結果
| 問題 | No.2801 Unique Maximum |
| ユーザー |
 noya2
|
| 提出日時 | 2024-08-23 01:50:54 |
| 言語 | C++23 (gcc 12.3.0 + boost 1.83.0) |
| 結果 |
AC
|
| 実行時間 | 1,410 ms / 4,000 ms |
| コード長 | 39,556 bytes |
| コンパイル時間 | 4,469 ms |
| コンパイル使用メモリ | 275,984 KB |
| 実行使用メモリ | 18,324 KB |
| 最終ジャッジ日時 | 2024-08-23 01:51:17 |
| 合計ジャッジ時間 | 21,198 ms |
|
ジャッジサーバーID （参考情報） |
judge5 / judge3 |
（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 | 7 ms
6,816 KB |
| testcase_01 | AC | 8 ms
6,940 KB |
| testcase_02 | AC | 327 ms
9,148 KB |
| testcase_03 | AC | 6 ms
6,940 KB |
| testcase_04 | AC | 8 ms
6,944 KB |
| testcase_05 | AC | 9 ms
6,940 KB |
| testcase_06 | AC | 8 ms
6,944 KB |
| testcase_07 | AC | 1,385 ms
18,324 KB |
| testcase_08 | AC | 1,395 ms
18,316 KB |
| testcase_09 | AC | 6 ms
6,944 KB |
| testcase_10 | AC | 1,369 ms
18,160 KB |
| testcase_11 | AC | 1,410 ms
18,324 KB |
| testcase_12 | AC | 1,409 ms
18,196 KB |
| testcase_13 | AC | 1,352 ms
18,192 KB |
| testcase_14 | AC | 1,382 ms
18,192 KB |
| testcase_15 | AC | 8 ms
6,940 KB |
| testcase_16 | AC | 7 ms
6,940 KB |
| testcase_17 | AC | 8 ms
6,944 KB |
| testcase_18 | AC | 526 ms
10,988 KB |
| testcase_19 | AC | 568 ms
11,184 KB |
| testcase_20 | AC | 605 ms
11,592 KB |
| testcase_21 | AC | 1,319 ms
17,328 KB |
| testcase_22 | AC | 1,137 ms
15,924 KB |
| testcase_23 | AC | 1,342 ms
17,776 KB |
ソースコード
#line 2 "/Users/noya2/Desktop/Noya2_library/template/template.hpp"
using namespace std;
#include<bits/stdc++.h>
#line 1 "/Users/noya2/Desktop/Noya2_library/template/inout_old.hpp"
namespace noya2 {
template <typename T, typename U>
ostream &operator<<(ostream &os, const pair<T, U> &p){
os << p.first << " " << p.second;
return os;
}
template <typename T, typename U>
istream &operator>>(istream &is, pair<T, U> &p){
is >> p.first >> p.second;
return is;
}
template <typename T>
ostream &operator<<(ostream &os, const vector<T> &v){
int s = (int)v.size();
for (int i = 0; i < s; i++) os << (i ? " " : "") << v[i];
return os;
}
template <typename T>
istream &operator>>(istream &is, vector<T> &v){
for (auto &x : v) is >> x;
return is;
}
void in() {}
template <typename T, class... U>
void in(T &t, U &...u){
cin >> t;
in(u...);
}
void out() { cout << "\n"; }
template <typename T, class... U, char sep = ' '>
void out(const T &t, const U &...u){
cout << t;
if (sizeof...(u)) cout << sep;
out(u...);
}
template<typename T>
void out(const vector<vector<T>> &vv){
int s = (int)vv.size();
for (int i = 0; i < s; i++) out(vv[i]);
}
struct IoSetup {
IoSetup(){
cin.tie(nullptr);
ios::sync_with_stdio(false);
cout << fixed << setprecision(15);
cerr << fixed << setprecision(7);
}
} iosetup_noya2;
} // namespace noya2
#line 1 "/Users/noya2/Desktop/Noya2_library/template/const.hpp"
namespace noya2{
const int iinf = 1'000'000'007;
const long long linf = 2'000'000'000'000'000'000LL;
const long long mod998 = 998244353;
const long long mod107 = 1000000007;
const long double pi = 3.14159265358979323;
const vector<int> dx = {0,1,0,-1,1,1,-1,-1};
const vector<int> dy = {1,0,-1,0,1,-1,-1,1};
const string ALP = "ABCDEFGHIJKLMNOPQRSTUVWXYZ";
const string alp = "abcdefghijklmnopqrstuvwxyz";
const string NUM = "0123456789";
void yes(){ cout << "Yes\n"; }
void no(){ cout << "No\n"; }
void YES(){ cout << "YES\n"; }
void NO(){ cout << "NO\n"; }
void yn(bool t){ t ? yes() : no(); }
void YN(bool t){ t ? YES() : NO(); }
} // namespace noya2
#line 2 "/Users/noya2/Desktop/Noya2_library/template/utils.hpp"
#line 6 "/Users/noya2/Desktop/Noya2_library/template/utils.hpp"
namespace noya2{
unsigned long long inner_binary_gcd(unsigned long long a, unsigned long long b){
if (a == 0 || b == 0) return a + b;
int n = __builtin_ctzll(a); a >>= n;
int m = __builtin_ctzll(b); b >>= m;
while (a != b) {
int mm = __builtin_ctzll(a - b);
bool f = a > b;
unsigned long long c = f ? a : b;
b = f ? b : a;
a = (c - b) >> mm;
}
return a << std::min(n, m);
}
template<typename T> T gcd_fast(T a, T b){ return static_cast<T>(inner_binary_gcd(std::abs(a),std::abs(b))); }
long long sqrt_fast(long long n) {
if (n <= 0) return 0;
long long x = sqrt(n);
while ((x + 1) * (x + 1) <= n) x++;
while (x * x > n) x--;
return x;
}
template<typename T> T floor_div(const T n, const T d) {
assert(d != 0);
return n / d - static_cast<T>((n ^ d) < 0 && n % d != 0);
}
template<typename T> T ceil_div(const T n, const T d) {
assert(d != 0);
return n / d + static_cast<T>((n ^ d) >= 0 && n % d != 0);
}
template<typename T> void uniq(std::vector<T> &v){
std::sort(v.begin(),v.end());
v.erase(unique(v.begin(),v.end()),v.end());
}
template <typename T, typename U> inline bool chmin(T &x, U y) { return (y < x) ? (x = y, true) : false; }
template <typename T, typename U> inline bool chmax(T &x, U y) { return (x < y) ? (x = y, true) : false; }
template<typename T> inline bool range(T l, T x, T r){ return l <= x && x < r; }
} // namespace noya2
#line 8 "/Users/noya2/Desktop/Noya2_library/template/template.hpp"
#define rep(i,n) for (int i = 0; i < (int)(n); i++)
#define repp(i,m,n) for (int i = (m); i < (int)(n); i++)
#define reb(i,n) for (int i = (int)(n-1); i >= 0; i--)
#define all(v) (v).begin(),(v).end()
using ll = long long;
using ld = long double;
using uint = unsigned int;
using ull = unsigned long long;
using pii = pair<int,int>;
using pll = pair<ll,ll>;
using pil = pair<int,ll>;
using pli = pair<ll,int>;
namespace noya2{
/* ~ (. _________ . /) */
}
using namespace noya2;
#line 2 "c.cpp"
#line 2 "/Users/noya2/Desktop/Noya2_library/fps998244353/fps998244353.hpp"
#line 2 "/Users/noya2/Desktop/Noya2_library/utility/modint.hpp"
#line 4 "/Users/noya2/Desktop/Noya2_library/utility/modint.hpp"
#line 2 "/Users/noya2/Desktop/Noya2_library/math/prime.hpp"
#line 4 "/Users/noya2/Desktop/Noya2_library/math/prime.hpp"
namespace noya2 {
constexpr long long safe_mod(long long x, long long m) {
x %= m;
if (x < 0) x += m;
return x;
}
constexpr long long pow_mod_constexpr(long long x, long long n, int m) {
if (m == 1) return 0;
unsigned int _m = (unsigned int)(m);
unsigned long long r = 1;
unsigned long long y = safe_mod(x, m);
while (n) {
if (n & 1) r = (r * y) % _m;
y = (y * y) % _m;
n >>= 1;
}
return r;
}
constexpr bool is_prime_constexpr(int n) {
if (n <= 1) return false;
if (n == 2 || n == 7 || n == 61) return true;
if (n % 2 == 0) return false;
long long d = n - 1;
while (d % 2 == 0) d /= 2;
constexpr long long bases[3] = {2, 7, 61};
for (long long a : bases) {
long long t = d;
long long y = pow_mod_constexpr(a, t, n);
while (t != n - 1 && y != 1 && y != n - 1) {
y = y * y % n;
t <<= 1;
}
if (y != n - 1 && t % 2 == 0) {
return false;
}
}
return true;
}
template <int n> constexpr bool is_prime_flag = is_prime_constexpr(n);
constexpr std::pair<long long, long long> inv_gcd(long long a, long long b) {
a = safe_mod(a, b);
if (a == 0) return {b, 0};
long long s = b, t = a;
long long m0 = 0, m1 = 1;
while (t) {
long long u = s / t;
s -= t * u;
m0 -= m1 * u;
auto tmp = s;
s = t;
t = tmp;
tmp = m0;
m0 = m1;
m1 = tmp;
}
if (m0 < 0) m0 += b / s;
return {s, m0};
}
constexpr int primitive_root_constexpr(int m) {
if (m == 2) return 1;
if (m == 167772161) return 3;
if (m == 469762049) return 3;
if (m == 754974721) return 11;
if (m == 998244353) return 3;
int divs[20] = {};
divs[0] = 2;
int cnt = 1;
int x = (m - 1) / 2;
while (x % 2 == 0) x /= 2;
for (int i = 3; (long long)(i)*i <= x; i += 2) {
if (x % i == 0) {
divs[cnt++] = i;
while (x % i == 0) {
x /= i;
}
}
}
if (x > 1) {
divs[cnt++] = x;
}
for (int g = 2;; g++) {
bool ok = true;
for (int i = 0; i < cnt; i++) {
if (pow_mod_constexpr(g, (m - 1) / divs[i], m) == 1) {
ok = false;
break;
}
}
if (ok) return g;
}
}
template <int m> constexpr int primitive_root_flag = primitive_root_constexpr(m);
constexpr long long primitive_root_constexpr(long long m){
if (m == (1LL << 47) - (1LL << 24) + 1) return 3;
return primitive_root_constexpr(static_cast<int>(m));
}
} // namespace noya2
#line 6 "/Users/noya2/Desktop/Noya2_library/utility/modint.hpp"
namespace noya2{
struct barrett {
unsigned int _m;
unsigned long long im;
explicit barrett(unsigned int m) : _m(m), im((unsigned long long)(-1) / m + 1) {}
unsigned int umod() const { return _m; }
unsigned int mul(unsigned int a, unsigned int b) const {
unsigned long long z = a;
z *= b;
unsigned long long x = (unsigned long long)((__uint128_t(z) * im) >> 64);
unsigned int v = (unsigned int)(z - x * _m);
if (_m <= v) v += _m;
return v;
}
};
template <int m>
struct static_modint {
using mint = static_modint;
public:
static constexpr int mod() { return m; }
static mint raw(int v) {
mint x;
x._v = v;
return x;
}
constexpr static_modint() : _v(0) {}
template<std::signed_integral T>
constexpr static_modint(T v){
long long x = (long long)(v % (long long)(umod()));
if (x < 0) x += umod();
_v = (unsigned int)(x);
}
template<std::unsigned_integral T>
constexpr static_modint(T v){
_v = (unsigned int)(v % umod());
}
constexpr unsigned int val() const { return _v; }
mint& operator++() {
_v++;
if (_v == umod()) _v = 0;
return *this;
}
mint& operator--() {
if (_v == 0) _v = umod();
_v--;
return *this;
}
mint operator++(int) {
mint result = *this;
++*this;
return result;
}
mint operator--(int) {
mint result = *this;
--*this;
return result;
}
constexpr mint& operator+=(const mint& rhs) {
_v += rhs._v;
if (_v >= umod()) _v -= umod();
return *this;
}
constexpr mint& operator-=(const mint& rhs) {
_v -= rhs._v;
if (_v >= umod()) _v += umod();
return *this;
}
constexpr mint& operator*=(const mint& rhs) {
unsigned long long z = _v;
z *= rhs._v;
_v = (uint)(z % umod());
return *this;
}
constexpr mint& operator/=(const mint& rhs) { return *this = *this * rhs.inv(); }
constexpr mint operator+() const { return *this; }
constexpr mint operator-() const { return mint() - *this; }
constexpr mint pow(long long n) const {
assert(0 <= n);
mint x = *this, r = 1;
while (n) {
if (n & 1) r *= x;
x *= x;
n >>= 1;
}
return r;
}
constexpr mint inv() const {
if (prime) {
assert(_v);
return pow(umod() - 2);
} else {
auto eg = inv_gcd(_v, m);
assert(eg.first == 1);
return eg.second;
}
}
friend constexpr mint operator+(const mint& lhs, const mint& rhs) {
return mint(lhs) += rhs;
}
friend constexpr mint operator-(const mint& lhs, const mint& rhs) {
return mint(lhs) -= rhs;
}
friend constexpr mint operator*(const mint& lhs, const mint& rhs) {
return mint(lhs) *= rhs;
}
friend constexpr mint operator/(const mint& lhs, const mint& rhs) {
return mint(lhs) /= rhs;
}
friend constexpr bool operator==(const mint& lhs, const mint& rhs) {
return lhs._v == rhs._v;
}
friend constexpr bool operator!=(const mint& lhs, const mint& rhs) {
return lhs._v != rhs._v;
}
friend std::ostream &operator<<(std::ostream &os, const mint& p) {
return os << p.val();
}
friend std::istream &operator>>(std::istream &is, mint &a) {
long long t; is >> t;
a = mint(t);
return (is);
}
private:
unsigned int _v;
static constexpr unsigned int umod() { return m; }
static constexpr bool prime = is_prime_flag<m>;
};
template <int id> struct dynamic_modint {
using mint = dynamic_modint;
public:
static int mod() { return (int)(bt.umod()); }
static void set_mod(int m) {
assert(1 <= m);
bt = barrett(m);
}
static mint raw(int v) {
mint x;
x._v = v;
return x;
}
dynamic_modint() : _v(0) {}
template<std::signed_integral T>
dynamic_modint(T v){
long long x = (long long)(v % (long long)(umod()));
if (x < 0) x += umod();
_v = (unsigned int)(x);
}
template<std::unsigned_integral T>
dynamic_modint(T v){
_v = (unsigned int)(v % umod());
}
uint val() const { return _v; }
mint& operator++() {
_v++;
if (_v == umod()) _v = 0;
return *this;
}
mint& operator--() {
if (_v == 0) _v = umod();
_v--;
return *this;
}
mint operator++(int) {
mint result = *this;
++*this;
return result;
}
mint operator--(int) {
mint result = *this;
--*this;
return result;
}
mint& operator+=(const mint& rhs) {
_v += rhs._v;
if (_v >= umod()) _v -= umod();
return *this;
}
mint& operator-=(const mint& rhs) {
_v += mod() - rhs._v;
if (_v >= umod()) _v -= umod();
return *this;
}
mint& operator*=(const mint& rhs) {
_v = bt.mul(_v, rhs._v);
return *this;
}
mint& operator/=(const mint& rhs) { return *this = *this * rhs.inv(); }
mint operator+() const { return *this; }
mint operator-() const { return mint() - *this; }
mint pow(long long n) const {
assert(0 <= n);
mint x = *this, r = 1;
while (n) {
if (n & 1) r *= x;
x *= x;
n >>= 1;
}
return r;
}
mint inv() const {
auto eg = noya2::inv_gcd(_v, mod());
assert(eg.first == 1);
return eg.second;
}
friend mint operator+(const mint& lhs, const mint& rhs) {
return mint(lhs) += rhs;
}
friend mint operator-(const mint& lhs, const mint& rhs) {
return mint(lhs) -= rhs;
}
friend mint operator*(const mint& lhs, const mint& rhs) {
return mint(lhs) *= rhs;
}
friend mint operator/(const mint& lhs, const mint& rhs) {
return mint(lhs) /= rhs;
}
friend bool operator==(const mint& lhs, const mint& rhs) {
return lhs._v == rhs._v;
}
friend bool operator!=(const mint& lhs, const mint& rhs) {
return lhs._v != rhs._v;
}
friend std::ostream &operator<<(std::ostream &os, const mint& p) {
return os << p.val();
}
friend std::istream &operator>>(std::istream &is, mint &a) {
long long t; is >> t;
a = mint(t);
return (is);
}
private:
unsigned int _v;
static barrett bt;
static unsigned int umod() { return bt.umod(); }
};
template <int id> noya2::barrett dynamic_modint<id>::bt(998244353);
using modint998244353 = static_modint<998244353>;
using modint1000000007 = static_modint<1000000007>;
using modint = dynamic_modint<-1>;
template<typename T>
concept Modint = requires (T &a){
T::mod();
a.inv();
a.val();
a.pow(declval<int>());
};
} // namespace noya2
#line 4 "/Users/noya2/Desktop/Noya2_library/fps998244353/fps998244353.hpp"
#line 2 "/Users/noya2/Desktop/Noya2_library/fps998244353/ntt998244353.hpp"
#line 2 "/Users/noya2/Desktop/Noya2_library/fps998244353/modint998244353.hpp"
#line 4 "/Users/noya2/Desktop/Noya2_library/fps998244353/modint998244353.hpp"
#line 6 "/Users/noya2/Desktop/Noya2_library/fps998244353/modint998244353.hpp"
namespace noya2 {
template <>
struct static_modint<998244353> {
using mint = static_modint;
public:
static constexpr int mod() { return 998244353; }
static mint raw(int v) {
mint x;
x._v = v;
return x;
}
constexpr static_modint() : _v(0) {}
template<std::signed_integral T>
constexpr static_modint(T v){
long long x = (long long)(v % (long long)(umod()));
if (x < 0) x += umod();
_v = (unsigned int)(x);
}
template<std::unsigned_integral T>
constexpr static_modint(T v){
_v = (unsigned int)(v % umod());
}
constexpr unsigned int val() const { return _v; }
mint& operator++() {
_v++;
if (_v == umod()) _v = 0;
return *this;
}
mint& operator--() {
if (_v == 0) _v = umod();
_v--;
return *this;
}
mint operator++(int) {
mint result = *this;
++*this;
return result;
}
mint operator--(int) {
mint result = *this;
--*this;
return result;
}
constexpr mint& operator+=(const mint& rhs) {
_v += rhs._v;
if (_v >= umod()) _v -= umod();
return *this;
}
constexpr mint& operator-=(const mint& rhs) {
_v -= rhs._v;
if (_v >= umod()) _v += umod();
return *this;
}
constexpr mint& operator*=(const mint& rhs) {
unsigned long long z = _v;
z *= rhs._v;
_v = (unsigned int)(z % umod());
return *this;
}
constexpr mint& operator/=(const mint& rhs) { return *this = *this * rhs.inv(); }
constexpr mint operator+() const { return *this; }
constexpr mint operator-() const { return mint() - *this; }
constexpr mint pow(long long n) const {
assert(0 <= n);
mint x = *this, r = 1;
while (n) {
if (n & 1) r *= x;
x *= x;
n >>= 1;
}
return r;
}
constexpr mint inv() const {
assert(_v);
return pow(umod() - 2);
}
friend constexpr mint operator+(const mint& lhs, const mint& rhs) {
return mint(lhs) += rhs;
}
friend constexpr mint operator-(const mint& lhs, const mint& rhs) {
return mint(lhs) -= rhs;
}
friend constexpr mint operator*(const mint& lhs, const mint& rhs) {
return mint(lhs) *= rhs;
}
friend constexpr mint operator/(const mint& lhs, const mint& rhs) {
return mint(lhs) /= rhs;
}
friend constexpr bool operator==(const mint& lhs, const mint& rhs) {
return lhs._v == rhs._v;
}
friend constexpr bool operator!=(const mint& lhs, const mint& rhs) {
return lhs._v != rhs._v;
}
friend std::ostream &operator<<(std::ostream &os, const mint& p) {
return os << p.val();
}
friend std::istream &operator>>(std::istream &is, mint &a) {
long long t; is >> t;
a = mint(t);
return (is);
}
unsigned int _v;
static constexpr int primitive_root_constexpr_v = 3;
private:
static constexpr unsigned int umod() { return 998244353u; }
static constexpr bool prime = true;
};
} // namespace noya2
#line 4 "/Users/noya2/Desktop/Noya2_library/fps998244353/ntt998244353.hpp"
#line 7 "/Users/noya2/Desktop/Noya2_library/fps998244353/ntt998244353.hpp"
namespace noya2 {
namespace internal {
constexpr int FFT_MAX = 23;
constexpr unsigned FFT_ROOTS[FFT_MAX + 1] = {1U, 998244352U, 911660635U, 372528824U, 929031873U, 452798380U, 922799308U, 781712469U, 476477967U, 166035806U, 258648936U, 584193783U, 63912897U, 350007156U, 666702199U, 968855178U, 629671588U, 24514907U, 996173970U, 363395222U, 565042129U, 733596141U, 267099868U, 15311432U};
constexpr unsigned INV_FFT_ROOTS[FFT_MAX + 1] = {1U, 998244352U, 86583718U, 509520358U, 337190230U, 87557064U, 609441965U, 135236158U, 304459705U, 685443576U, 381598368U, 335559352U, 129292727U, 358024708U, 814576206U, 708402881U, 283043518U, 3707709U, 121392023U, 704923114U, 950391366U, 428961804U, 382752275U, 469870224U};
constexpr unsigned FFT_RATIOS[FFT_MAX] = {911660635U, 509520358U, 369330050U, 332049552U, 983190778U, 123842337U, 238493703U, 975955924U, 603855026U, 856644456U, 131300601U, 842657263U, 730768835U, 942482514U, 806263778U, 151565301U, 510815449U, 503497456U, 743006876U, 741047443U, 56250497U, 867605899U};
constexpr unsigned INV_FFT_RATIOS[FFT_MAX] = {86583718U, 372528824U, 373294451U, 645684063U, 112220581U, 692852209U, 155456985U, 797128860U, 90816748U, 860285882U, 927414960U, 354738543U, 109331171U, 293255632U, 535113200U, 308540755U, 121186627U, 608385704U, 438932459U, 359477183U, 824071951U, 103369235U};
} // namespace noya2::internal
struct ntt998244353 {
using mint = modint998244353;
static constexpr unsigned MO = modint998244353::mod();
static constexpr unsigned MO2 = MO * 2;
static void ntt(mint *as, int n){
int m = n;
if (m >>= 1){
for (int i = 0; i < m; i++){
const unsigned x = as[i + m]._v;
as[i + m]._v = as[i]._v + MO - x;
as[i]._v += x;
}
}
if (m >>= 1){
mint prod = 1;
for (int h = 0, i0 = 0; i0 < n; i0 += (m << 1)){
for (int i = i0; i < i0 + m; i++){
const unsigned x = (prod * as[i + m])._v;
as[i + m]._v = as[i]._v + MO - x;
as[i]._v += x;
}
prod *= mint::raw(internal::FFT_RATIOS[__builtin_ctz(++h)]);
}
}
for (; m; ){
if (m >>= 1){
mint prod = 1;
for (int h = 0, i0 = 0; i0 < n; i0 += (m << 1)){
for (int i = i0; i < i0 + m; i++){
const unsigned x = (prod * as[i + m])._v;
as[i + m]._v = as[i]._v + MO - x;
as[i]._v += x;
}
prod *= mint::raw(internal::FFT_RATIOS[__builtin_ctz(++h)]);
}
}
if (m >>= 1){
mint prod = 1;
for (int h = 0, i0 = 0; i0 < n; i0 += (m << 1)){
for (int i = i0; i < i0 + m; i++){
const unsigned x = (prod * as[i + m])._v;
as[i]._v = (as[i]._v >= MO2 ? as[i]._v - MO2 : as[i]._v);
as[i + m]._v = as[i]._v + MO - x;
as[i]._v += x;
}
prod *= mint::raw(internal::FFT_RATIOS[__builtin_ctz(++h)]);
}
}
}
for (int i = 0; i < n; i++){
as[i]._v = (as[i]._v >= MO2 ? as[i]._v - MO2 : as[i]._v);
as[i]._v = (as[i]._v >= MO ? as[i]._v - MO : as[i]._v);
}
}
static void intt(mint *as, int n){
int m = 1;
if (m < (n >> 1)){
mint prod = 1;
for (int h = 0, i0 = 0; i0 < n; i0 += (m << 1)){
for (int i = i0; i < i0 + m; i++){
const unsigned long long y = as[i]._v + MO - as[i + m]._v;
as[i]._v += as[i + m]._v;
as[i + m]._v = prod._v * y % MO;
}
prod *= mint::raw(internal::INV_FFT_RATIOS[__builtin_ctz(++h)]);
}
m <<= 1;
}
for (; m < (n >> 1); m <<= 1){
mint prod = 1;
for (int h = 0, i0 = 0; i0 < n; i0 += (m << 1)){
for (int i = i0; i < i0 + (m >> 1); i++){
const unsigned long long y = as[i]._v + MO2 - as[i + m]._v;
as[i]._v += as[i + m]._v;
as[i]._v = (as[i]._v >= MO2 ? as[i]._v - MO2 : as[i]._v);
as[i + m]._v = prod._v * y % MO;
}
for (int i = i0 + (m >> 1); i < i0 + m; i++){
const unsigned long long y = as[i]._v + MO - as[i + m]._v;
as[i]._v += as[i + m]._v;
as[i + m]._v = prod._v * y % MO;
}
prod *= mint::raw(internal::INV_FFT_RATIOS[__builtin_ctz(++h)]);
}
}
if (m < n){
for (int i = 0; i < m; i++){
const unsigned y = as[i]._v + MO2 - as[i + m]._v;
as[i]._v += as[i + m]._v;
as[i + m]._v = y;
}
}
for (int i = 0; i < n; i++){
as[i]._v = (as[i]._v >= MO2 ? as[i]._v - MO2 : as[i]._v);
as[i]._v = (as[i]._v >= MO ? as[i]._v - MO : as[i]._v);
}
}
static void ntt(std::vector<mint> &as){
ntt(as.data(), as.size());
}
static void intt(std::vector<mint> &as){
intt(as.data(), as.size());
}
static void intt_div(std::vector<mint> &as){
intt(as);
int n = as.size();
const mint inv_n = mint::raw(n).inv();
for (int i = 0; i < n; i++){
as[i] *= inv_n;
}
}
static std::vector<mint> multiply(std::vector<mint> as, std::vector<mint> bs){
if (as.empty() || bs.empty()) return {};
const int len = as.size() + bs.size() - 1u;
if (std::min(as.size(), bs.size()) <= 40u){
std::vector<mint> s(len);
for (int i = 0; i < (int)(as.size()); i++){
for (int j = 0; j < (int)(bs.size()); j++){
s[i + j] += as[i] * bs[j];
}
}
return s;
}
int n = 1;
for (; n < len; n <<= 1) {}
if (as.size() == bs.size() && as == bs){
as.resize(n);
ntt(as);
for (int i = 0; i < n; i++){
as[i] *= as[i];
}
}
else {
as.resize(n);
ntt(as);
bs.resize(n);
ntt(bs);
for (int i = 0; i < n; i++){
as[i] *= bs[i];
}
}
intt_div(as);
as.resize(len);
return as;
}
static void ntt_doubling(std::vector<mint> &as){
auto bs = as;
intt(bs);
mint e = mint::raw(internal::FFT_ROOTS[std::countr_zero(as.size()) + 1]);
mint iv = mint::raw(as.size()).inv();
for (auto &x : bs){
x *= iv;
iv *= e;
}
ntt(bs);
as.insert(as.end(), bs.begin(), bs.end());
}
static void ntt_pick_parity(std::vector<mint> &f, int odd){
int n = f.size() / 2;
mint i2 = mint::raw((mint::mod() + 1) >> 1);
if (odd == 0){
for (int i = 0; i < n; i++){
f[i] = (f[i * 2] + f[i * 2 + 1]) * i2;
}
f.resize(n);
return ;
}
mint ie = mint::raw(internal::INV_FFT_ROOTS[std::countr_zero(f.size())]);
std::vector<mint> es = {i2};
while ((int)(es.size()) != n){
std::vector<mint> nes(es.size() * 2u);
for (int i = 0; i < (int)(es.size()); i++){
nes[i * 2 + 0] = es[i];
nes[i * 2 + 1] = es[i] * ie;
}
ie *= ie;
std::swap(es, nes);
}
for (int i = 0; i < n; i++){
f[i] = (f[i * 2] - f[i * 2 + 1]) * es[i];
}
f.resize(n);
}
};
} // namespace noya2
#line 2 "/Users/noya2/Desktop/Noya2_library/math/binomial.hpp"
#line 4 "/Users/noya2/Desktop/Noya2_library/math/binomial.hpp"
namespace noya2 {
template<typename mint>
struct binomial {
binomial(int len = 300000){ extend(len); }
static mint fact(int n){
if (n < 0) return 0;
while (n >= (int)_fact.size()) extend();
return _fact[n];
}
static mint ifact(int n){
if (n < 0) return 0;
while (n >= (int)_fact.size()) extend();
return _ifact[n];
}
static mint inv(int n){
return ifact(n) * fact(n-1);
}
static mint C(int n, int r){
if (!(0 <= r && r <= n)) return 0;
return fact(n) * ifact(r) * ifact(n-r);
}
static mint P(int n, int r){
if (!(0 <= r && r <= n)) return 0;
return fact(n) * ifact(n-r);
}
inline mint operator()(int n, int r) { return C(n, r); }
template<class... Cnts>
static mint M(const Cnts&... cnts){
return multinomial(0,1,cnts...);
}
static void initialize(int len = 2){
_fact.clear();
_ifact.clear();
extend(len);
}
private:
static mint multinomial(const int& sum, const mint& div_prod){
if (sum < 0) return 0;
return fact(sum) * div_prod;
}
template<class... Tail>
static mint multinomial(const int& sum, const mint& div_prod, const int& n1, const Tail&... tail){
if (n1 < 0) return 0;
return multinomial(sum+n1,div_prod*ifact(n1),tail...);
}
static inline std::vector<mint> _fact, _ifact;
static void extend(int len = -1){
if (_fact.empty()){
_fact = _ifact = {1,1};
}
int siz = _fact.size();
if (len == -1) len = siz * 2;
len = (int)min<long long>(len, mint::mod() - 1);
if (len < siz) return ;
_fact.resize(len+1), _ifact.resize(len+1);
for (int i = siz; i <= len; i++) _fact[i] = _fact[i-1] * i;
_ifact[len] = _fact[len].inv();
for (int i = len; i > siz; i--) _ifact[i-1] = _ifact[i] * i;
}
};
} // namespace noya2
#line 7 "/Users/noya2/Desktop/Noya2_library/fps998244353/fps998244353.hpp"
namespace noya2 {
// Formal Power Series for modint998244353
struct fps998244353 : std::vector<modint998244353> {
using mint = modint998244353;
using std::vector<mint>::vector;
using std::vector<mint>::operator=;
using fps = fps998244353;
static inline binomial<mint> bnm;
fps998244353 (const std::vector<mint> &init){
(*this) = init;
}
void shrink(){
while(!(this->empty()) && this->back().val() == 0){
this->pop_back();
}
}
fps &operator*= (const mint &r){
for (auto &x : *this) x *= r;
return *this;
}
fps &operator/= (const mint &r){
(*this) *= r.inv();
return *this;
}
fps &operator<<= (const int &d){
this->insert(this->begin(), d, mint(0));
return *this;
}
fps &operator>>= (const int &d){
if ((int)(this->size()) <= d) this->clear();
else this->erase(this->begin(),this->begin() + d);
return *this;
}
fps &operator+= (const fps &r){
if (this->size() < r.size()) this->resize(r.size());
for (int i = 0; auto x : r){
(*this)[i++] += x;
}
return *this;
}
fps &operator-= (const fps &r){
if (this->size() < r.size()) this->resize(r.size());
for (int i = 0; auto x : r){
(*this)[i++] -= x;
}
return *this;
}
fps &operator*= (const fps &r){
if (this->empty() || r.empty()){
this->clear();
return *this;
}
(*this) = ntt998244353::multiply(*this, r);
return *this;
}
fps operator* (const mint &r) const { return fps(*this) *= r; }
fps operator/ (const mint &r) const { return fps(*this) /= r; }
fps operator<< (const int &d) const { return fps(*this) <<= d; }
fps operator>> (const int &d) const { return fps(*this) >>= d; }
fps operator+ (const fps &r) const { return fps(*this) += r; }
fps operator- (const fps &r) const { return fps(*this) -= r; }
fps operator* (const fps &r) const { return fps(*this) *= r; }
fps operator+ () const { return *this; }
fps operator- () const {
fps ret(*this);
for (auto &x : ret) x = -x;
return ret;
}
mint eval(const mint &x) const {
mint res(0), w(1);
for (auto a : *this){
res += a * w;
w *= x;
}
return res;
}
[[nodiscard("Do not change but return changed object.")]]
fps pre(std::size_t sz) const {
fps ret(this->begin(), this->begin() + std::min(this->size(), sz));
if (ret.size() < sz) ret.resize(sz);
return ret;
}
[[nodiscard("Do not change but return changed object.")]]
fps rev() const {
fps ret(*this);
std::reverse(ret.begin(), ret.end());
return ret;
}
[[nodiscard("Do not change but return changed object.")]]
fps diff() const {
if (this->empty()){
return fps();
}
fps ret(this->begin() + 1, this->end());
for (int i = 1; auto &x : ret){
x *= i++;
}
return ret;
}
[[nodiscard("Do not change but return changed object.")]]
fps integral() const {
if (this->empty()){
return fps();
}
fps ret(1, mint(0));
ret.insert(ret.end(), this->begin(), this->end());
for (int i = 0; auto &x : ret){
x *= bnm.inv(i++); // inv(0) = 0
}
return ret;
}
[[nodiscard("Do not change but return changed object.")]]
fps inv(int d = -1) const {
const int n = this->size();
if (d == -1) d = n;
fps res = {(*this)[0].inv()};
for (int siz = 1; siz < d; siz <<= 1){
fps f(this->begin(),this->begin()+min(n,siz*2)), g(res);
f.resize(siz*2), g.resize(siz*2);
f.ntt(), g.ntt();
for (int i = 0; i < siz*2; i++) f[i] *= g[i];
f.intt();
f.erase(f.begin(),f.begin()+siz);
f.resize(siz*2);
f.ntt();
for (int i = 0; i < siz*2; i++) f[i] *= g[i];
f.intt();
mint siz2_inv = mint(siz*2).inv(); siz2_inv *= -siz2_inv;
for (int i = 0; i < siz; i++) f[i] *= siz2_inv;
res.insert(res.end(),f.begin(),f.begin()+siz);
}
res.resize(d);
return res;
}
[[nodiscard("Do not change but return changed object.")]]
fps log(int d = -1) const {
assert(this->empty() == false && (*this)[0].val() == 1u);
if (d == -1) d = this->size();
return (this->diff() * this->inv(d)).pre(d - 1).integral();
}
[[nodiscard("Do not change but return changed object.")]]
fps exp(int d = -1) const {
const int n = this->size();
if (d == -1) d = n;
assert(n == 0 || (*this)[0].val() == 0u);
if (n <= 1){
fps ret(1,1);
ret.resize(d);
return ret;
}
// n >= 2
fps f = {mint(1), (*this)[1]}, ret = f;
for (int sz = 2; sz < d; sz <<= 1){
f.insert(f.end(), this->begin()+std::min(n,sz), this->begin()+std::min(n,sz*2));
f.resize(sz*2);
ret *= f - ret.log(sz*2);
ret.resize(sz*2);
}
ret.resize(d);
return ret;
}
[[nodiscard("Do not change but return changed object.")]]
fps pow(long long k, int d = -1) const {
const int n = this->size();
if (d == -1) d = n;
if (k == 0){
fps ret(d, mint(0));
if (d >= 1) ret[0] = 1;
return ret;
}
// Find left-most nonzero term.
for (int i = 0; i < n; i++){
if ((*this)[i].val() != 0u){
mint iv = (*this)[i].inv();
fps ret = ((((*this) * iv) >> i).log(d) * mint(k)).exp(d);
ret *= (*this)[i].pow(k);
ret = (ret << (i * k)).pre(d);
return ret;
}
if ((i + 1) * k >= d) break;
}
return fps(d, mint(0));
}
void ntt(){
ntt998244353::ntt(*this);
}
// NOT /= len
void intt(){
ntt998244353::intt(*this);
}
// already /= len
void intt_div(){
ntt998244353::intt_div(*this);
}
// input : ntt( f[0, 2^n) )
// output : ntt( f[0, 2^n) ++ zero_padding[0, 2^n) )
void ntt_doubling(){
ntt998244353::ntt_doubling(*this);
}
// input : ntt( f[0, 2^n) )
// output : ntt( g[0, 2^{n-1}) ), g[i] = f[i * 2 + odd]
void ntt_pick_parity(int odd){
ntt998244353::ntt_pick_parity(*this, odd);
}
fps quotient(fps r) const {
r.shrink();
const int n = this->size(), m = r.size();
if (n < m){
return fps();
}
fps quo(*this);
const int sz = n - m + 1;
std::reverse(quo.begin(), quo.end());
std::reverse(r.begin(), r.end());
quo.resize(sz);
quo *= r.inv(sz);
quo.resize(sz);
std::reverse(quo.begin(), quo.end());
return quo;
}
fps remainder(fps r) const {
r.shrink();
const int n = this->size(), m = r.size();
if (n < m){
return fps(*this);
}
fps rem(*this);
rem -= quotient(r) * r;
rem.resize(m-1);
rem.shrink();
return rem;
}
std::pair<fps,fps> remquo(fps r) const {
r.shrink();
fps quo = quotient(r);
fps rem(*this);
rem -= quo * r;
rem.shrink();
return {rem, quo};
}
};
} // namespace noya2
#line 4 "c.cpp"
using mint = modint998244353;
using fps = fps998244353;
void solve(){
binomial<mint> bnm;
int n, mm; in(n,mm); n++;
// find [x^n](x + x^2)^<m>
// f = (x + x^2)^<m>
// a = f + f^2
// b = f(x + x^2)
fps f(n+2), a(n+2), b(n+2);
// dfs(l, r) :
// find [x^[l, r-2]] of f, a, b
// return sum[i in [l, r-2]] f[i] * (x + x^2)^{i - l}
//
// 1 : call dfs(l, m)
// 2 : propagate [l, m-2] -> [m, r)
// 3 : find [x^[m-1]]
// 4 : propagate [m-1] -> [m, r)
// 5 : call dfs(m, r)
// 6 : return sum
auto dfs = [&](auto sfs, int l, int r) -> fps {
if (r - l <= 1) return {};
int m = (l + r) / 2;
// 1
auto lhs = sfs(sfs,l,m);
// 2
{// a
// [0, r-l) * [l, m-1) --> [m, r)
// f[0, min(l,r-l))
fps lf(f.begin() + 0, f.begin() + min(l,r-l));
// f[l, m-1)
fps rf(f.begin() + l, f.begin() + m-1);
fps lfrf = lf * rf * 2;
for (int i = 0; i < (int)(lfrf.size()); i++){
int j = l + i;
if (m <= j && j < r){
a[j] += lfrf[i];
}
}
fps rfrf = rf * rf;
for (int i = 0; i < (int)(rfrf.size()); i++){
int j = l + l + i;
if (m <= j && j < r){
a[j] += rfrf[i];
}
}
}
{// b
int sz = lhs.size();
// (x + x^2)^l * lhs
// x^l * (1 + x)^l * lhs
// [l] * [m-sz+1-l, r-1-l] * [0, sz-1] --> [m, r-1]
int il = max(m-sz+1-l, 0);
fps bin(r-1-l - il + 1);
for (int i = 0; i < (int)(bin.size()); i++){
int j = il + i;
bin[i] = bnm(l, j);
}
bin *= lhs;
for (int i = 0; i < (int)(bin.size()); i++){
int j = l + il + i;
if (m <= j && j < r){
b[j] += bin[i];
}
}
}
// 3
if (m == 1){
f[m-1] = 0;
}
else if (m == 2){
f[m-1] = 1;
}
else if (m == 3){
f[m-1] = mm;
}
else {
f[m-1] = (a[m] - b[m]) * bnm.inv(m-3);
}
// 4
{// a
a[m-1] += f[m-1]; // no need
for (int i = m; i < r; i++){
if (i-(m-1) < m-1){
a[i] += f[m-1] * f[i-(m-1)] * 2;
}
if (i-(m-1) == m-1){
a[i] += f[m-1] * f[m-1];
}
}
}
{// b
// f[m-1] * (x + x^2)^{m-1}
// i = m-1 : no need (i = m : also ok)
for (int i = m-1; i < r; i++){
b[i] += f[m-1] * bnm(m-1, i-(m-1));
}
}
// 5
auto rhs = sfs(sfs,m,r);
// 6
{// lhs += f[m-1] * (x + x^2)^{m-1-l}
fps bin(m-1-l+1);
for (int i = 0; i < m-1-l+1; i++){
bin[i] = bnm(m-1-l,i);
}
bin *= f[m-1];
bin <<= m-1-l;
lhs += bin;
}
{// lhs += rhs * (x + x^2)^{m-l}
fps bin(m-l+1);
for (int i = 0; i < m-l+1; i++){
bin[i] = bnm(m-l,i);
}
bin <<= m-l;
lhs += rhs * bin;
}
return lhs;
};
dfs(dfs,0,n+2);
out(f[n]);
}
int main(){
int t = 1; //in(t);
while (t--) { solve(); }
}