結果
| 問題 | No.2747 Permutation Adjacent Sum |
| ユーザー |
 shiomusubi496
|
| 提出日時 | 2024-04-21 13:32:48 |
| 言語 | C++17 (gcc 12.3.0 + boost 1.83.0) |
| 結果 |
AC
|
| 実行時間 | 858 ms / 3,000 ms |
| コード長 | 50,714 bytes |
| コンパイル時間 | 5,149 ms |
| コンパイル使用メモリ | 260,864 KB |
| 実行使用メモリ | 56,068 KB |
| 最終ジャッジ日時 | 2024-04-21 13:33:14 |
| 合計ジャッジ時間 | 25,385 ms |
|
ジャッジサーバーID （参考情報） |
judge2 / judge4 |
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テストケース
テストケース表示| 入力 | 結果 | 実行時間 実行使用メモリ |
|---|---|---|
| testcase_00 | AC | 493 ms
27,412 KB |
| testcase_01 | AC | 170 ms
10,104 KB |
| testcase_02 | AC | 220 ms
17,560 KB |
| testcase_03 | AC | 55 ms
5,444 KB |
| testcase_04 | AC | 346 ms
26,228 KB |
| testcase_05 | AC | 836 ms
56,068 KB |
| testcase_06 | AC | 364 ms
27,772 KB |
| testcase_07 | AC | 462 ms
27,632 KB |
| testcase_08 | AC | 678 ms
41,640 KB |
| testcase_09 | AC | 858 ms
52,340 KB |
| testcase_10 | AC | 165 ms
10,816 KB |
| testcase_11 | AC | 483 ms
27,644 KB |
| testcase_12 | AC | 159 ms
9,908 KB |
| testcase_13 | AC | 238 ms
14,688 KB |
| testcase_14 | AC | 701 ms
40,512 KB |
| testcase_15 | AC | 720 ms
48,512 KB |
| testcase_16 | AC | 356 ms
25,684 KB |
| testcase_17 | AC | 764 ms
48,492 KB |
| testcase_18 | AC | 793 ms
48,240 KB |
| testcase_19 | AC | 105 ms
7,852 KB |
| testcase_20 | AC | 389 ms
27,388 KB |
| testcase_21 | AC | 746 ms
42,636 KB |
| testcase_22 | AC | 700 ms
42,244 KB |
| testcase_23 | AC | 447 ms
24,860 KB |
| testcase_24 | AC | 458 ms
25,988 KB |
| testcase_25 | AC | 272 ms
16,512 KB |
| testcase_26 | AC | 813 ms
43,212 KB |
| testcase_27 | AC | 718 ms
43,220 KB |
| testcase_28 | AC | 709 ms
41,708 KB |
| testcase_29 | AC | 426 ms
28,656 KB |
| testcase_30 | AC | 711 ms
50,908 KB |
| testcase_31 | AC | 684 ms
51,032 KB |
| testcase_32 | AC | 708 ms
50,912 KB |
| testcase_33 | AC | 695 ms
51,036 KB |
| testcase_34 | AC | 687 ms
51,036 KB |
| testcase_35 | AC | 2 ms
5,376 KB |
| testcase_36 | AC | 2 ms
5,376 KB |
| testcase_37 | AC | 2 ms
5,376 KB |
| testcase_38 | AC | 2 ms
5,376 KB |
| testcase_39 | AC | 2 ms
5,376 KB |
| testcase_40 | AC | 2 ms
5,376 KB |
| testcase_41 | AC | 2 ms
5,376 KB |
ソースコード
#line 2 "library/other/template.hpp"
#include <bits/stdc++.h>
#line 2 "library/template/macros.hpp"
#line 4 "library/template/macros.hpp"
#ifndef __COUNTER__
#define __COUNTER__ __LINE__
#endif
#define OVERLOAD5(a, b, c, d, e, ...) e
#define REP1_0(b, c) REP1_1(b, c)
#define REP1_1(b, c) \
for (ll REP_COUNTER_##c = 0; REP_COUNTER_##c < (ll)(b); ++REP_COUNTER_##c)
#define REP1(b) REP1_0(b, __COUNTER__)
#define REP2(i, b) for (ll i = 0; i < (ll)(b); ++i)
#define REP3(i, a, b) for (ll i = (ll)(a); i < (ll)(b); ++i)
#define REP4(i, a, b, c) for (ll i = (ll)(a); i < (ll)(b); i += (ll)(c))
#define rep(...) OVERLOAD5(__VA_ARGS__, REP4, REP3, REP2, REP1)(__VA_ARGS__)
#define RREP2(i, a) for (ll i = (ll)(a)-1; i >= 0; --i)
#define RREP3(i, a, b) for (ll i = (ll)(a)-1; i >= (ll)(b); --i)
#define RREP4(i, a, b, c) for (ll i = (ll)(a)-1; i >= (ll)(b); i -= (ll)(c))
#define rrep(...) OVERLOAD5(__VA_ARGS__, RREP4, RREP3, RREP2)(__VA_ARGS__)
#define REPS2(i, b) for (ll i = 1; i <= (ll)(b); ++i)
#define REPS3(i, a, b) for (ll i = (ll)(a) + 1; i <= (ll)(b); ++i)
#define REPS4(i, a, b, c) for (ll i = (ll)(a) + 1; i <= (ll)(b); i += (ll)(c))
#define reps(...) OVERLOAD5(__VA_ARGS__, REPS4, REPS3, REPS2)(__VA_ARGS__)
#define RREPS2(i, a) for (ll i = (ll)(a); i > 0; --i)
#define RREPS3(i, a, b) for (ll i = (ll)(a); i > (ll)(b); --i)
#define RREPS4(i, a, b, c) for (ll i = (ll)(a); i > (ll)(b); i -= (ll)(c))
#define rreps(...) OVERLOAD5(__VA_ARGS__, RREPS4, RREPS3, RREPS2)(__VA_ARGS__)
#define each_for(...) for (auto&& __VA_ARGS__)
#define each_const(...) for (const auto& __VA_ARGS__)
#define all(v) std::begin(v), std::end(v)
#if __cplusplus >= 201402L
#define rall(v) std::rbegin(v), std::rend(v)
#else
#define rall(v) v.rbegin(), v.rend()
#endif
#if __cpp_constexpr >= 201304L
#define CONSTEXPR constexpr
#else
#define CONSTEXPR
#endif
#if __cpp_if_constexpr >= 201606L
#define IF_CONSTEXPR constexpr
#else
#define IF_CONSTEXPR
#endif
#define IO_BUFFER_SIZE 2048
#line 2 "library/template/alias.hpp"
#line 4 "library/template/alias.hpp"
using ll = long long;
using uint = unsigned int;
using ull = unsigned long long;
using i128 = __int128_t;
using u128 = __uint128_t;
using ld = long double;
using PLL = std::pair<ll, ll>;
template<class T>
using prique = std::priority_queue<T, std::vector<T>, std::greater<T>>;
template<class T> struct infinity {
static constexpr T value = std::numeric_limits<T>::max() / 2;
static constexpr T mvalue = std::numeric_limits<T>::lowest() / 2;
static constexpr T max = std::numeric_limits<T>::max();
static constexpr T min = std::numeric_limits<T>::lowest();
};
#if __cplusplus <= 201402L
template<class T> constexpr T infinity<T>::value;
template<class T> constexpr T infinity<T>::mvalue;
template<class T> constexpr T infinity<T>::max;
template<class T> constexpr T infinity<T>::min;
#endif
#if __cpp_variable_templates >= 201304L
template<class T> constexpr T INF = infinity<T>::value;
#endif
constexpr ll inf = infinity<ll>::value;
constexpr ld EPS = 1e-8;
constexpr ld PI = 3.1415926535897932384626;
#line 2 "library/template/type_traits.hpp"
#line 5 "library/template/type_traits.hpp"
template<class T, class... Args> struct function_traits_impl {
using result_type = T;
template<std::size_t idx>
using argument_type =
typename std::tuple_element<idx, std::tuple<Args...>>::type;
using argument_tuple = std::tuple<Args...>;
static constexpr std::size_t arg_size() { return sizeof...(Args); }
};
template<class> struct function_traits_helper;
template<class Res, class Tp, class... Args>
struct function_traits_helper<Res (Tp::*)(Args...)> {
using type = function_traits_impl<Res, Args...>;
};
template<class Res, class Tp, class... Args>
struct function_traits_helper<Res (Tp::*)(Args...)&> {
using type = function_traits_impl<Res, Args...>;
};
template<class Res, class Tp, class... Args>
struct function_traits_helper<Res (Tp::*)(Args...) const> {
using type = function_traits_impl<Res, Args...>;
};
template<class Res, class Tp, class... Args>
struct function_traits_helper<Res (Tp::*)(Args...) const&> {
using type = function_traits_impl<Res, Args...>;
};
#if __cpp_noexcept_function_type >= 201510L
template<class Res, class Tp, class... Args>
struct function_traits_helper<Res (Tp::*)(Args...) noexcept> {
using type = function_traits_impl<Res, Args...>;
};
template<class Res, class Tp, class... Args>
struct function_traits_helper<Res (Tp::*)(Args...)& noexcept> {
using type = function_traits_impl<Res, Args...>;
};
template<class Res, class Tp, class... Args>
struct function_traits_helper<Res (Tp::*)(Args...) const noexcept> {
using type = function_traits_impl<Res, Args...>;
};
template<class Res, class Tp, class... Args>
struct function_traits_helper<Res (Tp::*)(Args...) const& noexcept> {
using type = function_traits_impl<Res, Args...>;
};
#endif
template<class F>
using function_traits = typename function_traits_helper<
decltype(&std::remove_reference<F>::type::operator())>::type;
template<class F>
using function_result_type = typename function_traits<F>::result_type;
template<class F, std::size_t idx>
using function_argument_type =
typename function_traits<F>::template argument_type<idx>;
template<class F>
using function_argument_tuple = typename function_traits<F>::argument_tuple;
template<class T>
using is_signed_int =
std::integral_constant<bool, (std::is_integral<T>::value &&
std::is_signed<T>::value) ||
std::is_same<T, i128>::value>;
template<class T>
using is_unsigned_int =
std::integral_constant<bool, (std::is_integral<T>::value &&
std::is_unsigned<T>::value) ||
std::is_same<T, u128>::value>;
template<class T>
using is_int = std::integral_constant<bool, is_signed_int<T>::value ||
is_unsigned_int<T>::value>;
template<class T>
using make_signed_int = typename std::conditional<
std::is_same<T, i128>::value || std::is_same<T, u128>::value,
std::common_type<i128>, std::make_signed<T>>::type;
template<class T>
using make_unsigned_int = typename std::conditional<
std::is_same<T, i128>::value || std::is_same<T, u128>::value,
std::common_type<u128>, std::make_unsigned<T>>::type;
template<class T, class = void> struct is_range : std::false_type {};
template<class T>
struct is_range<
T,
decltype(all(std::declval<typename std::add_lvalue_reference<T>::type>()),
(void)0)> : std::true_type {};
template<class T, bool = is_range<T>::value>
struct range_rank : std::integral_constant<std::size_t, 0> {};
template<class T>
struct range_rank<T, true>
: std::integral_constant<std::size_t,
range_rank<typename T::value_type>::value + 1> {};
template<std::size_t size> struct int_least {
static_assert(size <= 128, "size must be less than or equal to 128");
using type = typename std::conditional<
size <= 8, std::int_least8_t,
typename std::conditional<
size <= 16, std::int_least16_t,
typename std::conditional<
size <= 32, std::int_least32_t,
typename std::conditional<size <= 64, std::int_least64_t,
i128>::type>::type>::type>::type;
};
template<std::size_t size> using int_least_t = typename int_least<size>::type;
template<std::size_t size> struct uint_least {
static_assert(size <= 128, "size must be less than or equal to 128");
using type = typename std::conditional<
size <= 8, std::uint_least8_t,
typename std::conditional<
size <= 16, std::uint_least16_t,
typename std::conditional<
size <= 32, std::uint_least32_t,
typename std::conditional<size <= 64, std::uint_least64_t,
u128>::type>::type>::type>::type;
};
template<std::size_t size> using uint_least_t = typename uint_least<size>::type;
template<class T>
using double_size_int = int_least<std::numeric_limits<T>::digits * 2 + 1>;
template<class T> using double_size_int_t = typename double_size_int<T>::type;
template<class T>
using double_size_uint = uint_least<std::numeric_limits<T>::digits * 2>;
template<class T> using double_size_uint_t = typename double_size_uint<T>::type;
template<class T>
using double_size =
typename std::conditional<is_signed_int<T>::value, double_size_int<T>,
double_size_uint<T>>::type;
template<class T> using double_size_t = typename double_size<T>::type;
#line 7 "library/other/template.hpp"
// #include "../template/in.hpp"
// #include "../template/out.hpp"
#line 2 "library/template/bitop.hpp"
#line 6 "library/template/bitop.hpp"
namespace bitop {
#define KTH_BIT(b, k) (((b) >> (k)) & 1)
#define POW2(k) (1ull << (k))
inline ull next_combination(int n, ull x) {
if (n == 0) return 1;
ull a = x & -x;
ull b = x + a;
return (x & ~b) / a >> 1 | b;
}
#define rep_comb(i, n, k) \
for (ull i = (1ull << (k)) - 1; i < (1ull << (n)); \
i = bitop::next_combination((n), i))
inline CONSTEXPR int msb(ull x) {
int res = x ? 0 : -1;
if (x & 0xFFFFFFFF00000000) x &= 0xFFFFFFFF00000000, res += 32;
if (x & 0xFFFF0000FFFF0000) x &= 0xFFFF0000FFFF0000, res += 16;
if (x & 0xFF00FF00FF00FF00) x &= 0xFF00FF00FF00FF00, res += 8;
if (x & 0xF0F0F0F0F0F0F0F0) x &= 0xF0F0F0F0F0F0F0F0, res += 4;
if (x & 0xCCCCCCCCCCCCCCCC) x &= 0xCCCCCCCCCCCCCCCC, res += 2;
return res + ((x & 0xAAAAAAAAAAAAAAAA) ? 1 : 0);
}
inline CONSTEXPR int ceil_log2(ull x) { return x ? msb(x - 1) + 1 : 0; }
inline CONSTEXPR ull reverse(ull x) {
x = ((x & 0xAAAAAAAAAAAAAAAA) >> 1) | ((x & 0x5555555555555555) << 1);
x = ((x & 0xCCCCCCCCCCCCCCCC) >> 2) | ((x & 0x3333333333333333) << 2);
x = ((x & 0xF0F0F0F0F0F0F0F0) >> 4) | ((x & 0x0F0F0F0F0F0F0F0F) << 4);
x = ((x & 0xFF00FF00FF00FF00) >> 8) | ((x & 0x00FF00FF00FF00FF) << 8);
x = ((x & 0xFFFF0000FFFF0000) >> 16) | ((x & 0x0000FFFF0000FFFF) << 16);
return (x >> 32) | (x << 32);
}
inline CONSTEXPR ull reverse(ull x, int n) { return reverse(x) >> (64 - n); }
} // namespace bitop
inline CONSTEXPR int popcnt(ull x) noexcept {
#if __cplusplus >= 202002L
return std::popcount(x);
#endif
x = (x & 0x5555555555555555) + ((x >> 1) & 0x5555555555555555);
x = (x & 0x3333333333333333) + ((x >> 2) & 0x3333333333333333);
x = (x & 0x0f0f0f0f0f0f0f0f) + ((x >> 4) & 0x0f0f0f0f0f0f0f0f);
x = (x & 0x00ff00ff00ff00ff) + ((x >> 8) & 0x00ff00ff00ff00ff);
x = (x & 0x0000ffff0000ffff) + ((x >> 16) & 0x0000ffff0000ffff);
return (x & 0x00000000ffffffff) + ((x >> 32) & 0x00000000ffffffff);
}
#line 2 "library/template/func.hpp"
#line 6 "library/template/func.hpp"
template<class T, class U, class Comp = std::less<>>
inline constexpr bool chmin(T& a, const U& b,
Comp cmp = Comp()) noexcept(noexcept(cmp(b, a))) {
return cmp(b, a) ? a = b, true : false;
}
template<class T, class U, class Comp = std::less<>>
inline constexpr bool chmax(T& a, const U& b,
Comp cmp = Comp()) noexcept(noexcept(cmp(a, b))) {
return cmp(a, b) ? a = b, true : false;
}
inline CONSTEXPR ll gcd(ll a, ll b) {
if (a < 0) a = -a;
if (b < 0) b = -b;
while (b) {
const ll c = a;
a = b;
b = c % b;
}
return a;
}
inline CONSTEXPR ll lcm(ll a, ll b) { return a / gcd(a, b) * b; }
inline CONSTEXPR bool is_prime(ll N) {
if (N <= 1) return false;
for (ll i = 2; i * i <= N; ++i) {
if (N % i == 0) return false;
}
return true;
}
inline std::vector<ll> prime_factor(ll N) {
std::vector<ll> res;
for (ll i = 2; i * i <= N; ++i) {
while (N % i == 0) {
res.push_back(i);
N /= i;
}
}
if (N != 1) res.push_back(N);
return res;
}
inline CONSTEXPR ll my_pow(ll a, ll b) {
ll res = 1;
while (b) {
if (b & 1) res *= a;
b >>= 1;
a *= a;
}
return res;
}
inline CONSTEXPR ll mod_pow(ll a, ll b, ll mod) {
assert(mod > 0);
if (mod == 1) return 0;
a %= mod;
ll res = 1;
while (b) {
if (b & 1) (res *= a) %= mod;
b >>= 1;
(a *= a) %= mod;
}
return res;
}
inline PLL extGCD(ll a, ll b) {
const ll n = a, m = b;
ll x = 1, y = 0, u = 0, v = 1;
ll t;
while (b) {
t = a / b;
std::swap(a -= t * b, b);
std::swap(x -= t * u, u);
std::swap(y -= t * v, v);
}
if (x < 0) {
x += m;
y -= n;
}
return {x, y};
}
inline ll mod_inv(ll a, ll mod) {
ll b = mod;
ll x = 1, u = 0;
ll t;
while (b) {
t = a / b;
std::swap(a -= t * b, b);
std::swap(x -= t * u, u);
}
if (x < 0) x += mod;
assert(a == 1);
return x;
}
#line 2 "library/template/util.hpp"
#line 6 "library/template/util.hpp"
template<class F> class RecLambda {
private:
F f;
public:
explicit constexpr RecLambda(F&& f_) : f(std::forward<F>(f_)) {}
template<class... Args>
constexpr auto operator()(Args&&... args)
-> decltype(f(*this, std::forward<Args>(args)...)) {
return f(*this, std::forward<Args>(args)...);
}
};
template<class F> inline constexpr RecLambda<F> rec_lambda(F&& f) {
return RecLambda<F>(std::forward<F>(f));
}
template<class Head, class... Tail> struct multi_dim_vector {
using type = std::vector<typename multi_dim_vector<Tail...>::type>;
};
template<class T> struct multi_dim_vector<T> { using type = T; };
template<class T, class Arg>
constexpr std::vector<T> make_vec(int n, Arg&& arg) {
return std::vector<T>(n, std::forward<Arg>(arg));
}
template<class T, class... Args>
constexpr typename multi_dim_vector<Args..., T>::type make_vec(int n,
Args&&... args) {
return typename multi_dim_vector<Args..., T>::type(
n, make_vec<T>(std::forward<Args>(args)...));
}
template<class T, class Comp = std::less<T>> class compressor {
private:
std::vector<T> dat;
Comp cmp;
bool sorted = false;
public:
compressor() : compressor(Comp()) {}
compressor(const Comp& cmp) : cmp(cmp) {}
compressor(const std::vector<T>& vec, bool f = false,
const Comp& cmp = Comp())
: dat(vec), cmp(cmp) {
if (f) build();
}
compressor(std::vector<T>&& vec, bool f = false, const Comp& cmp = Comp())
: dat(std::move(vec)), cmp(cmp) {
if (f) build();
}
compressor(std::initializer_list<T> il, bool f = false,
const Comp& cmp = Comp())
: dat(all(il)), cmp(cmp) {
if (f) build();
}
void reserve(int n) {
assert(!sorted);
dat.reserve(n);
}
void push_back(const T& v) {
assert(!sorted);
dat.push_back(v);
}
void push_back(T&& v) {
assert(!sorted);
dat.push_back(std::move(v));
}
template<class... Args> void emplace_back(Args&&... args) {
assert(!sorted);
dat.emplace_back(std::forward<Args>(args)...);
}
void push(const std::vector<T>& vec) {
assert(!sorted);
const int n = dat.size();
dat.resize(n + vec.size());
rep (i, vec.size()) dat[n + i] = vec[i];
}
int build() {
assert(!sorted);
sorted = true;
std::sort(all(dat), cmp);
dat.erase(std::unique(all(dat),
[&](const T& a, const T& b) -> bool {
return !cmp(a, b) && !cmp(b, a);
}),
dat.end());
return dat.size();
}
const T& operator[](int k) const& {
assert(sorted);
assert(0 <= k && k < (int)dat.size());
return dat[k];
}
int get(const T& val) const {
assert(sorted);
auto itr = std::lower_bound(all(dat), val, cmp);
assert(itr != dat.end() && !cmp(val, *itr));
return itr - dat.begin();
}
int lower_bound(const T& val) const {
assert(sorted);
auto itr = std::lower_bound(all(dat), val, cmp);
return itr - dat.begin();
}
int upper_bound(const T& val) const {
assert(sorted);
auto itr = std::upper_bound(all(dat), val, cmp);
return itr - dat.begin();
}
bool contains(const T& val) const {
assert(sorted);
return std::binary_search(all(dat), val, cmp);
}
std::vector<int> pressed(const std::vector<T>& vec) const {
assert(sorted);
std::vector<int> res(vec.size());
rep (i, vec.size()) res[i] = get(vec[i]);
return res;
}
void press(std::vector<T>& vec) const {
assert(sorted);
each_for (i : vec) i = get(i);
}
int size() const {
assert(sorted);
return dat.size();
}
};
#line 2 "library/math/Combinatorics.hpp"
#line 2 "library/math/ModInt.hpp"
#line 4 "library/math/ModInt.hpp"
template<class T, T mod> class StaticModInt {
static_assert(std::is_integral<T>::value, "T must be integral");
static_assert(std::is_unsigned<T>::value, "T must be unsigned");
static_assert(mod > 0, "mod must be positive");
static_assert(mod <= std::numeric_limits<T>::max() / 2,
"mod * 2 must be less than or equal to T::max()");
private:
using large_t = typename double_size_uint<T>::type;
using signed_t = typename std::make_signed<T>::type;
T val;
static constexpr unsigned int inv1000000007[] = {
0, 1, 500000004, 333333336, 250000002, 400000003,
166666668, 142857144, 125000001, 111111112, 700000005};
static constexpr unsigned int inv998244353[] = {
0, 1, 499122177, 332748118, 748683265, 598946612,
166374059, 855638017, 873463809, 443664157, 299473306};
public:
constexpr StaticModInt() : val(0) {}
template<class U,
typename std::enable_if<std::is_integral<U>::value &&
std::is_signed<U>::value>::type* = nullptr>
constexpr StaticModInt(U v) : val{} {
v %= static_cast<signed_t>(mod);
if (v < 0) v += static_cast<signed_t>(mod);
val = static_cast<T>(v);
}
template<class U, typename std::enable_if<
std::is_integral<U>::value &&
std::is_unsigned<U>::value>::type* = nullptr>
constexpr StaticModInt(U v) : val(v % mod) {}
T get() const { return val; }
static constexpr T get_mod() { return mod; }
static StaticModInt raw(T v) {
StaticModInt res;
res.val = v;
return res;
}
StaticModInt inv() const {
if IF_CONSTEXPR (mod == 1000000007) {
if (val <= 10) return inv1000000007[val];
}
else if IF_CONSTEXPR (mod == 998244353) {
if (val <= 10) return inv998244353[val];
}
return mod_inv(val, mod);
}
StaticModInt& operator++() {
++val;
if (val == mod) val = 0;
return *this;
}
StaticModInt operator++(int) {
StaticModInt res = *this;
++*this;
return res;
}
StaticModInt& operator--() {
if (val == 0) val = mod;
--val;
return *this;
}
StaticModInt operator--(int) {
StaticModInt res = *this;
--*this;
return res;
}
StaticModInt& operator+=(const StaticModInt& other) {
val += other.val;
if (val >= mod) val -= mod;
return *this;
}
StaticModInt& operator-=(const StaticModInt& other) {
if (val < other.val) val += mod;
val -= other.val;
return *this;
}
StaticModInt& operator*=(const StaticModInt& other) {
large_t a = val;
a *= other.val;
a %= mod;
val = a;
return *this;
}
StaticModInt& operator/=(const StaticModInt& other) {
*this *= other.inv();
return *this;
}
friend StaticModInt operator+(const StaticModInt& lhs,
const StaticModInt& rhs) {
return StaticModInt(lhs) += rhs;
}
friend StaticModInt operator-(const StaticModInt& lhs,
const StaticModInt& rhs) {
return StaticModInt(lhs) -= rhs;
}
friend StaticModInt operator*(const StaticModInt& lhs,
const StaticModInt& rhs) {
return StaticModInt(lhs) *= rhs;
}
friend StaticModInt operator/(const StaticModInt& lhs,
const StaticModInt& rhs) {
return StaticModInt(lhs) /= rhs;
}
StaticModInt operator+() const { return StaticModInt(*this); }
StaticModInt operator-() const { return StaticModInt() - *this; }
friend bool operator==(const StaticModInt& lhs, const StaticModInt& rhs) {
return lhs.val == rhs.val;
}
friend bool operator!=(const StaticModInt& lhs, const StaticModInt& rhs) {
return lhs.val != rhs.val;
}
StaticModInt pow(ll a) const {
StaticModInt v = *this, res = 1;
while (a) {
if (a & 1) res *= v;
a >>= 1;
v *= v;
}
return res;
}
template<class Pr> void print(Pr& a) const { a.print(val); }
template<class Pr> void debug(Pr& a) const { a.print(val); }
template<class Sc> void scan(Sc& a) {
ll v;
a.scan(v);
*this = v;
}
};
#if __cplusplus < 201703L
template<class T, T mod>
constexpr unsigned int StaticModInt<T, mod>::inv1000000007[];
template<class T, T mod>
constexpr unsigned int StaticModInt<T, mod>::inv998244353[];
#endif
template<unsigned int p> using static_modint = StaticModInt<unsigned int, p>;
using modint1000000007 = static_modint<1000000007>;
using modint998244353 = static_modint<998244353>;
template<class T, int id> class DynamicModInt {
static_assert(std::is_integral<T>::value, "T must be integral");
static_assert(std::is_unsigned<T>::value, "T must be unsigned");
private:
using large_t = typename double_size_uint<T>::type;
using signed_t = typename std::make_signed<T>::type;
T val;
static T mod;
public:
constexpr DynamicModInt() : val(0) {}
template<class U,
typename std::enable_if<std::is_integral<U>::value &&
std::is_signed<U>::value>::type* = nullptr>
constexpr DynamicModInt(U v) : val{} {
v %= static_cast<signed_t>(mod);
if (v < 0) v += static_cast<signed_t>(mod);
val = static_cast<T>(v);
}
template<class U, typename std::enable_if<
std::is_integral<U>::value &&
std::is_unsigned<U>::value>::type* = nullptr>
constexpr DynamicModInt(U v) : val(v % mod) {}
T get() const { return val; }
static T get_mod() { return mod; }
static void set_mod(T v) {
assert(v > 0);
assert(v <= std::numeric_limits<T>::max() / 2);
mod = v;
}
static DynamicModInt raw(T v) {
DynamicModInt res;
res.val = v;
return res;
}
DynamicModInt inv() const { return mod_inv(val, mod); }
DynamicModInt& operator++() {
++val;
if (val == mod) val = 0;
return *this;
}
DynamicModInt operator++(int) {
DynamicModInt res = *this;
++*this;
return res;
}
DynamicModInt& operator--() {
if (val == 0) val = mod;
--val;
return *this;
}
DynamicModInt operator--(int) {
DynamicModInt res = *this;
--*this;
return res;
}
DynamicModInt& operator+=(const DynamicModInt& other) {
val += other.val;
if (val >= mod) val -= mod;
return *this;
}
DynamicModInt& operator-=(const DynamicModInt& other) {
if (val < other.val) val += mod;
val -= other.val;
return *this;
}
DynamicModInt& operator*=(const DynamicModInt& other) {
large_t a = val;
a *= other.val;
a %= mod;
val = a;
return *this;
}
DynamicModInt& operator/=(const DynamicModInt& other) {
*this *= other.inv();
return *this;
}
friend DynamicModInt operator+(const DynamicModInt& lhs,
const DynamicModInt& rhs) {
return DynamicModInt(lhs) += rhs;
}
friend DynamicModInt operator-(const DynamicModInt& lhs,
const DynamicModInt& rhs) {
return DynamicModInt(lhs) -= rhs;
}
friend DynamicModInt operator*(const DynamicModInt& lhs,
const DynamicModInt& rhs) {
return DynamicModInt(lhs) *= rhs;
}
friend DynamicModInt operator/(const DynamicModInt& lhs,
const DynamicModInt& rhs) {
return DynamicModInt(lhs) /= rhs;
}
DynamicModInt operator+() const { return DynamicModInt(*this); }
DynamicModInt operator-() const { return DynamicModInt() - *this; }
friend bool operator==(const DynamicModInt& lhs, const DynamicModInt& rhs) {
return lhs.val == rhs.val;
}
friend bool operator!=(const DynamicModInt& lhs, const DynamicModInt& rhs) {
return lhs.val != rhs.val;
}
DynamicModInt pow(ll a) const {
DynamicModInt v = *this, res = 1;
while (a) {
if (a & 1) res *= v;
a >>= 1;
v *= v;
}
return res;
}
template<class Pr> void print(Pr& a) const { a.print(val); }
template<class Pr> void debug(Pr& a) const { a.print(val); }
template<class Sc> void scan(Sc& a) {
ll v;
a.scan(v);
*this = v;
}
};
template<class T, int id> T DynamicModInt<T, id>::mod = 998244353;
template<int id> using dynamic_modint = DynamicModInt<unsigned int, id>;
using modint = dynamic_modint<-1>;
/**
* @brief ModInt
* @docs docs/math/ModInt.md
*/
#line 5 "library/math/Combinatorics.hpp"
template<class T> class Combinatorics {
private:
static std::vector<T> factorial;
static std::vector<T> factinv;
public:
static void init(ll n) {
const int b = factorial.size();
if (n < b) return;
factorial.resize(n + 1);
rep (i, b, n + 1) factorial[i] = factorial[i - 1] * i;
factinv.resize(n + 1);
factinv[n] = T(1) / factorial[n];
rreps (i, n, b) factinv[i - 1] = factinv[i] * i;
}
static T fact(ll x) {
if (x < 0) return 0;
init(x);
return factorial[x];
}
static T finv(ll x) {
if (x < 0) return 0;
init(x);
return factinv[x];
}
static T inv(ll x) {
if (x <= 0) return 0;
init(x);
return factorial[x - 1] * factinv[x];
}
static T perm(ll n, ll r) {
if (r < 0 || r > n) return 0;
init(n);
return factorial[n] * factinv[n - r];
}
static T comb(ll n, ll r) {
if (n < 0) return 0;
if (r < 0 || r > n) return 0;
init(n);
return factorial[n] * factinv[n - r] * factinv[r];
}
static T homo(ll n, ll r) { return comb(n + r - 1, r); }
static T small_perm(ll n, ll r) {
if (r < 0 || r > n) return 0;
T res = 1;
reps (i, r) res *= n - r + i;
return res;
}
static T small_comb(ll n, ll r) {
if (r < 0 || r > n) return 0;
chmin(r, n - r);
init(r);
T res = factinv[r];
reps (i, r) res *= n - r + i;
return res;
}
static T small_homo(ll n, ll r) { return small_comb(n + r - 1, r); }
};
template<class T>
std::vector<T> Combinatorics<T>::factorial = std::vector<T>(1, 1);
template<class T>
std::vector<T> Combinatorics<T>::factinv = std::vector<T>(1, 1);
/**
* @brief Combinatorics
* @docs docs/math/Combinatorics.md
*/
CONSTEXPR ull primitive_root_for_convolution(ull p) {
if (p == 2) return 1;
if (p == 998244353) return 3;
if (p == 469762049) return 3;
if (p == 1811939329) return 11;
if (p == 2013265921) return 11;
rep (g, 2, p) {
if (mod_pow(g, (p - 1) >> 1, p) != 1) return g;
}
return -1;
}
/**
* @brief PrimitiveRoot(原始根)
* @docs docs/math/PrimitiveRoot.md
*/
#line 6 "library/math/convolution/Convolution.hpp"
namespace internal {
template<unsigned int p> class NthRoot {
private:
static constexpr unsigned int lg = bitop::msb((p - 1) & (1 - p));
unsigned int root[lg + 1];
unsigned int inv_root[lg + 1];
unsigned int rate[lg + 1];
unsigned int inv_rate[lg + 1];
public:
constexpr NthRoot() : root{}, inv_root{}, rate{}, inv_rate{} {
root[lg] = mod_pow(primitive_root_for_convolution(p), (p - 1) >> lg, p);
inv_root[lg] = mod_pow(root[lg], p - 2, p);
rrep (i, lg) {
root[i] = (ull)root[i + 1] * root[i + 1] % p;
inv_root[i] = (ull)inv_root[i + 1] * inv_root[i + 1] % p;
}
ull r = 1;
rep (i, 2, lg + 1) {
rate[i - 2] = r * root[i] % p;
r = r * inv_root[i] % p;
}
r = 1;
rep (i, 2, lg + 1) {
inv_rate[i - 2] = r * inv_root[i] % p;
r = r * root[i] % p;
}
}
static constexpr unsigned int get_lg() { return lg; }
constexpr unsigned int get(int n) const { return root[n]; }
constexpr unsigned int inv(int n) const { return inv_root[n]; }
constexpr unsigned int get_rate(int n) const { return rate[n]; }
constexpr unsigned int get_inv_rate(int n) const { return inv_rate[n]; }
};
template<unsigned int p> constexpr NthRoot<p> nth_root;
template<class T> void number_theoretic_transform(std::vector<T>& a) {
int n = a.size();
int lg = bitop::msb(n - 1) + 1;
rrep (i, lg) {
T z = T(1);
rep (j, 1 << (lg - i - 1)) {
int offset = j << (i + 1);
rep (k, 1 << i) {
T x = a[offset + k];
T y = a[offset + k + (1 << i)] * z;
a[offset + k] = x + y;
a[offset + k + (1 << i)] = x - y;
}
if (j != (1 << (lg - i - 1)) - 1) {
z *= nth_root<T::get_mod()>.get_rate(popcnt(j & ~(j + 1)));
}
}
}
}
template<class T> void inverse_number_theoretic_transform(std::vector<T>& a) {
int n = a.size();
int lg = bitop::msb(n - 1) + 1;
rep (i, lg) {
T z = T(1);
rep (j, 1 << (lg - i - 1)) {
int offset = j << (i + 1);
rep (k, 1 << i) {
T x = a[offset + k];
T y = a[offset + k + (1 << i)];
a[offset + k] = x + y;
a[offset + k + (1 << i)] = (x - y) * z;
}
if (j != (1 << (lg - i - 1)) - 1) {
z *= nth_root<T::get_mod()>.get_inv_rate(popcnt(j & ~(j + 1)));
}
}
}
T inv_n = T(1) / n;
each_for (x : a) x *= inv_n;
}
template<class T>
std::vector<T> convolution_naive(const std::vector<T>& a,
const std::vector<T>& b) {
int n = a.size(), m = b.size();
std::vector<T> c(n + m - 1);
rep (i, n)
rep (j, m) c[i + j] += a[i] * b[j];
return c;
}
template<class T> std::vector<T> convolution_pow2(std::vector<T> a) {
int n = a.size() * 2 - 1;
int lg = bitop::msb(n - 1) + 1;
if (n - (1 << (lg - 1)) <= 5) {
--lg;
int m = a.size() - (1 << (lg - 1));
std::vector<T> a1(a.begin(), a.begin() + m), a2(a.begin() + m, a.end());
std::vector<T> c(n);
std::vector<T> c1 = convolution_naive(a1, a1);
std::vector<T> c2 = convolution_naive(a1, a2);
std::vector<T> c3 = convolution_pow2(a2);
rep (i, c1.size()) c[i] += c1[i];
rep (i, c2.size()) c[i + m] += c2[i] * 2;
rep (i, c3.size()) c[i + m * 2] += c3[i];
return c;
}
int m = 1 << lg;
a.resize(m);
number_theoretic_transform(a);
rep (i, m) a[i] *= a[i];
inverse_number_theoretic_transform(a);
a.resize(n);
return a;
}
template<class T>
std::vector<T> convolution(std::vector<T> a, std::vector<T> b) {
int n = a.size() + b.size() - 1;
int lg = bitop::ceil_log2(n);
int m = 1 << lg;
if (n - (1 << (lg - 1)) <= 5) {
--lg;
if (a.size() < b.size()) std::swap(a, b);
int m = n - (1 << lg);
std::vector<T> a1(a.begin(), a.begin() + m), a2(a.begin() + m, a.end());
std::vector<T> c(n);
std::vector<T> c1 = convolution_naive(a1, b);
std::vector<T> c2 = convolution(a2, b);
rep (i, c1.size()) c[i] += c1[i];
rep (i, c2.size()) c[i + m] += c2[i];
return c;
}
a.resize(m);
b.resize(m);
number_theoretic_transform(a);
number_theoretic_transform(b);
rep (i, m) a[i] *= b[i];
inverse_number_theoretic_transform(a);
a.resize(n);
return a;
}
} // namespace internal
using internal::inverse_number_theoretic_transform;
using internal::number_theoretic_transform;
template<unsigned int p>
std::vector<static_modint<p>>
convolution_for_any_mod(const std::vector<static_modint<p>>& a,
const std::vector<static_modint<p>>& b);
template<unsigned int p>
std::vector<static_modint<p>>
convolution(const std::vector<static_modint<p>>& a,
const std::vector<static_modint<p>>& b) {
unsigned int n = a.size(), m = b.size();
if (n == 0 || m == 0) return {};
if (n <= 60 || m <= 60) return internal::convolution_naive(a, b);
if (n + m - 1 > ((1 - p) & (p - 1))) return convolution_for_any_mod(a, b);
if (n == m && a == b) return internal::convolution_pow2(a);
return internal::convolution(a, b);
}
template<unsigned int p>
std::vector<ll> convolution(const std::vector<ll>& a,
const std::vector<ll>& b) {
int n = a.size(), m = b.size();
std::vector<static_modint<p>> a2(n), b2(m);
rep (i, n) a2[i] = a[i];
rep (i, m) b2[i] = b[i];
auto c2 = convolution(a2, b2);
std::vector<ll> c(n + m - 1);
rep (i, n + m - 1) c[i] = c2[i].get();
return c;
}
template<unsigned int p>
std::vector<static_modint<p>>
convolution_for_any_mod(const std::vector<static_modint<p>>& a,
const std::vector<static_modint<p>>& b) {
int n = a.size(), m = b.size();
assert(n + m - 1 <= (1 << 26));
std::vector<ll> a2(n), b2(m);
rep (i, n) a2[i] = a[i].get();
rep (i, m) b2[i] = b[i].get();
static constexpr ll MOD1 = 469762049;
static constexpr ll MOD2 = 1811939329;
static constexpr ll MOD3 = 2013265921;
static constexpr ll INV1_2 = mod_pow(MOD1, MOD2 - 2, MOD2);
static constexpr ll INV1_3 = mod_pow(MOD1, MOD3 - 2, MOD3);
static constexpr ll INV2_3 = mod_pow(MOD2, MOD3 - 2, MOD3);
auto c1 = convolution<MOD1>(a2, b2);
auto c2 = convolution<MOD2>(a2, b2);
auto c3 = convolution<MOD3>(a2, b2);
std::vector<static_modint<p>> res(n + m - 1);
rep (i, n + m - 1) {
ll t1 = c1[i];
ll t2 = (c2[i] - t1 + MOD2) * INV1_2 % MOD2;
if (t2 < 0) t2 += MOD2;
ll t3 =
((c3[i] - t1 + MOD3) * INV1_3 % MOD3 - t2 + MOD3) * INV2_3 % MOD3;
if (t3 < 0) t3 += MOD3;
res[i] = static_modint<p>(t1 + (t2 + t3 * MOD2) % p * MOD1);
}
return res;
}
template<class T> void ntt_doubling_(std::vector<T>& a) {
int n = a.size();
auto b = a;
inverse_number_theoretic_transform(b);
const T z = internal::nth_root<T::get_mod()>.get(bitop::msb(n) + 1);
T r = 1;
rep (i, n) {
b[i] *= r;
r *= z;
}
number_theoretic_transform(b);
std::copy(all(b), std::back_inserter(a));
}
template<unsigned int p> struct is_ntt_friendly : std::false_type {};
template<> struct is_ntt_friendly<998244353> : std::true_type {};
/**
* @brief Convolution(畳み込み)
* @docs docs/math/convolution/Convolution.md
*/
#line 2 "library/math/poly/FormalPowerSeries.hpp"
#line 2 "library/math/SqrtMod.hpp"
#line 5 "library/math/SqrtMod.hpp"
/**
* @brief SqrtMod(平方剰余)
* @docs docs/math/SqrtMod.md
* @see https://37zigen.com/tonelli-shanks-algorithm/
*/
#line 7 "library/math/poly/FormalPowerSeries.hpp"
template<class T> class FormalPowerSeries : public std::vector<T> {
private:
using Base = std::vector<T>;
using Comb = Combinatorics<T>;
public:
using Base::Base;
FormalPowerSeries(const Base& v) : Base(v) {}
FormalPowerSeries(Base&& v) : Base(std::move(v)) {}
FormalPowerSeries& shrink() {
while (!this->empty() && this->back() == T{0}) this->pop_back();
return *this;
}
T eval(T x) const {
T res = 0;
rrep (i, this->size()) {
res *= x;
res += (*this)[i];
}
return res;
}
FormalPowerSeries prefix(int deg) const {
assert(0 <= deg);
if (deg < (int)this->size()) {
return FormalPowerSeries(this->begin(), this->begin() + deg);
}
FormalPowerSeries res(*this);
res.resize(deg);
return res;
}
FormalPowerSeries operator+() const { return *this; }
FormalPowerSeries operator-() const {
FormalPowerSeries res(this->size());
rep (i, this->size()) res[i] = -(*this)[i];
return res;
}
FormalPowerSeries& operator<<=(int n) {
this->insert(this->begin(), n, T{0});
return *this;
}
FormalPowerSeries& operator>>=(int n) {
this->erase(this->begin(),
this->begin() + std::min(n, (int)this->size()));
return *this;
}
friend FormalPowerSeries operator<<(const FormalPowerSeries& lhs, int rhs) {
return FormalPowerSeries(lhs) <<= rhs;
}
friend FormalPowerSeries operator>>(const FormalPowerSeries& lhs, int rhs) {
return FormalPowerSeries(lhs) >>= rhs;
}
FormalPowerSeries& operator+=(const FormalPowerSeries& rhs) {
if (this->size() < rhs.size()) this->resize(rhs.size());
rep (i, rhs.size()) (*this)[i] += rhs[i];
return *this;
}
FormalPowerSeries& operator-=(const FormalPowerSeries& rhs) {
if (this->size() < rhs.size()) this->resize(rhs.size());
rep (i, rhs.size()) (*this)[i] -= rhs[i];
return *this;
}
friend FormalPowerSeries operator+(const FormalPowerSeries& lhs,
const FormalPowerSeries& rhs) {
return FormalPowerSeries(lhs) += rhs;
}
friend FormalPowerSeries operator-(const FormalPowerSeries& lhs,
const FormalPowerSeries& rhs) {
return FormalPowerSeries(lhs) -= rhs;
}
friend FormalPowerSeries operator*(const FormalPowerSeries& lhs,
const FormalPowerSeries& rhs) {
return FormalPowerSeries(convolution(lhs, rhs));
}
FormalPowerSeries& operator*=(const FormalPowerSeries& rhs) {
return *this = *this * rhs;
}
FormalPowerSeries& operator*=(const T& rhs) {
rep (i, this->size()) (*this)[i] *= rhs;
return *this;
}
friend FormalPowerSeries operator*(const FormalPowerSeries& lhs,
const T& rhs) {
return FormalPowerSeries(lhs) *= rhs;
}
friend FormalPowerSeries operator*(const T& lhs,
const FormalPowerSeries& rhs) {
return FormalPowerSeries(rhs) *= lhs;
}
FormalPowerSeries& operator/=(const T& rhs) {
rep (i, this->size()) (*this)[i] /= rhs;
return *this;
}
friend FormalPowerSeries operator/(const FormalPowerSeries& lhs,
const T& rhs) {
return FormalPowerSeries(lhs) /= rhs;
}
FormalPowerSeries rev() const {
FormalPowerSeries res(*this);
std::reverse(all(res));
return res;
}
friend FormalPowerSeries div(FormalPowerSeries lhs, FormalPowerSeries rhs) {
lhs.shrink();
rhs.shrink();
if (lhs.size() < rhs.size()) {
return FormalPowerSeries{};
}
int n = lhs.size() - rhs.size() + 1;
if (rhs.size() <= 32) {
FormalPowerSeries res(n);
T iv = rhs.back().inv();
rrep (i, n) {
T d = lhs[i + rhs.size() - 1] * iv;
res[i] = d;
rep (j, rhs.size()) lhs[i + j] -= d * rhs[j];
}
return res;
}
return (lhs.rev().prefix(n) * rhs.rev().inv(n)).prefix(n).rev();
}
friend FormalPowerSeries operator%(FormalPowerSeries lhs,
FormalPowerSeries rhs) {
lhs.shrink();
rhs.shrink();
if (lhs.size() < rhs.size()) {
return lhs;
}
int n = lhs.size() - rhs.size() + 1;
if (rhs.size() <= 32) {
T iv = rhs.back().inv();
rrep (i, n) {
T d = lhs[i + rhs.size() - 1] * iv;
rep (j, rhs.size()) lhs[i + j] -= d * rhs[j];
}
return lhs.shrink();
}
return (lhs - div(lhs, rhs) * rhs).shrink();
}
friend std::pair<FormalPowerSeries, FormalPowerSeries>
divmod(FormalPowerSeries lhs, FormalPowerSeries rhs) {
lhs.shrink();
rhs.shrink();
if (lhs.size() < rhs.size()) {
return {FormalPowerSeries{}, lhs};
}
int n = lhs.size() - rhs.size() + 1;
if (rhs.size() <= 32) {
FormalPowerSeries res(n);
T iv = rhs.back().inv();
rrep (i, n) {
T d = lhs[i + rhs.size() - 1] * iv;
res[i] = d;
rep (j, rhs.size()) lhs[i + j] -= d * rhs[j];
}
return {res, lhs.shrink()};
}
FormalPowerSeries q = div(lhs, rhs);
return {q, (lhs - q * rhs).shrink()};
}
FormalPowerSeries& operator%=(const FormalPowerSeries& rhs) {
return *this = *this % rhs;
}
FormalPowerSeries diff() const {
if (this->empty()) return {};
FormalPowerSeries res(this->size() - 1);
rep (i, res.size()) res[i] = (*this)[i + 1] * (i + 1);
return res;
}
FormalPowerSeries integral() const {
FormalPowerSeries res(this->size() + 1);
res[0] = 0;
Comb::init(this->size());
rep (i, this->size()) res[i + 1] = (*this)[i] * Comb::inv(i + 1);
return res;
}
template<bool AlwaysTrue = true,
typename std::enable_if<
AlwaysTrue && is_ntt_friendly<T::get_mod()>::value>::type* =
nullptr>
FormalPowerSeries inv(int deg = -1) const {
assert(this->size() > 0 && (*this)[0] != 0);
if (deg == -1) deg = this->size();
FormalPowerSeries res(1, (*this)[0].inv());
for (int m = 1; m < deg; m <<= 1) {
FormalPowerSeries f(2 * m);
for (int i = 0; i < std::min(2 * m, (int)this->size()); i++)
f[i] = (*this)[i];
res.resize(2 * m);
FormalPowerSeries dft = res;
number_theoretic_transform(f);
number_theoretic_transform(dft);
rep (i, 2 * m) f[i] *= dft[i];
inverse_number_theoretic_transform(f);
std::fill(f.begin(), f.begin() + m, T{0});
number_theoretic_transform(f);
rep (i, 2 * m) dft[i] *= f[i];
inverse_number_theoretic_transform(dft);
rep (i, m, 2 * m) res[i] = -dft[i];
}
return res.prefix(deg);
}
template<bool AlwaysTrue = true,
typename std::enable_if<
AlwaysTrue && !is_ntt_friendly<T::get_mod()>::value>::type* =
nullptr>
FormalPowerSeries inv(int deg = -1) const {
assert(this->size() > 0 && (*this)[0] != 0);
if (deg == -1) deg = this->size();
FormalPowerSeries res(1, (*this)[0].inv());
for (int m = 1; m < deg; m <<= 1) {
res = (res * 2 - (res * res * this->prefix(2 * m)).prefix(2 * m))
.prefix(2 * m);
}
return res.prefix(deg);
}
template<bool AlwaysTrue = true,
typename std::enable_if<
AlwaysTrue && is_ntt_friendly<T::get_mod()>::value>::type* =
nullptr>
FormalPowerSeries& ntt_doubling() {
ntt_doubling_(*this);
return *this;
}
};
/**
* @brief FormalPowerSeries(形式的冪級数)
* @docs docs/math/poly/FormalPowerSeries.md
* @see https://nyaannyaan.github.io/library/fps/formal-power-series.hpp
*/
#line 2 "library/math/poly/TaylorShift.hpp"
#line 7 "library/math/poly/TaylorShift.hpp"
template<class T, class Comb = Combinatorics<T>>
FormalPowerSeries<T> taylor_shift(FormalPowerSeries<T> f, T a) {
const int n = f.size();
Comb::init(n);
rep (i, n) f[i] *= Comb::fact(i);
FormalPowerSeries<T> g(n);
T p = 1;
rep (i, n) {
g[n - 1 - i] = p * Comb::finv(i);
p *= a;
}
f *= g;
f >>= n - 1;
rep (i, n) f[i] *= Comb::finv(i);
return f;
}
/**
* @brief TaylorShift
* @docs docs/math/poly/TaylorShift.md
*/
#line 8 "library/math/poly/SamplingPointsShift.hpp"
template<class T, class Comb = Combinatorics<T>>
std::vector<T> sampling_points_shift(std::vector<T> a, int m, T t) {
const int n = a.size();
Comb::init(std::max(n, m));
FormalPowerSeries<T> f(n), g(n);
rep (i, n) f[i] = i & 1 ? -Comb::finv(i) : Comb::finv(i);
rep (i, n) g[i] = a[i] * Comb::finv(i);
f = (f * g).prefix(n);
rep (i, n) f[i] *= Comb::fact(i);
T p = 1;
rep (i, n) {
g[n - 1 - i] = p * Comb::finv(i);
p *= t--;
}
f = (f * g) >> (n - 1);
rep (i, n) f[i] *= Comb::finv(i);
g.resize(m);
rep (i, m) g[i] = Comb::finv(i);
f = (f * g).prefix(m);
rep (i, m) f[i] *= Comb::fact(i);
return std::vector<T>(f);
}
/**
* @brief SamplingPointsShift(標本点シフト)
* @docs docs/math/poly/SamplingPointsShift.md
*/
#line 2 "library/math/Factorial.hpp"
#line 2 "library/math/poly/MultipointEvaluation.hpp"
#line 5 "library/math/poly/MultipointEvaluation.hpp"
namespace internal {
template<class T> class ProductTree {
private:
int n;
std::vector<FormalPowerSeries<T>> dat;
public:
ProductTree(const std::vector<T>& xs) {
n = xs.size();
dat.resize(n << 1);
rep (i, n) dat[i + n] = FormalPowerSeries<T>{-xs[i], 1};
rrep (i, n, 1) dat[i] = dat[i << 1] * dat[i << 1 | 1];
}
const FormalPowerSeries<T>& operator[](int k) const& { return dat[k]; }
FormalPowerSeries<T> operator[](int k) && { return std::move(dat[k]); }
};
template<class T>
std::vector<T> multipoint_evaluation(const FormalPowerSeries<T>& a,
const std::vector<T>& b,
const ProductTree<T>& c) {
int m = b.size();
std::vector<FormalPowerSeries<T>> d(m << 1);
d[1] = a % c[1];
rep (i, 2, m << 1) d[i] = d[i >> 1] % c[i];
std::vector<T> e(m);
rep (i, m) e[i] = d[m + i].empty() ? T{0} : d[m + i][0];
return e;
}
} // namespace internal
template<class T>
std::vector<T> multipoint_evaluation(const FormalPowerSeries<T>& a,
const std::vector<T>& b) {
if (a.empty() || b.empty()) return std::vector<T>(b.size(), T{0});
if (a.size() <= 32 || b.size() <= 32) {
std::vector<T> res(b.size());
rep (i, b.size()) res[i] = a.eval(b[i]);
return res;
}
return internal::multipoint_evaluation(a, b, internal::ProductTree<T>(b));
}
template<class T>
std::vector<T> multipoint_evaluation_geometric(const FormalPowerSeries<T>& f,
T a, T r, int m) {
if (f.empty() || m == 0) return std::vector<T>(m, T{0});
if (a == 0 || r == 1) return std::vector<T>(m, f.eval(a));
if (f.size() <= 32 || m <= 32) {
std::vector<T> res(m);
rep (i, m) {
res[i] = f.eval(a);
a *= r;
}
return res;
}
if (r == 0) {
std::vector<T> res(m, f.eval(0));
res[0] = f.eval(a);
return res;
}
int n = f.size();
int l = 1 << bitop::ceil_log2(n + m - 1);
std::vector<T> p(l), q(l);
T ir = T{1} / r, t = 1, t2 = 1;
rep (i, n) {
p[n - i - 1] = f[i] * t;
t *= a * t2;
t2 *= ir;
}
t = t2 = 1;
rep (i, n + m - 1) {
q[i] = t;
t *= t2;
t2 *= r;
}
number_theoretic_transform(p);
number_theoretic_transform(q);
rep (i, l) p[i] *= q[i];
inverse_number_theoretic_transform(p);
std::vector<T> ans(p.begin() + (n - 1), p.begin() + (n + m - 1));
t = t2 = 1;
rep (i, m) {
ans[i] *= t;
t *= t2;
t2 *= ir;
}
return ans;
}
/**
* @brief MultipointEvaluation(多点評価)
* @docs docs/math/poly/MultipointEvaluation.md
*/
#line 6 "library/math/Factorial.hpp"
template<class T> T factorial(ll n) {
assert(n >= 0);
if (n >= T::get_mod()) return 0;
if (n * 2 > T::get_mod()) {
T res = factorial<T>(T::get_mod() - 1 - n);
if ((T::get_mod() - n) & 1) res = -res;
return 1 / res;
}
if (n <= 1000) {
T res = 1;
reps (i, n) res *= i;
return res;
}
const ll bs = sqrt(n), bn = n / bs;
std::vector<T> v1(bs), v2(bn);
rep (i, bs) v1[i] = -1 - i;
rep (i, bn) v2[i] = i * bs;
auto f = internal::ProductTree<T>(v1)[1];
T res = 1;
for (const auto& x : multipoint_evaluation(f, v2)) res *= x;
rep (i, bn * bs + 1, n + 1) res *= i;
return res;
}
/**
* @brief Factorial(階乗)
* @docs docs/math/Factorial.md
*/
#line 5 "main.cpp"
using namespace std;
using mint = modint998244353;
using comb = Combinatorics<mint>;
int main() {
ll N, K; cin >> N >> K;
mint f = factorial<mint>(N - 1);
mint ans = 0;
if (N <= K + 10) {
rep (i, 1, N) ans += mint{i}.pow(K) * (N - i) * 2 * f;
cout << ans.get() << endl;
return 0;
}
vector<mint> a(K + 3);
rep (i, 1, K + 3) {
a[i] = mint{i}.pow(K) * (N - i) * 2 * f + a[i - 1];
}
cout << sampling_points_shift(a, 1, mint{N})[0].get() << endl;
}