { // f(x+c)int n = this->size();vector<T> ifac(n, 1);Formal_Power_Series f(n), g(n);for (int i = 0; i < n; i++) {f[n - 1 - i] = (*this)[i] * ifac[n - 1];if (i < n - 1) ifac[n - 1] *= i + 1;}ifac[n - 1] = ifac[n - 1].inverse();for (int i = n - 1; i > 0; i--) ifac[i - 1] = ifac[i] * i;T pw = 1;for (int i = 0; i < n; i++) {g[i] = pw * ifac[i];pw *= c;}f *= g;Formal_Power_Series b(n);for (int i = 0; i < n; i++) b[i] = f[n - 1 - i] * ifac[i];return b;}};using fps = Formal_Power_Series<mint>;template <typename T>T Bostan_Mori(vector<T> P, vector<T> Q, long long k) {using NTT_ = Number_Theoretic_Transform<T>;int n = max((int)P.size(), (int)Q.size());assert(n > 0 && Q[0] == 1);P.resize(n, 0), Q.resize(n, 0);int t = 1;while (t < 2 * n - 1) t <<= 1;for (; k > 0; k >>= 1) {vector<T> R = Q;for (int i = 1; i < n; i += 2) R[i] = -R[i];P.resize(t, 0), NTT_::ntt(P);Q.resize(t, 0), NTT_::ntt(Q);R.resize(t, 0), NTT_::ntt(R);vector<T> A(t), B(t);for (int i = 0; i < t; i++) {A[i] = P[i] * R[i];B[i] = Q[i] * R[i];}NTT_::intt(A), NTT_::intt(B);Q.resize(n);for (int i = 0; i < n; i++) Q[i] = B[2 * i];P.resize(n);if (k & 1) {for (int i = 0; i < n - 1; i++) P[i] = A[2 * i + 1];P[n - 1] = 0;} else {for (int i = 0; i < n; i++) P[i] = A[2 * i];}}return P[0];}int main() {int N, M;cin >> N >> M;fps P(1, 0), Q(1, 1);rep2(i, 1, M) {fps A(i + 1, 0), B(i + 2, 0);A[1]++, A[i]--;B[0]++, B[i] -= 2, B[i + 1]++;fps X = P * B + Q * A;fps Y = Q * B;swap(P, X), swap(Q, Y);}cout << Bostan_Mori(Q, Q - P, N) << '\n';}