結果
| 問題 | No.2633 Subsequence Combination Score |
| ユーザー |
 shiomusubi496
|
| 提出日時 | 2024-02-16 23:52:22 |
| 言語 | C++17 (gcc 12.3.0 + boost 1.83.0) |
| 結果 |
AC
|
| 実行時間 | 1,862 ms / 2,000 ms |
| コード長 | 62,745 bytes |
| コンパイル時間 | 5,111 ms |
| コンパイル使用メモリ | 271,424 KB |
| 実行使用メモリ | 15,788 KB |
| 最終ジャッジ日時 | 2024-02-16 23:53:02 |
| 合計ジャッジ時間 | 33,220 ms |
|
ジャッジサーバーID （参考情報） |
judge16 / judge14 |
（要ログイン）
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 | 2 ms
6,676 KB |
| testcase_01 | AC | 2 ms
6,676 KB |
| testcase_02 | AC | 4 ms
6,676 KB |
| testcase_03 | AC | 115 ms
9,072 KB |
| testcase_04 | AC | 52 ms
8,924 KB |
| testcase_05 | AC | 53 ms
8,940 KB |
| testcase_06 | AC | 114 ms
9,076 KB |
| testcase_07 | AC | 55 ms
8,948 KB |
| testcase_08 | AC | 33 ms
6,676 KB |
| testcase_09 | AC | 1,212 ms
13,492 KB |
| testcase_10 | AC | 1,149 ms
13,276 KB |
| testcase_11 | AC | 1,172 ms
13,340 KB |
| testcase_12 | AC | 1,128 ms
13,208 KB |
| testcase_13 | AC | 1,131 ms
13,236 KB |
| testcase_14 | AC | 1,128 ms
13,204 KB |
| testcase_15 | AC | 1,187 ms
13,440 KB |
| testcase_16 | AC | 1,139 ms
13,268 KB |
| testcase_17 | AC | 1,104 ms
13,196 KB |
| testcase_18 | AC | 1,100 ms
13,204 KB |
| testcase_19 | AC | 78 ms
9,648 KB |
| testcase_20 | AC | 35 ms
6,676 KB |
| testcase_21 | AC | 34 ms
6,676 KB |
| testcase_22 | AC | 33 ms
6,676 KB |
| testcase_23 | AC | 33 ms
6,676 KB |
| testcase_24 | AC | 32 ms
6,676 KB |
| testcase_25 | AC | 33 ms
6,676 KB |
| testcase_26 | AC | 33 ms
6,676 KB |
| testcase_27 | AC | 33 ms
6,676 KB |
| testcase_28 | AC | 32 ms
6,676 KB |
| testcase_29 | AC | 2 ms
6,676 KB |
| testcase_30 | AC | 3 ms
6,676 KB |
| testcase_31 | AC | 2 ms
6,676 KB |
| testcase_32 | AC | 2 ms
6,676 KB |
| testcase_33 | AC | 1,836 ms
15,788 KB |
| testcase_34 | AC | 1,862 ms
15,788 KB |
| testcase_35 | AC | 1,835 ms
15,788 KB |
| testcase_36 | AC | 1,859 ms
15,788 KB |
| testcase_37 | AC | 1,823 ms
15,720 KB |
| testcase_38 | AC | 1,797 ms
15,648 KB |
| testcase_39 | AC | 1,799 ms
15,580 KB |
| testcase_40 | AC | 1,777 ms
15,508 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>
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"
#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 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 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)...));
}
#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
*/
#line 2 "library/math/poly/FormalPowerSeries.hpp"
#line 2 "library/math/convolution/Convolution.hpp"
#line 2 "library/math/PrimitiveRoot.hpp"
#line 2 "library/random/Random.hpp"
#line 4 "library/random/Random.hpp"
template<class Engine> class Random {
private:
Engine rnd;
public:
using result_type = typename Engine::result_type;
Random() : Random(std::random_device{}()) {}
Random(result_type seed) : rnd(seed) {}
result_type operator()() { return rnd(); }
template<class IntType = ll> IntType uniform(IntType l, IntType r) {
static_assert(std::is_integral<IntType>::value,
"template argument must be an integral type");
assert(l <= r);
return std::uniform_int_distribution<IntType>{l, r}(rnd);
}
template<class RealType = double>
RealType uniform_real(RealType l, RealType r) {
static_assert(std::is_floating_point<RealType>::value,
"template argument must be an floating point type");
assert(l <= r);
return std::uniform_real_distribution<RealType>{l, r}(rnd);
}
bool uniform_bool() { return uniform<int>(0, 1) == 1; }
template<class T = ll> std::pair<T, T> uniform_pair(T l, T r) {
assert(l < r);
T a, b;
do {
a = uniform<T>(l, r);
b = uniform<T>(l, r);
} while (a == b);
if (a > b) swap(a, b);
return {a, b};
}
template<class T = ll> std::vector<T> choice(int n, T l, T r) {
assert(l <= r);
assert(T(n) <= (r - l + 1));
std::set<T> res;
while ((int)res.size() < n) res.insert(uniform<T>(l, r));
return {res.begin(), res.end()};
}
template<class Iter> void shuffle(const Iter& first, const Iter& last) {
std::shuffle(first, last, rnd);
}
template<class T> std::vector<T> permutation(T n) {
std::vector<T> res(n);
rep (i, n) res[i] = i;
shuffle(all(res));
return res;
}
template<class T = ll>
std::vector<T> choice_shuffle(int n, T l, T r, bool sorted = true) {
assert(l <= r);
assert(T(n) <= (r - l + 1));
std::vector<T> res(r - l + 1);
rep (i, l, r + 1) res[i - l] = i;
shuffle(all(res));
res.erase(res.begin() + n, res.end());
if (sorted) sort(all(res));
return res;
}
};
using Random32 = Random<std::mt19937>;
Random32 rand32;
using Random64 = Random<std::mt19937_64>;
Random64 rand64;
/**
* @brief Random
* @docs docs/random/Random.md
*/
#line 2 "library/math/MontgomeryModInt.hpp"
#line 4 "library/math/MontgomeryModInt.hpp"
template<class T> class MontgomeryReduction {
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;
static constexpr int lg = std::numeric_limits<T>::digits;
T mod;
T r;
T r2; // r^2 mod m
T calc_minv() {
T t = 0, res = 0;
rep (i, lg) {
if (~t & 1) {
t += mod;
res += static_cast<T>(1) << i;
}
t >>= 1;
}
return res;
}
T minv;
public:
MontgomeryReduction(T v) { set_mod(v); }
static constexpr int get_lg() { return lg; }
void set_mod(T v) {
assert(v > 0);
assert(v & 1);
assert(v <= std::numeric_limits<T>::max() / 2);
mod = v;
r = (-static_cast<T>(mod)) % mod;
r2 = (-static_cast<large_t>(mod)) % mod;
minv = calc_minv();
}
inline T get_mod() const { return mod; }
inline T get_r() const { return r; }
T reduce(large_t x) const {
large_t tmp =
(x + static_cast<large_t>(static_cast<T>(x) * minv) * mod) >> lg;
return tmp >= mod ? tmp - mod : tmp;
}
T transform(large_t x) const { return reduce(x * r2); }
};
template<class T, int id> class MontgomeryModInt {
private:
using large_t = typename double_size_uint<T>::type;
using signed_t = typename std::make_signed<T>::type;
T val;
static MontgomeryReduction<T> mont;
public:
MontgomeryModInt() : val(0) {}
template<class U, typename std::enable_if<
std::is_integral<U>::value &&
std::is_unsigned<U>::value>::type* = nullptr>
MontgomeryModInt(U x)
: val(mont.transform(
x < (static_cast<large_t>(mont.get_mod()) << mont.get_lg())
? x
: x % mont.get_mod())) {}
template<class U,
typename std::enable_if<std::is_integral<U>::value &&
std::is_signed<U>::value>::type* = nullptr>
MontgomeryModInt(U x)
: MontgomeryModInt(static_cast<typename std::make_unsigned<U>::type>(
x < 0 ? -x : x)) {
if (x < 0 && val) val = mont.get_mod() - val;
}
T get() const { return mont.reduce(val); }
static T get_mod() { return mont.get_mod(); }
static void set_mod(T v) { mont.set_mod(v); }
MontgomeryModInt operator+() const { return *this; }
MontgomeryModInt operator-() const {
MontgomeryModInt res;
if (val) res.val = mont.get_mod() - val;
return res;
}
MontgomeryModInt& operator++() {
val += mont.get_r();
if (val >= mont.get_mod()) val -= mont.get_mod();
return *this;
}
MontgomeryModInt& operator--() {
if (val < mont.get_r()) val += mont.get_mod();
val -= mont.get_r();
return *this;
}
MontgomeryModInt operator++(int) {
MontgomeryModInt res = *this;
++*this;
return res;
}
MontgomeryModInt operator--(int) {
MontgomeryModInt res = *this;
--*this;
return res;
}
MontgomeryModInt& operator+=(const MontgomeryModInt& rhs) {
val += rhs.val;
if (val >= mont.get_mod()) val -= mont.get_mod();
return *this;
}
MontgomeryModInt& operator-=(const MontgomeryModInt& rhs) {
if (val < rhs.val) val += mont.get_mod();
val -= rhs.val;
return *this;
}
MontgomeryModInt& operator*=(const MontgomeryModInt& rhs) {
val = mont.reduce(static_cast<large_t>(val) * rhs.val);
return *this;
}
MontgomeryModInt pow(ull n) const {
MontgomeryModInt res = 1, x = *this;
while (n) {
if (n & 1) res *= x;
x *= x;
n >>= 1;
}
return res;
}
MontgomeryModInt inv() const { return pow(mont.get_mod() - 2); }
MontgomeryModInt& operator/=(const MontgomeryModInt& rhs) {
return *this *= rhs.inv();
}
friend MontgomeryModInt operator+(const MontgomeryModInt& lhs,
const MontgomeryModInt& rhs) {
return MontgomeryModInt(lhs) += rhs;
}
friend MontgomeryModInt operator-(const MontgomeryModInt& lhs,
const MontgomeryModInt& rhs) {
return MontgomeryModInt(lhs) -= rhs;
}
friend MontgomeryModInt operator*(const MontgomeryModInt& lhs,
const MontgomeryModInt& rhs) {
return MontgomeryModInt(lhs) *= rhs;
}
friend MontgomeryModInt operator/(const MontgomeryModInt& lhs,
const MontgomeryModInt& rhs) {
return MontgomeryModInt(lhs) /= rhs;
}
friend bool operator==(const MontgomeryModInt& lhs,
const MontgomeryModInt& rhs) {
return lhs.val == rhs.val;
}
friend bool operator!=(const MontgomeryModInt& lhs,
const MontgomeryModInt& rhs) {
return lhs.val != rhs.val;
}
template<class Pr> void print(Pr& a) const { a.print(mont.reduce(val)); }
template<class Pr> void debug(Pr& a) const { a.print(mont.reduce(val)); }
template<class Sc> void scan(Sc& a) {
ll v;
a.scan(v);
*this = v;
}
};
template<class T, int id>
MontgomeryReduction<T>
MontgomeryModInt<T, id>::mont = MontgomeryReduction<T>(998244353);
using mmodint = MontgomeryModInt<unsigned int, -1>;
/**
* @brief MontgomeryModInt(モンゴメリ乗算)
* @docs docs/math/MontgomeryModInt.md
*/
#line 2 "library/math/MillerRabin.hpp"
#line 5 "library/math/MillerRabin.hpp"
constexpr ull base_miller_rabin_int[3] = {2, 7, 61};
constexpr ull base_miller_rabin_ll[7] = {2, 325, 9375, 28178,
450775, 9780504, 1795265022};
template<class T> CONSTEXPR bool miller_rabin(ull n, const ull base[], int s) {
if (T::get_mod() != n) T::set_mod(n);
ull d = n - 1;
while (~d & 1) d >>= 1;
T e{1}, re{n - 1};
rep (i, s) {
ull a = base[i];
if (a >= n) return true;
ull t = d;
T y = T(a).pow(t);
while (t != n - 1 && y != e && y != re) {
y *= y;
t <<= 1;
}
if (y != re && !(t & 1)) return false;
}
return true;
}
CONSTEXPR bool is_prime_mr(ll n) {
if (n == 2) return true;
if (n < 2 || n % 2 == 0) return false;
if (n < (1u << 31))
return miller_rabin<MontgomeryModInt<unsigned int, -2>>(
n, base_miller_rabin_int, 3);
return miller_rabin<MontgomeryModInt<ull, -2>>(n, base_miller_rabin_ll, 7);
}
#if __cpp_variable_templates >= 201304L && __cpp_constexpr >= 201304L
template<ull n> constexpr bool is_prime_v = is_prime_mr(n);
#endif
/**
* @brief MillerRabin(ミラーラビン素数判定)
* @docs docs/math/MillerRabin.md
*/
#line 2 "library/math/PollardRho.hpp"
#line 2 "library/string/RunLength.hpp"
#line 4 "library/string/RunLength.hpp"
template<class Cont, class Comp>
std::vector<std::pair<typename Cont::value_type, int>>
RunLength(const Cont& str, const Comp& cmp) {
std::vector<std::pair<typename Cont::value_type, int>> res;
if (str.size() == 0) return res;
res.emplace_back(str[0], 1);
rep (i, 1, str.size()) {
if (cmp(res.back().first, str[i])) ++res.back().second;
else res.emplace_back(str[i], 1);
}
return res;
}
template<class Cont>
std::vector<std::pair<typename Cont::value_type, int>>
RunLength(const Cont& str) {
return RunLength(str, std::equal_to<typename Cont::value_type>());
}
/**
* @brief RunLength(ランレングス圧縮)
* @docs docs/string/RunLength.md
*/
#line 8 "library/math/PollardRho.hpp"
template<class T, class Rnd> ull pollard_rho(ull n, Rnd& rnd) {
if (~n & 1) return 2;
if (T::get_mod() != n) T::set_mod(n);
T c, one = 1;
auto f = [&](T x) -> T { return x * x + c; };
constexpr int M = 128;
while (1) {
c = rnd.uniform(1ull, n - 1);
T x = rnd.uniform(2ull, n - 1), y = x;
ull g = 1;
while (g == 1) {
T p = one, tx = x, ty = y;
rep (M) {
x = f(x);
y = f(f(y));
p *= x - y;
}
g = gcd(p.get(), n);
if (g == 1) continue;
rep (M) {
tx = f(tx);
ty = f(f(ty));
g = gcd((tx - ty).get(), n);
if (g != 1) {
if (g != n) return g;
break;
}
}
}
}
return -1;
}
template<class T = MontgomeryModInt<ull, -3>, class Rnd = Random64>
std::vector<ull> factorize(ull n, Rnd& rnd = rand64) {
if (n == 1) return {};
std::vector<ull> res;
std::vector<ull> st = {n};
while (!st.empty()) {
ull t = st.back();
st.pop_back();
if (t == 1) continue;
if (is_prime_mr(t)) {
res.push_back(t);
continue;
}
ull f = pollard_rho<T>(t, rnd);
st.push_back(f);
st.push_back(t / f);
}
std::sort(all(res));
return res;
}
template<class T = MontgomeryModInt<ull, -3>, class Rnd = Random64>
std::vector<std::pair<ull, int>> expfactorize(ull n, Rnd& rnd = rand64) {
auto f = factorize<T, Rnd>(n, rnd);
return RunLength(f);
}
/**
* @brief PollardRho(素因数分解)
* @docs docs/math/PollardRho.md
*/
#line 9 "library/math/PrimitiveRoot.hpp"
template<class T = MontgomeryModInt<ull, -4>> ull primitive_root(ull p) {
assert(is_prime_mr(p));
if (p == 2) return 1;
if (T::get_mod() != p) T::set_mod(p);
auto pf = factorize(p - 1);
pf.erase(std::unique(all(pf)), pf.end());
each_for (x : pf) x = (p - 1) / x;
T one = 1;
while (1) {
ull g = rand64.uniform(2ull, p - 1);
bool ok = true;
each_const (x : pf) {
if (T(g).pow(x) == one) {
ok = false;
break;
}
}
if (ok) return g;
}
}
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::msb(n - 1) + 1;
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/SqrtMod.hpp"
#line 5 "library/math/SqrtMod.hpp"
template<class T> ll sqrt_mod(ll a) {
const ll p = T::get_mod();
if (p == 2) return a;
if (a == 0) return 0;
if (T{a}.pow((p - 1) >> 1) != 1) return -1;
T b = 2;
while (T{b}.pow((p - 1) >> 1) == 1) ++b;
ll s = 0, t = p - 1;
while ((t & 1) == 0) t >>= 1, ++s;
T x = T{a}.pow((t + 1) >> 1);
T w = T{a}.pow(t);
T v = T{b}.pow(t);
while (w != 1) {
ll k = 0;
T y = w;
while (y != 1) {
y *= y;
++k;
}
T z = v;
rep (s - k - 1) z *= z;
x *= z;
w *= z * z;
}
return std::min<ll>(x.get(), p - x.get());
}
ll sqrt_mod(ll a, ll p) {
if (p == 2) return a;
using mint = MontgomeryModInt<unsigned int, 493174342>;
mint::set_mod(p);
return sqrt_mod<mint>(a);
}
/**
* @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);
}
FormalPowerSeries log(int deg = -1) const {
assert(this->size() > 0 && (*this)[0] == 1);
if (deg == -1) deg = this->size();
return (diff() * inv(deg)).prefix(deg - 1).integral();
}
template<bool AlwaysTrue = true,
typename std::enable_if<
AlwaysTrue && is_ntt_friendly<T::get_mod()>::value>::type* =
nullptr>
FormalPowerSeries exp(int deg = -1) const {
assert(this->size() > 0 && (*this)[0] == 0);
if (deg == -1) deg = this->size();
FormalPowerSeries f(1, 1);
FormalPowerSeries g(1, 1);
FormalPowerSeries dft_f(1, 1);
for (int m = 1; m < deg; m <<= 1) {
FormalPowerSeries q = prefix(m).diff();
q.resize(m);
number_theoretic_transform(q);
rep (i, m) q[i] *= dft_f[i];
inverse_number_theoretic_transform(q);
FormalPowerSeries s = f.diff();
s.resize(m);
rep (i, m) s[i] -= q[i];
s.insert(s.begin(), (T)s.back());
s.pop_back();
FormalPowerSeries dft_g = g;
s.resize(2 * m);
dft_g.resize(2 * m);
number_theoretic_transform(s);
number_theoretic_transform(dft_g);
rep (i, 2 * m) s[i] *= dft_g[i];
inverse_number_theoretic_transform(s);
FormalPowerSeries u =
(prefix(2 * m) - (s.prefix(m) << (m - 1)).integral()) >> m;
u.resize(2 * m);
FormalPowerSeries dft_f_2 = f;
dft_f_2.resize(2 * m);
number_theoretic_transform(u);
number_theoretic_transform(dft_f_2);
rep (i, 2 * m) u[i] *= dft_f_2[i];
inverse_number_theoretic_transform(u);
f = f + (u.prefix(m) << m);
if (2 * m < deg) {
g.resize(2 * m);
FormalPowerSeries dft_g_2 = g;
FormalPowerSeries dft_f_2 = f;
number_theoretic_transform(dft_g_2);
number_theoretic_transform(dft_f_2);
dft_f = dft_f_2;
rep (i, 2 * m) dft_f_2[i] *= dft_g_2[i];
inverse_number_theoretic_transform(dft_f_2);
std::fill(dft_f_2.begin(), dft_f_2.begin() + m, T{0});
number_theoretic_transform(dft_f_2);
rep (i, 2 * m) dft_f_2[i] *= dft_g_2[i];
inverse_number_theoretic_transform(dft_f_2);
rep (i, m, 2 * m) g[i] = -dft_f_2[i];
}
}
return f.prefix(deg);
}
template<bool AlwaysTrue = true,
typename std::enable_if<
AlwaysTrue && !is_ntt_friendly<T::get_mod()>::value>::type* =
nullptr>
FormalPowerSeries exp(int deg = -1) const {
assert(this->size() > 0 && (*this)[0] == 0);
if (deg == -1) deg = this->size();
FormalPowerSeries res(1, 1);
for (int m = 1; m < deg; m <<= 1) {
res = (res * (prefix(2 * m) - res.log(2 * m)) + res).prefix(2 * m);
}
return res.prefix(deg);
}
FormalPowerSeries pow(ll k, int deg = -1) const {
if (deg == -1) deg = this->size();
if (deg == 0) return {};
if (k == 0) {
FormalPowerSeries res(deg);
res[0] = 1;
return res;
}
if (k == 1) return prefix(deg);
if (k == 2) return (*this * *this).prefix(deg);
T a;
int d = -1;
rep (i, this->size()) {
if ((*this)[i] != 0) {
a = (*this)[i];
d = i;
break;
}
}
if (d == -1) {
FormalPowerSeries res(deg);
return res;
}
if ((i128)(d)*k >= deg) {
FormalPowerSeries res(deg);
return res;
}
deg -= d * k;
FormalPowerSeries res = (((*this >> d) / a).log(deg) * k).exp(deg);
res *= a.pow(k);
res <<= d * k;
return res;
}
FormalPowerSeries sqrt(int deg = -1) const {
if (deg == -1) deg = this->size();
T a;
int d = -1;
rep (i, this->size()) {
if ((*this)[i] != 0) {
a = (*this)[i];
d = i;
break;
}
}
if (d == -1) {
FormalPowerSeries res(deg);
return res;
}
if (d & 1) return {};
deg -= (d >> 1);
if (deg <= 0) {
FormalPowerSeries res(deg);
return res;
}
FormalPowerSeries f = (*this >> d);
T sq = sqrt_mod<T>(a.get());
if (sq == -1) return {};
FormalPowerSeries g(1, sq);
for (int m = 1; m < deg; m <<= 1) {
g = (g + (f.prefix(2 * m) * g.inv(2 * m)).prefix(2 * m)) / 2;
}
g.resize(deg);
return g << (d >> 1);
}
FormalPowerSeries compose(FormalPowerSeries g, int deg = -1) const {
if (this->empty()) return {};
if (g.empty()) return {(*this)[0]};
assert(g[0] == 0);
int n = deg == -1 ? this->size() : deg;
int m = 1 << (bitop::ceil_log2(std::max<int>(1, std::sqrt(n / std::log2(n)))) + 1);
FormalPowerSeries p = g.prefix(m), q = g >> m;
p.shrink();
q.shrink();
int l = (n + m - 1) / m;
std::vector<FormalPowerSeries> fs(this->size());
rep (i, this->size()) fs[i] = FormalPowerSeries{(*this)[i]};
FormalPowerSeries pd = p.diff();
int z = 0;
while (z < (int)pd.size() && pd[z] == T{0}) z++;
if (z == (int)pd.size()) {
FormalPowerSeries ans;
rrep (i, l) {
ans = ((ans * q) << m).prefix(n - i * m) + FormalPowerSeries{(*this)[i]};
}
return ans;
}
pd = (pd >> z).inv(n);
FormalPowerSeries t = p;
for (int k = 1; fs.size() > 1; k <<= 1) {
std::vector<FormalPowerSeries> nfs((fs.size() + 1) / 2);
t.resize(1 << (bitop::ceil_log2(t.size()) + 1));
number_theoretic_transform(t);
rep (i, fs.size() / 2) {
nfs[i] = std::move(fs[2 * i]);
fs[2 * i + 1].resize(t.size());
number_theoretic_transform(fs[2 * i + 1]);
rep (j, t.size()) fs[2 * i + 1][j] *= t[j];
inverse_number_theoretic_transform(fs[2 * i + 1]);
if ((int)fs[2 * i + 1].size() > n) fs[2 * i + 1].resize(n);
nfs[i] += fs[2 * i + 1];
}
if (fs.size() & 1) nfs.back() = std::move(fs.back());
fs = std::move(nfs);
if (fs.size() > 1) {
rep (i, t.size()) t[i] *= t[i];
inverse_number_theoretic_transform(t);
if ((int)t.size() > n) t.resize(n);
}
}
FormalPowerSeries fp = fs[0].prefix(n);
FormalPowerSeries res = fp;
int n2 = 1 << (bitop::ceil_log2(n) + 1);
FormalPowerSeries qpow(n2);
qpow[0] = 1;
q.resize(n2);
number_theoretic_transform(q);
pd.resize(n2);
number_theoretic_transform(pd);
rep (i, 1, l) {
if ((n - i * m) * 4 <= n2) {
while ((n - i * m) * 4 <= n2) {
n2 /= 2;
}
inverse_number_theoretic_transform(q);
q.resize(n - i * m);
q.resize(n2);
number_theoretic_transform(q);
inverse_number_theoretic_transform(pd);
pd.resize(n - i * m);
pd.resize(n2);
number_theoretic_transform(pd);
}
qpow.resize(n - i * m);
qpow.resize(n2);
number_theoretic_transform(qpow);
rep (j, n2) qpow[j] *= q[j];
inverse_number_theoretic_transform(qpow);
qpow.resize(n - i * m);
fp = fp.diff() >> z;
fp.resize(n - i * m);
fp.resize(n2);
number_theoretic_transform(fp);
rep (j, n2) fp[j] *= pd[j];
inverse_number_theoretic_transform(fp);
fp.resize(n - i * m);
res += ((qpow * fp).prefix(n - i * m) * Comb::finv(i)) << (i * m);
}
return res;
}
FormalPowerSeries compinv(int deg = -1) const {
assert(this->size() >= 2 && (*this)[0] == 0 && (*this)[1] != 0);
if (deg == -1) deg = this->size();
FormalPowerSeries fd = diff();
FormalPowerSeries x{0, 1};
FormalPowerSeries res{0, (*this)[1].inv()};
for (int m = 2; m < deg; m <<= 1) {
auto tmp = prefix(2 * m).compose(res);
auto d = tmp.diff();
auto gd = res.diff();
res -= ((tmp - x) * (d.inv(2 * m) * gd).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 5 "main.cpp"
using namespace std;
using mint = modint998244353;
using comb = Combinatorics<mint>;
using fps = FormalPowerSeries<mint>;
int main() {
int N; cin >> N;
vector<ll> A(N);
rep (i, N) cin >> A[i];
map<ll, ll, greater<ll>> mp;
for (auto x : A) ++mp[x];
int M = A[0] + 1;
mint sm = 0;
fps B(M);
fps f(M);
vector<pair<ll, mint>> C;
int i = 0;
for (auto [a, b] : mp) {
if ((++i) % 1500 == 0) {
f += taylor_shift(B, mint{1});
B.assign(a + 1, 0);
C.clear();
}
mint t = f[a] + 1;
for (auto [c, d] : C) t += comb::comb(c, a) * d;
t *= mint{2}.pow(b) - 1;
sm += t;
B[a] += t;
C.emplace_back(a, t);
}
cout << sm.get() << endl;
}