結果

問題 No.1962 Not Divide
ユーザー tokusakuraitokusakurai
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
このコードへのチャレンジ
(要ログイン)
ファイルパターン 結果
sample AC * 3
other AC * 21
権限があれば一括ダウンロードができます

ソースコード

diff #
プレゼンテーションモードにする

#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 2^(i+2)
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/dx
int 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)dx
int 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)^k
int 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';
}
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