結果
| 問題 |
No.2747 Permutation Adjacent Sum
|
| コンテスト | |
| ユーザー |
 rogi52
|
| 提出日時 | 2024-04-20 12:47:08 |
| 言語 | C++23 (gcc 13.3.0 + boost 1.87.0) |
| 結果 |
AC
|
| 実行時間 | 120 ms / 3,000 ms |
| コード長 | 23,579 bytes |
| コンパイル時間 | 5,167 ms |
| コンパイル使用メモリ | 306,832 KB |
| 実行使用メモリ | 30,828 KB |
| 最終ジャッジ日時 | 2024-10-12 08:10:30 |
| 合計ジャッジ時間 | 9,469 ms |
|
ジャッジサーバーID （参考情報） |
judge1 / judge4 |
（要ログイン）
| ファイルパターン | 結果 |
|---|---|
| sample | AC * 2 |
| other | AC * 40 |
ソースコード
#line 2 "cp-library/src/cp-template.hpp"
#include <bits/stdc++.h>
using namespace std;
using ll = long long;
using ld = long double;
using uint = unsigned int;
using ull = unsigned long long;
using i32 = int;
using u32 = unsigned int;
using i64 = long long;
using u64 = unsigned long long;
using i128 = __int128_t;
template < class T > bool chmin(T& a, T b) { if(a > b) { a = b; return true; } return false; }
template < class T > bool chmax(T& a, T b) { if(a < b) { a = b; return true; } return false; }
template < class T, class U > T ceil (T x, U y) { return (x > 0 ? (x + y - 1) / y : x / y); }
template < class T, class U > T floor(T x, U y) { return (x > 0 ? x / y : (x - y + 1) / y); }
int popcnt(i32 x) { return __builtin_popcount(x); }
int popcnt(u32 x) { return __builtin_popcount(x); }
int popcnt(i64 x) { return __builtin_popcountll(x); }
int popcnt(u64 x) { return __builtin_popcountll(x); }
#line 2 "cp-library/src/utility/rep_itr.hpp"
template < class T > struct itr_rep {
T i, d;
constexpr itr_rep(const T i) noexcept : i(i), d(1) {}
constexpr itr_rep(const T i, const T d) noexcept : i(i), d(d) {}
void operator++() noexcept { i += d; }
constexpr int operator*() const noexcept { return i; }
constexpr bool operator!=(const itr_rep x) const noexcept { return d > 0 ? i < x.i : i > x.i; }
};
template < class T > struct rep {
const itr_rep< T > s, t;
constexpr rep(const T t) noexcept : s(0), t(t) {}
constexpr rep(const T s, const T t) noexcept : s(s), t(t) {}
constexpr rep(const T s, const T t, const T d) noexcept : s(s, d), t(t, d) {}
constexpr auto begin() const noexcept { return s; }
constexpr auto end () const noexcept { return t; }
};
template < class T > struct revrep {
const itr_rep < T > s, t;
constexpr revrep(const T t) noexcept : s(t - 1, -1), t(-1, -1) {}
constexpr revrep(const T s, const T t) noexcept : s(t - 1, -1), t(s - 1, -1) {}
constexpr revrep(const T s, const T t, const T d) noexcept : s(t - 1, -d), t(s - 1, -d) {}
constexpr auto begin() const noexcept { return s; }
constexpr auto end () const noexcept { return t; }
};
#line 3 "cp-library/src/utility/io.hpp"
/* 128bit integer */
istream& operator>>(istream& is, i128& x) {
std::string s; is >> s;
int pm = (s[0] == '-');
x = 0;
for(int i : rep(pm, int(s.size()))) x = x * 10 + (s[i] - '0');
if(pm) x *= -1;
return is;
}
ostream& operator<<(ostream& os, const i128& x) {
if(x == 0) return os << '0';
i128 y = x;
if(y < 0) { os << '-'; y *= -1; }
std::vector<int> ny;
while(y > 0) { ny.push_back(y % 10); y /= 10; }
for(int i : revrep(ny.size())) os << ny[i];
return os;
}
template < class S, class T > istream& operator>>(istream& is, std::pair< S, T >& x) { is >> x.first >> x.second; return is; }
template < class S, class T > ostream& operator<<(ostream& os, const std::pair< S, T >& x) { os << x.first << " " << x.second; return os; }
namespace scanner {
struct sca {
template < class T > operator T() {
T s; std::cin >> s; return s;
}
};
struct vec {
int n;
vec(int n) : n(n) {}
template < class T > operator std::vector< T >() {
std::vector< T > v(n);
for(T& x : v) std::cin >> x;
return v;
}
};
struct mat {
int h, w;
mat(int h, int w) : h(h), w(w) {}
template < class T > operator std::vector< std::vector< T > >() {
std::vector m(h, std::vector< T >(w));
for(std::vector< T >& v : m) for(T& x : v) std::cin >> x;
return m;
}
};
struct speedup {
speedup() {
std::cin.tie(0);
std::ios::sync_with_stdio(0);
}
} speedup_instance;
}
scanner::sca in() { return scanner::sca(); }
scanner::vec in(int n) { return scanner::vec(n); }
scanner::mat in(int h, int w) { return scanner::mat(h, w); }
namespace printer {
void precision(int d) { std::cout << std::fixed << std::setprecision(d); }
void flush() { std::cout.flush(); }
}
template < class T >
ostream& operator<<(ostream& os, const std::vector< T > a) {
int n = a.size();
for(int i : rep(n)) { os << a[i]; if(i != n - 1) os << ' '; }
return os;
}
int print() { std::cout << '\n'; return 0; }
template < class head, class... tail > int print(head&& h, tail&&... t) {
std::cout << h; if(sizeof...(tail)) std::cout << ' ';
return print(std::forward<tail>(t)...);
}
template < class T > int print_n(const std::vector< T > a) {
int n = a.size();
for(int i : rep(n)) std::cout << a[i] << "\n";
return 0;
}
#line 2 "cp-library/src/utility/key_val.hpp"
template < class K, class V >
struct key_val {
K key; V val;
key_val() {}
key_val(K key, V val) : key(key), val(val) {}
template < std::size_t Index >
std::tuple_element_t< Index, key_val >& get() {
if constexpr (Index == 0) return key;
if constexpr (Index == 1) return val;
}
};
namespace std {
template < class K, class V > struct tuple_size < key_val< K, V > > : integral_constant< size_t, 2 > {};
template < class K, class V > struct tuple_element < 0, key_val< K, V > > { using type = K; };
template < class K, class V > struct tuple_element < 1, key_val< K, V > > { using type = V; };
}
#line 2 "cp-library/src/utility/vec_op.hpp"
template < class T > key_val< int, T > max_of(const vector< T >& a) {
int i = std::max_element(a.begin(), a.end()) - a.begin();
return {i, a[i]};
}
template < class T > key_val< int, T > min_of(const vector< T >& a) {
int i = std::min_element(a.begin(), a.end()) - a.begin();
return {i, a[i]};
}
template < class S, class T > S sum_of(const vector< T >& a) {
S sum = 0;
for(const T x : a) sum += x;
return sum;
}
template < class S, class T > vector< S > freq_of(const vector< T >& a, T L, T R) {
vector< S > res(R - L, S(0));
for(const T x : a) res[x - L] += 1;
return res;
}
template < class S, class T > struct prefix_sum {
vector< S > s;
prefix_sum(const vector< T >& a) : s(a) {
s.insert(s.begin(), S(0));
for(int i : rep(a.size())) s[i + 1] += s[i];
}
// [L, R)
S sum(int L, int R) { return s[R] - s[L]; }
};
#line 3 "cp-library/src/utility/heap.hpp"
template < class T > using heap_min = std::priority_queue< T, std::vector< T >, std::greater< T > >;
template < class T > using heap_max = std::priority_queue< T, std::vector< T >, std::less< T > >;
#line 27 "cp-library/src/cp-template.hpp"
#line 1 "cp-library/src/algorithm/bin_search.hpp"
template < class T, class F >
T bin_search(T ok, T ng, F f) {
while(abs(ng - ok) > 1) {
T mid = (ok + ng) / 2;
(f(mid) ? ok : ng) = mid;
}
return ok;
}
template < class T, class F >
T bin_search_real(T ok, T ng, F f, int step = 80) {
while(step--) {
T mid = (ok + ng) / 2;
(f(mid) ? ok : ng) = mid;
}
return ok;
}
#line 2 "cp-library/src/algorithm/argsort.hpp"
template < class T > std::vector< int > argsort(const std::vector< T > &a) {
std::vector< int > ids((int)a.size());
std::iota(ids.begin(), ids.end(), 0);
std::sort(ids.begin(), ids.end(), [&](int i, int j) {
return a[i] < a[j] || (a[i] == a[j] && i < j);
});
return ids;
}
#line 1 "macro.hpp"
namespace macro {
using size_type = int;
template < class container > void sort(container& a) { std::sort(std:: begin(a), std:: end(a)); }
template < class container > void rsort(container& a) { std::sort(std::rbegin(a), std::rend(a)); }
template < class container > void reverse(container& a) { std::reverse(std::begin(a), std::end(a)); }
template < class container > void unique(container& a) {
std::sort(std::begin(a), std::end(a));
a.erase(std::unique(std::begin(a), std::end(a)), std::end(a));
}
template < class container > container sorted(const container& a) { container b = a; sort(b); return std::move(b); }
template < class container > container rsorted(const container& a) { container b = a; rsort(b); return std::move(b); }
template < class container, class compare > void sort(container& a, const compare& cmp) { std::sort(std::begin(a), std::end(a), cmp); }
template < class container, class compare > container sorted(const container& a, const compare& cmp) { container b = a; sort(b, cmp); return std::move(b); }
template < class container, class value > size_type lower_bound(const container& a, const value& x) { return std::lower_bound(std::begin(a), std::end(a), x) - std::begin(a); }
template < class container, class value > size_type upper_bound(const container& a, const value& x) { return std::upper_bound(std::begin(a), std::end(a), x) - std::begin(a); }
const std::vector<std::pair<size_type, size_type>> dir4 = { {+1, 0}, {-1, 0}, { 0, +1}, { 0, -1} };
const std::vector<std::pair<size_type, size_type>> dir8 = { {-1, -1}, {-1, 0}, {-1, +1}, { 0, -1}, { 0, +1}, {+1, -1}, {+1, 0}, {+1, +1} };
#ifdef _DEBUG
#define debug(x) std::cout << "[" << __LINE__ << "] " << #x << ": " << x << std::endl
#else
#define debug(x)
#endif
template < class container > void concat(container& a, const container& b) {
a.insert(std::end(a), std::begin(b), std::end(b));
}
std::vector<size_type> iota(const size_type n) {
std::vector<size_type> I(n);
std::iota(std::begin(I), std::end(I), 0);
return I;
}
template < class container > std::vector<size_type> sort_idx(const container& a) {
const size_type n = a.size();
std::vector<size_type> I = iota(n);
std::sort(std::begin(I), std::end(I), [&](size_type i, size_type j) { return a[i] < a[j] or (a[i] == a[j] and i < j); });
return I;
}
template < class container, class compare > std::vector<size_type> sort_idx(const container& a, const compare& cmp) {
const size_type n = a.size();
std::vector<size_type> I = iota(n);
std::sort(std::begin(I), std::end(I), [&](size_type i, size_type j) { return cmp(a[i], a[j]) or (a[i] == a[j] and i < j); });
return std::move(I);
}
struct grid {
using size_type = int;
size_type H, W;
grid(const size_type H, const size_type W) : H(H), W(W) {}
bool contains(const size_type i, const size_type j) {
return 0 <= i and i < H and 0 <= j and j < W;
}
};
using f64 = long double;
template < class T > vector< T >& operator++(vector< T >& a) { for(T& x : a) x++; return a; }
template < class T > vector< T >& operator--(vector< T >& a) { for(T& x : a) x--; return a; }
template < class T > vector< T > operator++(vector< T >& a, signed) { vector< T > res = a; for(T& x : a) x++; return res; }
template < class T > vector< T > operator--(vector< T >& a, signed) { vector< T > res = a; for(T& x : a) x--; return res; }
} // namespace macro
using namespace macro;
#line 3 "C.cpp"
#include <atcoder/convolution>
// https://judge.yosupo.jp/submission/129637
template <uint32_t mod>
struct LazyMontgomeryModInt {
using mint = LazyMontgomeryModInt;
using i32 = int32_t;
using u32 = uint32_t;
using u64 = uint64_t;
static constexpr u32 get_r() {
u32 ret = mod;
for (i32 i = 0; i < 4; ++i) ret *= 2 - mod * ret;
return ret;
}
static constexpr u32 r = get_r();
static constexpr u32 n2 = -u64(mod) % mod;
static_assert(r * mod == 1, "invalid, r * mod != 1");
static_assert(mod < (1 << 30), "invalid, mod >= 2 ^ 30");
static_assert((mod & 1) == 1, "invalid, mod % 2 == 0");
u32 a;
constexpr LazyMontgomeryModInt() : a(0) {}
constexpr LazyMontgomeryModInt(const int64_t &b)
: a(reduce(u64(b % mod + mod) * n2)){};
static constexpr u32 reduce(const u64 &b) {
return (b + u64(u32(b) * u32(-r)) * mod) >> 32;
}
constexpr mint &operator+=(const mint &b) {
if (i32(a += b.a - 2 * mod) < 0) a += 2 * mod;
return *this;
}
constexpr mint &operator-=(const mint &b) {
if (i32(a -= b.a) < 0) a += 2 * mod;
return *this;
}
constexpr mint &operator*=(const mint &b) {
a = reduce(u64(a) * b.a);
return *this;
}
constexpr mint &operator/=(const mint &b) {
*this *= b.inverse();
return *this;
}
constexpr mint operator+(const mint &b) const { return mint(*this) += b; }
constexpr mint operator-(const mint &b) const { return mint(*this) -= b; }
constexpr mint operator*(const mint &b) const { return mint(*this) *= b; }
constexpr mint operator/(const mint &b) const { return mint(*this) /= b; }
constexpr bool operator==(const mint &b) const {
return (a >= mod ? a - mod : a) == (b.a >= mod ? b.a - mod : b.a);
}
constexpr bool operator!=(const mint &b) const {
return (a >= mod ? a - mod : a) != (b.a >= mod ? b.a - mod : b.a);
}
constexpr mint operator-() const { return mint() - mint(*this); }
constexpr mint pow(u64 n) const {
mint ret(1), mul(*this);
while (n > 0) {
if (n & 1) ret *= mul;
mul *= mul;
n >>= 1;
}
return ret;
}
constexpr mint inverse() const { return pow(mod - 2); }
friend ostream &operator<<(ostream &os, const mint &b) {
return os << b.get();
}
friend istream &operator>>(istream &is, mint &b) {
int64_t t;
is >> t;
b = LazyMontgomeryModInt<mod>(t);
return (is);
}
constexpr u32 get() const {
u32 ret = reduce(a);
return ret >= mod ? ret - mod : ret;
}
static constexpr u32 get_mod() { return mod; }
};
using namespace std;
template <typename T>
struct Binomial {
vector<T> fac_, finv_, inv_;
Binomial(int MAX) : fac_(MAX + 10), finv_(MAX + 10), inv_(MAX + 10) {
MAX += 9;
fac_[0] = finv_[0] = inv_[0] = 1;
for (int i = 1; i <= MAX; i++) fac_[i] = fac_[i - 1] * i;
finv_[MAX] = fac_[MAX].inverse();
for (int i = MAX - 1; i > 0; i--) finv_[i] = finv_[i + 1] * (i + 1);
for (int i = 1; i <= MAX; i++) inv_[i] = finv_[i] * fac_[i - 1];
}
inline T fac(int i) const { return fac_[i]; }
inline T finv(int i) const { return finv_[i]; }
inline T inv(int i) const { return inv_[i]; }
T C(int n, int r) const {
if (n < r || r < 0) return T(0);
return fac_[n] * finv_[n - r] * finv_[r];
}
T C_naive(int n, int r) const {
if (n < r || r < 0) return T(0);
T ret = 1;
for (T i = 1; i <= r; i += T(1)) {
ret *= n--;
ret *= i.inverse();
}
return ret;
}
T P(int n, int r) const {
if (n < r || r < 0) return T(0);
return fac_[n] * finv_[n - r];
}
T H(int n, int r) const {
if (n < 0 || r < 0) return (0);
return r == 0 ? 1 : C(n + r - 1, r);
}
};
// given y(x=0)...y(k) , return y(x)
template <typename mint>
mint lagrange_interpolation(const vector<mint>& y, long long x,
const Binomial<mint>& C) {
int N = (int)y.size() - 1;
if (x <= N) return y[x];
mint ret = 0;
vector<mint> dp(N + 1, 1), pd(N + 1, 1);
mint a = x, one = 1;
for (int i = 0; i < N; i++) dp[i + 1] = dp[i] * a, a -= one;
for (int i = N; i > 0; i--) pd[i - 1] = pd[i] * a, a += one;
for (int i = 0; i <= N; i++) {
mint tmp = y[i] * dp[i] * pd[i] * C.finv(i) * C.finv(N - i);
ret += ((N - i) & 1) ? -tmp : tmp;
}
return ret;
}
// given f(0)...f(k) (deg(f) = k)
// return \sum_{i=0...n-1} a^i f(i)
template <typename mint>
mint sum_of_exp(const vector<mint>& f, mint a, long long n,
const Binomial<mint>& C) {
if (n == 0) return mint(0);
if (a == mint(0)) return f[0];
if (a == mint(1)) {
vector<mint> g(f.size() + 1, mint(0));
for (int i = 1; i < (int)g.size(); i++) g[i] = g[i - 1] + f[i - 1];
return lagrange_interpolation(g, n, C);
}
int K = f.size() - 1;
vector<mint> g(f.size());
mint buf = 1;
for (int i = 0; i < (int)g.size(); i++) g[i] = f[i] * buf, buf *= a;
for (int i = 1; i < (int)g.size(); i++) g[i] += g[i - 1];
mint c = 0, buf2 = 1;
for (int i = 0; i <= K; i++) c += C.C(K + 1, i) * buf2 * g[K - i], buf2 *= -a;
c /= (-a + 1).pow(K + 1);
mint buf3 = 1, ia = a.inverse();
for (int i = 0; i < (int)g.size(); i++) g[i] = (g[i] - c) * buf3, buf3 *= ia;
mint tn = lagrange_interpolation(g, n - 1, C);
return tn * a.pow(n - 1) + c;
}
// given f(0)...f(k) (deg(f) = k)
// return \sum_{i=0...infty} a^i f(i)
template <typename mint>
mint sum_of_exp_limit(const vector<mint>& f, mint a, const Binomial<mint>& C) {
if (a == mint(0)) return f[0];
int K = f.size() - 1;
vector<mint> g(f.size());
mint buf = 1;
for (int i = 0; i < (int)g.size(); i++) g[i] = f[i] * buf, buf *= a;
for (int i = 1; i < (int)g.size(); i++) g[i] += g[i - 1];
mint c = 0, buf2 = 1;
for (int i = 0; i <= K; i++) c += C.C(K + 1, i) * buf2 * g[K - i], buf2 *= -a;
c /= (-a + 1).pow(K + 1);
return c;
}
template <typename mint>
vector<mint> exp_enamurate(int p, int n) {
vector<mint> f(n + 1, mint(0));
if (!p) {
f[0] = 1;
return std::move(f);
}
f[1] = 1;
vector<bool> sieve(n + 1, false);
vector<int> ps;
for (int i = 2; i <= n; i++) {
if (!sieve[i]) {
f[i] = mint(i).pow(p);
ps.push_back(i);
}
for (int j = 0; j < (int)ps.size() && i * ps[j] <= n; j++) {
sieve[i * ps[j]] = 1;
f[i * ps[j]] = f[i] * f[ps[j]];
if (i % ps[j] == 0) break;
}
}
return std::move(f);
}
template <typename mint>
mint sum_of_exp2(int d, mint r, long long n, const Binomial<mint>& C) {
vector<mint> f = exp_enamurate<mint>(d, d);
return sum_of_exp(f, r, n, C);
}
template <typename mint>
mint sum_of_exp_limit2(int d, mint r, const Binomial<mint>& C) {
vector<mint> f = exp_enamurate<mint>(d, d);
return sum_of_exp_limit(f, r, C);
}
using mint = LazyMontgomeryModInt<998244353>;
Binomial<mint> C(1000100);
mint solve(i64 r, i64 d, i64 n) {
if(n <= 1000) {
mint ans = 0;
for(i64 i = 0; i < n; i++) ans += mint(i).pow(d);
return ans;
}
return sum_of_exp2<mint>(d, r, n, C).get();
}
namespace lib {
#define PROBLEM "https://judge.yosupo.jp/problem/factorial"
#line 254 "C.cpp"
#include <atcoder/modint>
using mint = atcoder::modint998244353;
#line 261 "C.cpp"
#line 264 "C.cpp"
namespace suisen {
template <typename T, typename U = T>
struct factorial {
factorial() = default;
factorial(int n) { ensure(n); }
static void ensure(const int n) {
int sz = _fac.size();
if (n + 1 <= sz) return;
int new_size = std::max(n + 1, sz * 2);
_fac.resize(new_size), _fac_inv.resize(new_size);
for (int i = sz; i < new_size; ++i) _fac[i] = _fac[i - 1] * i;
_fac_inv[new_size - 1] = U(1) / _fac[new_size - 1];
for (int i = new_size - 1; i > sz; --i) _fac_inv[i - 1] = _fac_inv[i] * i;
}
T fac(const int i) {
ensure(i);
return _fac[i];
}
T operator()(int i) {
return fac(i);
}
U fac_inv(const int i) {
ensure(i);
return _fac_inv[i];
}
U binom(const int n, const int r) {
if (n < 0 or r < 0 or n < r) return 0;
ensure(n);
return _fac[n] * _fac_inv[r] * _fac_inv[n - r];
}
U perm(const int n, const int r) {
if (n < 0 or r < 0 or n < r) return 0;
ensure(n);
return _fac[n] * _fac_inv[n - r];
}
private:
static std::vector<T> _fac;
static std::vector<U> _fac_inv;
};
template <typename T, typename U>
std::vector<T> factorial<T, U>::_fac{ 1 };
template <typename T, typename U>
std::vector<U> factorial<T, U>::_fac_inv{ 1 };
} // namespace suisen
#line 313 "C.cpp"
namespace suisen {
template <typename mint>
std::vector<mint> shift_of_sampling_points(const std::vector<mint>& ys, mint t, int m) {
const int n = ys.size();
factorial<mint> fac(std::max(n, m));
std::vector<mint> b = [&] {
std::vector<mint> f(n), g(n);
for (int i = 0; i < n; ++i) {
f[i] = ys[i] * fac.fac_inv(i);
g[i] = (i & 1 ? -1 : 1) * fac.fac_inv(i);
}
std::vector<mint> b = atcoder::convolution(f, g);
b.resize(n);
return b;
}();
std::vector<mint> e = [&] {
std::vector<mint> c(n);
mint prd = 1;
std::reverse(b.begin(), b.end());
for (int i = 0; i < n; ++i) {
b[i] *= fac.fac(n - i - 1);
c[i] = prd * fac.fac_inv(i);
prd *= t - i;
}
std::vector<mint> e = atcoder::convolution(b, c);
e.resize(n);
return e;
}();
std::reverse(e.begin(), e.end());
for (int i = 0; i < n; ++i) {
e[i] *= fac.fac_inv(i);
}
std::vector<mint> f(m);
for (int i = 0; i < m; ++i) f[i] = fac.fac_inv(i);
std::vector<mint> res = atcoder::convolution(e, f);
res.resize(m);
for (int i = 0; i < m; ++i) res[i] *= fac.fac(i);
return res;
}
} // namespace suisen
namespace suisen {
template <typename mint>
struct FactorialLarge {
static constexpr int _p = mint::mod();
static constexpr int _log_b = 15;
static constexpr int _b = 1 << _log_b;
static constexpr int _q = _p >> _log_b;
FactorialLarge() {
// f_d(x) := (dx+1)*...*(dx+d-1)
// Suppose that we have f_d(0),...,f_d(d-1). (Note that (deg f_d)+1=d)
// f_{2d}(x) = ((2dx+1)*...*(2dx+d-1)) * (2dx+d) * (((2dx+d)+1)* ...*((2dx+d)+d-1))
// = f_d(2x) * f_d(2x+1) * (2dx+d)
// We can calculate f_{2d}(0), ..., f_{2d}(2d-1) from f_d(0), f_d(1), ..., f_d(4d-2), f_d(4d-1)
std::vector<mint> f{ 1 };
f.reserve(_b);
for (int i = 0; i < _log_b; ++i) {
std::vector<mint> g = shift_of_sampling_points<mint>(f, 1 << i, 3 << i);
const auto get = [&](int j) { return j < (1 << i) ? f[j] : g[j - (1 << i)]; };
f.resize(2 << i);
for (int j = 0; j < 2 << i; ++j) {
// (2*j+1)*2^i <= 2^(2*_log_b) + 2^(_log_b-1) < 2^31 holds if _log_b <= 15
f[j] = get(2 * j) * get(2 * j + 1) * ((2 * j + 1) << i);
}
}
// f_B(x) = (x+1) * ... * (x+B-1)
if (_q > _b) {
std::vector<mint> g = shift_of_sampling_points<mint>(f, _b, _q - _b);
std::move(g.begin(), g.end(), std::back_inserter(f));
} else {
f.resize(_q);
}
for (int i = 0; i < _q; ++i) {
f[i] *= mint(i + 1) * _b;
}
// f[i] = (i*B + 1) * ... * (i*B + B)
_acc = std::move(f);
_acc.insert(_acc.begin(), 1);
for (int i = 1; i <= _q; ++i) {
_acc[i] *= _acc[i - 1];
}
}
mint operator()(long long n) {
if (_p <= n) return 0;
const int q = n >> _log_b, r = n & (_b - 1);
// n! = (qb)! * (n-r+1)(n-r+2)...(n)
mint ans = _acc[q];
for (int j = 0; j < r; ++j) {
ans *= mint::raw(n - j);
}
return ans;
}
private:
std::vector<mint> _acc;
};
} // namespace suisen
}
int main() {
i64 N = in(), K = in();
mint ans = 0;
ans += solve(1, K, N) * N - solve(1, K + 1, N);
lib::suisen::FactorialLarge<atcoder::modint998244353> fact;
print(ans * fact(N - 1).val() * 2);
}