結果

問題 No.1100 Boxes
ユーザー ei1333333
提出日時 2020-06-26 22:54:32
言語 C++17
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 80 ms / 2,000 ms
コード長 19,219 bytes
コンパイル時間 3,193 ms
コンパイル使用メモリ 215,284 KB
最終ジャッジ日時 2025-01-11 12:02:04
ジャッジサーバーID
(参考情報)
judge5 / judge5
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ファイルパターン 結果
sample AC * 4
other AC * 36
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;
using int64 = long long;
const int mod = 998244353;
const int64 infll = (1LL << 62) - 1;
const int inf = (1 << 30) - 1;
struct IoSetup {
IoSetup() {
cin.tie(nullptr);
ios::sync_with_stdio(false);
cout << fixed << setprecision(10);
cerr << fixed << setprecision(10);
}
} iosetup;
template< typename T1, typename T2 >
ostream &operator<<(ostream &os, const pair< T1, T2 > &p) {
os << p.first << " " << p.second;
return os;
}
template< typename T1, typename T2 >
istream &operator>>(istream &is, pair< T1, T2 > &p) {
is >> p.first >> p.second;
return is;
}
template< typename T >
ostream &operator<<(ostream &os, const vector< T > &v) {
for(int i = 0; i < (int) v.size(); i++) {
os << v[i] << (i + 1 != v.size() ? " " : "");
}
return os;
}
template< typename T >
istream &operator>>(istream &is, vector< T > &v) {
for(T &in : v) is >> in;
return is;
}
template< typename T1, typename T2 >
inline bool chmax(T1 &a, T2 b) { return a < b && (a = b, true); }
template< typename T1, typename T2 >
inline bool chmin(T1 &a, T2 b) { return a > b && (a = b, true); }
template< typename T = int64 >
vector< T > make_v(size_t a) {
return vector< T >(a);
}
template< typename T, typename... Ts >
auto make_v(size_t a, Ts... ts) {
return vector< decltype(make_v< T >(ts...)) >(a, make_v< T >(ts...));
}
template< typename T, typename V >
typename enable_if< is_class< T >::value == 0 >::type fill_v(T &t, const V &v) {
t = v;
}
template< typename T, typename V >
typename enable_if< is_class< T >::value != 0 >::type fill_v(T &t, const V &v) {
for(auto &e : t) fill_v(e, v);
}
template< typename F >
struct FixPoint : F {
FixPoint(F &&f) : F(forward< F >(f)) {}
template< typename... Args >
decltype(auto) operator()(Args &&... args) const {
return F::operator()(*this, forward< Args >(args)...);
}
};
template< typename F >
inline decltype(auto) MFP(F &&f) {
return FixPoint< F >{forward< F >(f)};
}
template< typename T >
struct FormalPowerSeries : vector< T > {
using vector< T >::vector;
using P = FormalPowerSeries;
using MULT = function< P(P, P) >;
using FFT = function< void(P &) >;
using SQRT = function< T(T) >;
static MULT &get_mult() {
static MULT mult = nullptr;
return mult;
}
static void set_mult(MULT f) {
get_mult() = f;
}
static FFT &get_fft() {
static FFT fft = nullptr;
return fft;
}
static FFT &get_ifft() {
static FFT ifft = nullptr;
return ifft;
}
static void set_fft(FFT f, FFT g) {
get_fft() = f;
get_ifft() = g;
}
static SQRT &get_sqrt() {
static SQRT sqr = nullptr;
return sqr;
}
static void set_sqrt(SQRT sqr) {
get_sqrt() = sqr;
}
void shrink() {
while(this->size() && this->back() == T(0)) this->pop_back();
}
P operator+(const P &r) const { return P(*this) += r; }
P operator+(const T &v) const { return P(*this) += v; }
P operator-(const P &r) const { return P(*this) -= r; }
P operator-(const T &v) const { return P(*this) -= v; }
P operator*(const P &r) const { return P(*this) *= r; }
P operator*(const T &v) const { return P(*this) *= v; }
P operator/(const P &r) const { return P(*this) /= r; }
P operator%(const P &r) const { return P(*this) %= r; }
P &operator+=(const P &r) {
if(r.size() > this->size()) this->resize(r.size());
for(int i = 0; i < r.size(); i++) (*this)[i] += r[i];
return *this;
}
P &operator+=(const T &r) {
if(this->empty()) this->resize(1);
(*this)[0] += r;
return *this;
}
P &operator-=(const P &r) {
if(r.size() > this->size()) this->resize(r.size());
for(int i = 0; i < r.size(); i++) (*this)[i] -= r[i];
shrink();
return *this;
}
P &operator-=(const T &r) {
if(this->empty()) this->resize(1);
(*this)[0] -= r;
shrink();
return *this;
}
P &operator*=(const T &v) {
const int n = (int) this->size();
for(int k = 0; k < n; k++) (*this)[k] *= v;
return *this;
}
P &operator*=(const P &r) {
if(this->empty() || r.empty()) {
this->clear();
return *this;
}
assert(get_mult() != nullptr);
return *this = get_mult()(*this, r);
}
P &operator%=(const P &r) { return *this -= *this / r * r; }
P operator-() const {
P ret(this->size());
for(int i = 0; i < this->size(); i++) ret[i] = -(*this)[i];
return ret;
}
P &operator/=(const P &r) {
if(this->size() < r.size()) {
this->clear();
return *this;
}
int n = this->size() - r.size() + 1;
return *this = (rev().pre(n) * r.rev().inv(n)).pre(n).rev(n);
}
P dot(P r) const {
P ret(min(this->size(), r.size()));
for(int i = 0; i < ret.size(); i++) ret[i] = (*this)[i] * r[i];
return ret;
}
P pre(int sz) const { return P(begin(*this), begin(*this) + min((int) this->size(), sz)); }
P operator>>(int sz) const {
if(this->size() <= sz) return {};
P ret(*this);
ret.erase(ret.begin(), ret.begin() + sz);
return ret;
}
P operator<<(int sz) const {
P ret(*this);
ret.insert(ret.begin(), sz, T(0));
return ret;
}
P rev(int deg = -1) const {
P ret(*this);
if(deg != -1) ret.resize(deg, T(0));
reverse(begin(ret), end(ret));
return ret;
}
P diff() const {
const int n = (int) this->size();
P ret(max(0, n - 1));
for(int i = 1; i < n; i++) ret[i - 1] = (*this)[i] * T(i);
return ret;
}
P integral() const {
const int n = (int) this->size();
P ret(n + 1);
ret[0] = T(0);
for(int i = 0; i < n; i++) ret[i + 1] = (*this)[i] / T(i + 1);
return ret;
}
// F(0) must not be 0
P inv(int deg = -1) const {
assert(((*this)[0]) != T(0));
const int n = (int) this->size();
if(deg == -1) deg = n;
if(get_fft() != nullptr) {
P ret(*this);
ret.resize(deg, T(0));
return ret.inv_fast();
}
P ret({T(1) / (*this)[0]});
for(int i = 1; i < deg; i <<= 1) {
ret = (ret + ret - ret * ret * pre(i << 1)).pre(i << 1);
}
return ret.pre(deg);
}
// F(0) must be 1
P log(int deg = -1) const {
assert((*this)[0] == 1);
const int n = (int) this->size();
if(deg == -1) deg = n;
return (this->diff() * this->inv(deg)).pre(deg - 1).integral();
}
P sqrt(int deg = -1) const {
const int n = (int) this->size();
if(deg == -1) deg = n;
if((*this)[0] == T(0)) {
for(int i = 1; i < n; i++) {
if((*this)[i] != T(0)) {
if(i & 1) return {};
if(deg - i / 2 <= 0) break;
auto ret = (*this >> i).sqrt(deg - i / 2);
if(ret.empty()) return {};
ret = ret << (i / 2);
if(ret.size() < deg) ret.resize(deg, T(0));
return ret;
}
}
return P(deg, 0);
}
P ret;
if(get_sqrt() == nullptr) {
assert((*this)[0] == T(1));
ret = {T(1)};
} else {
auto sqr = get_sqrt()((*this)[0]);
if(sqr * sqr != (*this)[0]) return {};
ret = {T(sqr)};
}
T inv2 = T(1) / T(2);
for(int i = 1; i < deg; i <<= 1) {
ret = (ret + pre(i << 1) * ret.inv(i << 1)) * inv2;
}
return ret.pre(deg);
}
// F(0) must be 0
P exp(int deg = -1) const {
assert((*this)[0] == T(0));
const int n = (int) this->size();
if(deg == -1) deg = n;
if(get_fft() != nullptr) {
P ret(*this);
ret.resize(deg, T(0));
return ret.exp_rec();
}
P ret({T(1)});
for(int i = 1; i < deg; i <<= 1) {
ret = (ret * (pre(i << 1) + T(1) - ret.log(i << 1))).pre(i << 1);
}
return ret.pre(deg);
}
P online_convolution_exp(const P &conv_coeff) const {
const int n = (int) conv_coeff.size();
assert((n & (n - 1)) == 0);
vector< P > conv_ntt_coeff;
for(int i = n; i >= 1; i >>= 1) {
P g(conv_coeff.pre(i));
get_fft()(g);
conv_ntt_coeff.emplace_back(g);
}
P conv_arg(n), conv_ret(n);
auto rec = [&](auto rec, int l, int r, int d) -> void {
if(r - l <= 16) {
for(int i = l; i < r; i++) {
T sum = 0;
for(int j = l; j < i; j++) sum += conv_arg[j] * conv_coeff[i - j];
conv_ret[i] += sum;
conv_arg[i] = i == 0 ? T(1) : conv_ret[i] / i;
}
} else {
int m = (l + r) / 2;
rec(rec, l, m, d + 1);
P pre(r - l);
for(int i = 0; i < m - l; i++) pre[i] = conv_arg[l + i];
get_fft()(pre);
for(int i = 0; i < r - l; i++) pre[i] *= conv_ntt_coeff[d][i];
get_ifft()(pre);
for(int i = 0; i < r - m; i++) conv_ret[m + i] += pre[m + i - l];
rec(rec, m, r, d + 1);
}
};
rec(rec, 0, n, 0);
return conv_arg;
}
P exp_rec() const {
assert((*this)[0] == T(0));
const int n = (int) this->size();
int m = 1;
while(m < n) m *= 2;
P conv_coeff(m);
for(int i = 1; i < n; i++) conv_coeff[i] = (*this)[i] * i;
return online_convolution_exp(conv_coeff).pre(n);
}
P inv_fast() const {
assert(((*this)[0]) != T(0));
const int n = (int) this->size();
P res{T(1) / (*this)[0]};
for(int d = 1; d < n; d <<= 1) {
P f(2 * d), g(2 * d);
for(int j = 0; j < min(n, 2 * d); j++) f[j] = (*this)[j];
for(int j = 0; j < d; j++) g[j] = res[j];
get_fft()(f);
get_fft()(g);
for(int j = 0; j < 2 * d; j++) f[j] *= g[j];
get_ifft()(f);
for(int j = 0; j < d; j++) {
f[j] = 0;
f[j + d] = -f[j + d];
}
get_fft()(f);
for(int j = 0; j < 2 * d; j++) f[j] *= g[j];
get_ifft()(f);
for(int j = 0; j < d; j++) f[j] = res[j];
res = f;
}
return res.pre(n);
}
P pow(int64_t k, int deg = -1) const {
const int n = (int) this->size();
if(deg == -1) deg = n;
for(int i = 0; i < n; i++) {
if((*this)[i] != T(0)) {
T rev = T(1) / (*this)[i];
P ret = (((*this * rev) >> i).log() * k).exp() * ((*this)[i].pow(k));
if(i * k > deg) return P(deg, T(0));
ret = (ret << (i * k)).pre(deg);
if(ret.size() < deg) ret.resize(deg, T(0));
return ret;
}
}
return *this;
}
T eval(T x) const {
T r = 0, w = 1;
for(auto &v : *this) {
r += w * v;
w *= x;
}
return r;
}
P pow_mod(int64_t n, P mod) const {
P modinv = mod.rev().inv();
auto get_div = [&](P base) {
if(base.size() < mod.size()) {
base.clear();
return base;
}
int n = base.size() - mod.size() + 1;
return (base.rev().pre(n) * modinv.pre(n)).pre(n).rev(n);
};
P x(*this), ret{1};
while(n > 0) {
if(n & 1) {
ret *= x;
ret -= get_div(ret) * mod;
}
x *= x;
x -= get_div(x) * mod;
n >>= 1;
}
return ret;
}
};
template< typename Mint >
struct NumberTheoreticTransformFriendlyModInt {
vector< int > rev;
vector< Mint > rts;
int base, max_base;
Mint root;
NumberTheoreticTransformFriendlyModInt() : base(1), rev{0, 1}, rts{0, 1} {
const int mod = Mint::get_mod();
assert(mod >= 3 && mod % 2 == 1);
auto tmp = mod - 1;
max_base = 0;
while(tmp % 2 == 0) tmp >>= 1, max_base++;
root = 2;
while(root.pow((mod - 1) >> 1) == 1) root += 1;
assert(root.pow(mod - 1) == 1);
root = root.pow((mod - 1) >> max_base);
}
void ensure_base(int nbase) {
if(nbase <= base)
return;
rev.resize(1 << nbase);
rts.resize(1 << nbase);
for(int i = 0; i < (1 << nbase); i++) {
rev[i] = (rev[i >> 1] >> 1) + ((i & 1) << (nbase - 1));
}
assert(nbase <= max_base);
while(base < nbase) {
Mint z = root.pow(1 << (max_base - 1 - base));
for(int i = 1 << (base - 1); i < (1 << base); i++) {
rts[i << 1] = rts[i];
rts[(i << 1) + 1] = rts[i] * z;
}
++base;
}
}
void ntt(vector< Mint > &a) {
const int n = (int) a.size();
assert((n & (n - 1)) == 0);
int zeros = __builtin_ctz(n);
ensure_base(zeros);
int shift = base - zeros;
for(int i = 0; i < n; i++) {
if(i < (rev[i] >> shift)) {
swap(a[i], a[rev[i] >> shift]);
}
}
for(int k = 1; k < n; k <<= 1) {
for(int i = 0; i < n; i += 2 * k) {
for(int j = 0; j < k; j++) {
Mint z = a[i + j + k] * rts[j + k];
a[i + j + k] = a[i + j] - z;
a[i + j] = a[i + j] + z;
}
}
}
}
void intt(vector< Mint > &a) {
const int n = (int) a.size();
ntt(a);
reverse(a.begin() + 1, a.end());
Mint inv_sz = Mint(1) / n;
for(int i = 0; i < n; i++) a[i] *= inv_sz;
}
vector< Mint > multiply(vector< Mint > a, vector< Mint > b) {
int need = a.size() + b.size() - 1;
int nbase = 1;
while((1 << nbase) < need) nbase++;
ensure_base(nbase);
int sz = 1 << nbase;
a.resize(sz, 0);
b.resize(sz, 0);
ntt(a);
ntt(b);
Mint inv_sz = Mint(1) / sz;
for(int i = 0; i < sz; i++) {
a[i] *= b[i] * inv_sz;
}
reverse(a.begin() + 1, a.end());
ntt(a);
a.resize(need);
return a;
}
};
template< int mod >
struct ModInt {
int x;
ModInt() : x(0) {}
ModInt(int64_t y) : x(y >= 0 ? y % mod : (mod - (-y) % mod) % mod) {}
ModInt &operator+=(const ModInt &p) {
if((x += p.x) >= mod) x -= mod;
return *this;
}
ModInt &operator-=(const ModInt &p) {
if((x += mod - p.x) >= mod) x -= mod;
return *this;
}
ModInt &operator*=(const ModInt &p) {
x = (int) (1LL * x * p.x % mod);
return *this;
}
ModInt &operator/=(const ModInt &p) {
*this *= p.inverse();
return *this;
}
ModInt operator-() const { return ModInt(-x); }
ModInt operator+(const ModInt &p) const { return ModInt(*this) += p; }
ModInt operator-(const ModInt &p) const { return ModInt(*this) -= p; }
ModInt operator*(const ModInt &p) const { return ModInt(*this) *= p; }
ModInt operator/(const ModInt &p) const { return ModInt(*this) /= p; }
bool operator==(const ModInt &p) const { return x == p.x; }
bool operator!=(const ModInt &p) const { return x != p.x; }
ModInt inverse() const {
int a = x, b = mod, u = 1, v = 0, t;
while(b > 0) {
t = a / b;
swap(a -= t * b, b);
swap(u -= t * v, v);
}
return ModInt(u);
}
ModInt pow(int64_t n) const {
ModInt ret(1), mul(x);
while(n > 0) {
if(n & 1) ret *= mul;
mul *= mul;
n >>= 1;
}
return ret;
}
friend ostream &operator<<(ostream &os, const ModInt &p) {
return os << p.x;
}
friend istream &operator>>(istream &is, ModInt &a) {
int64_t t;
is >> t;
a = ModInt< mod >(t);
return (is);
}
static int get_mod() { return mod; }
};
using modint = ModInt< mod >;
template< typename T >
FormalPowerSeries< T > bernoulli(int N) {
FormalPowerSeries< T > poly(N + 1);
poly[0] = T(1);
for(int i = 1; i <= N; i++) {
poly[i] = poly[i - 1] / T(i + 1);
}
poly = poly.inv();
T tmp(1);
for(int i = 1; i <= N; i++) {
tmp *= T(i);
poly[i] *= tmp;
}
return poly;
}
template< typename T >
FormalPowerSeries< T > partition(int N) {
FormalPowerSeries< T > poly(N + 1);
poly[0] = 1;
for(int k = 1; k <= N; k++) {
if(1LL * k * (3 * k + 1) / 2 <= N) poly[k * (3 * k + 1) / 2] += (k % 2 ? -1 : 1);
if(1LL * k * (3 * k - 1) / 2 <= N) poly[k * (3 * k - 1) / 2] += (k % 2 ? -1 : 1);
}
return poly.inv();
}
template< typename T >
FormalPowerSeries< T > bell(int N) {
FormalPowerSeries< T > poly(N + 1), ret(N + 1);
poly[1] = 1;
poly = poly.exp();
poly[0] -= 1;
poly = poly.exp();
T mul = 1;
for(int i = 0; i <= N; i++) {
ret[i] = poly[i] * mul;
mul *= i + 1;
}
return ret;
}
template< typename T >
FormalPowerSeries< T > stirling_first(int N) {
if(N == 0) return {1};
int M = N / 2;
FormalPowerSeries< T > A = stirling_first< T >(M), B, C(N - M + 1);
if(N % 2 == 0) {
B = A;
} else {
B.resize(M + 2);
B[M + 1] = 1;
for(int i = 1; i < M + 1; i++) B[i] = A[i - 1] + A[i] * M;
}
T tmp = 1;
for(int i = 0; i <= N - M; i++) {
C[N - M - i] = T(M).pow(i) / tmp;
B[i] *= tmp;
tmp *= T(i + 1);
}
C *= B;
tmp = 1;
for(int i = 0; i <= N - M; i++) {
B[i] = C[N - M + i] / tmp;
tmp *= T(i + 1);
}
return A * B;
}
template< typename T >
FormalPowerSeries< T > stirling_second(int N, int K) {
FormalPowerSeries< T > A(min(N, K) + 1), B(min(N, K) + 1);
modint tmp = 1;
for(int i = 0; i <= min(N, K); i++) {
T rev = T(1) / tmp;
A[i] = T(i).pow(N) * rev;
B[i] = T(1) * rev;
if(i & 1) B[i] *= -1;
tmp *= i + 1;
}
return (A * B);
}
template< typename T >
FormalPowerSeries< T > stirling_second_kth_column(int N, int K) {
FormalPowerSeries< T > poly(N + 1), ret(N + 1);
poly[1] = 1;
poly = poly.exp();
poly[0] -= 1;
poly = poly.pow(K);
T rev = 1, mul = 1;
for(int i = 2; i <= K; i++) rev *= i;
rev = T(1) / rev;
poly *= rev;
for(int i = 0; i <= N; i++) {
ret[i] = poly[i] * mul;
mul *= i + 1;
}
return ret;
}
template< typename T >
FormalPowerSeries< T > eulerian(int N, int K) {
vector< T > fact(N + 2), rfact(N + 2);
fact[0] = rfact[N + 1] = 1;
for(int i = 1; i <= N + 1; i++) fact[i] = fact[i - 1] * i;
rfact[N + 1] /= fact[N + 1];
for(int i = N; i >= 0; i--) rfact[i] = rfact[i + 1] * (i + 1);
FormalPowerSeries< T > A(min(N + 1, K + 1)), B(min(N + 1, K + 1));
for(int i = 0; i <= min(N, K); i++) {
A[i] = fact[N + 1] * rfact[i] * rfact[N + 1 - i];
if(i & 1) A[i] *= -1;
B[i] = T(i + 1).pow(N);
}
return (A * B);
}
template< typename T >
struct Combination {
vector< T > _fact, _rfact, _inv;
Combination(int sz) : _fact(sz + 1), _rfact(sz + 1), _inv(sz + 1) {
_fact[0] = _rfact[sz] = _inv[0] = 1;
for(int i = 1; i <= sz; i++) _fact[i] = _fact[i - 1] * i;
_rfact[sz] /= _fact[sz];
for(int i = sz - 1; i >= 0; i--) _rfact[i] = _rfact[i + 1] * (i + 1);
for(int i = 1; i <= sz; i++) _inv[i] = _rfact[i] * _fact[i - 1];
}
inline T fact(int k) const { return _fact[k]; }
inline T rfact(int k) const { return _rfact[k]; }
inline T inv(int k) const { return _inv[k]; }
T P(int n, int r) const {
if(r < 0 || n < r) return 0;
return fact(n) * rfact(n - r);
}
T C(int p, int q) const {
if(q < 0 || p < q) return 0;
return fact(p) * rfact(q) * rfact(p - q);
}
T H(int n, int r) const {
if(n < 0 || r < 0) return (0);
return r == 0 ? 1 : C(n + r - 1, r);
}
};
int main() {
NumberTheoreticTransformFriendlyModInt< modint > ntt;
using FPS = FormalPowerSeries< modint >;
auto mult = [&](const FPS::P &a, const FPS::P &b) {
auto ret = ntt.multiply(a, b);
return FPS::P(ret.begin(), ret.end());
};
FPS::set_mult(mult);
FPS::set_fft([&](FPS::P &a) { ntt.ntt(a); }, [&](FPS::P &a) { ntt.intt(a); });
int N, K;
cin >> N >> K;
auto tap = stirling_second< modint >(N, K);
modint mul = 1;
modint ret = 0;
Combination< modint > uku(K);
for(int i = 1; i <= min(N, K); i++) {
tap[i] *= mul;
mul *= i + 1;
if((K - i) % 2 == 1) {
ret += tap[i] * uku.C(K, i);
}
}
cout << ret << endl;
}
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