結果
| 問題 | No.1889 K Consecutive Ks (Hard) |
| ユーザー |
 suisen
|
| 提出日時 | 2022-03-26 01:45:53 |
| 言語 | C++17 (gcc 13.3.0 + boost 1.87.0) |
| 結果 |
CE
(最新)
AC
(最初)
|
| 実行時間 | - |
| コード長 | 50,870 bytes |
| コンパイル時間 | 1,950 ms |
| コンパイル使用メモリ | 208,208 KB |
| 最終ジャッジ日時 | 2025-01-28 12:45:53 |
|
ジャッジサーバーID （参考情報） |
judge2 / judge3 |
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コンパイルエラー時のメッセージ・ソースコードは、提出者また管理者しか表示できないようにしております。（リジャッジ後のコンパイルエラーは公開されます）
ただし、clay言語の場合は開発者のデバッグのため、公開されます。
ただし、clay言語の場合は開発者のデバッグのため、公開されます。
コンパイルメッセージ
main.cpp: In instantiation of ‘void print(const Head&, const Tail& ...) [with Head = atcoder::static_modint<998244353>; Tail = {}]’:
main.cpp:1524:10: required from here
main.cpp:147:15: error: no match for ‘operator<<’ (operand types are ‘std::ostream’ {aka ‘std::basic_ostream<char>’} and ‘const atcoder::static_modint<998244353>’)
147 | std::cout << head;
| ~~~~~~~~~~^~~~~~~
In file included from /usr/include/c++/13/istream:41,
from /usr/include/c++/13/sstream:40,
from /usr/include/c++/13/complex:45,
from /usr/include/c++/13/ccomplex:39,
from /usr/include/x86_64-linux-gnu/c++/13/bits/stdc++.h:127,
from main.cpp:3:
/usr/include/c++/13/ostream:110:7: note: candidate: ‘std::basic_ostream<_CharT, _Traits>::__ostream_type& std::basic_ostream<_CharT, _Traits>::operator<<(__ostream_type& (*)(__ostream_type&)) [with _CharT = char; _Traits = std::char_traits<char>; __ostream_type = std::basic_ostream<char>]’
110 | operator<<(__ostream_type& (*__pf)(__ostream_type&))
| ^~~~~~~~
/usr/include/c++/13/ostream:110:36: note: no known conversion for argument 1 from ‘const atcoder::static_modint<998244353>’ to ‘std::basic_ostream<char>::__ostream_type& (*)(std::basic_ostream<char>::__ostream_type&)’ {aka ‘std::basic_ostream<char>& (*)(std::basic_ostream<char>&)’}
110 | operator<<(__ostream_type& (*__pf)(__ostream_type&))
| ~~~~~~~~~~~~~~~~~~^~~~~~~~~~~~~~~~~~~~~~
/usr/include/c++/13/ostream:119:7: note: candidate: ‘std::basic_ostream<_CharT, _Traits>::__ostream_type& std::basic_ostream<_CharT, _Traits>::operator<<(__ios_type& (*)(__ios_type&)) [with _CharT = char; _Traits = std::char_traits<char>; __ostream_type = std::basic_ostream<char>; __ios_type = std::basic_ios<char>]’
119 | operator<<(__ios_type& (*__pf)(__ios_type&))
| ^~~~~~~~
/usr/include/c++/13/ostream:119:32:
ソースコード
// #pragma comment(linker, "/stack:200000000")#include <bits/stdc++.h>#include <limits>#include <type_traits>namespace suisen {// ! utilitytemplate <typename ...Types>using constraints_t = std::enable_if_t<std::conjunction_v<Types...>, std::nullptr_t>;template <bool cond_v, typename Then, typename OrElse>constexpr decltype(auto) constexpr_if(Then&& then, OrElse&& or_else) {if constexpr (cond_v) {return std::forward<Then>(then);} else {return std::forward<OrElse>(or_else);}}// ! functiontemplate <typename ReturnType, typename Callable, typename ...Args>using is_same_as_invoke_result = std::is_same<std::invoke_result_t<Callable, Args...>, ReturnType>;template <typename F, typename T>using is_uni_op = is_same_as_invoke_result<T, F, T>;template <typename F, typename T>using is_bin_op = is_same_as_invoke_result<T, F, T, T>;template <typename Comparator, typename T>using is_comparator = std::is_same<std::invoke_result_t<Comparator, T, T>, bool>;// ! integraltemplate <typename T, typename = constraints_t<std::is_integral<T>>>constexpr int bit_num = std::numeric_limits<std::make_unsigned_t<T>>::digits;template <typename T, unsigned int n>struct is_nbit { static constexpr bool value = bit_num<T> == n; };template <typename T, unsigned int n>static constexpr bool is_nbit_v = is_nbit<T, n>::value;// ?template <typename T>struct safely_multipliable {};template <>struct safely_multipliable<int> { using type = long long; };template <>struct safely_multipliable<long long> { using type = __int128_t; };template <>struct safely_multipliable<unsigned int> { using type = unsigned long long; };template <>struct safely_multipliable<unsigned long long> { using type = __uint128_t; };template <>struct safely_multipliable<float> { using type = float; };template <>struct safely_multipliable<double> { using type = double; };template <>struct safely_multipliable<long double> { using type = long double; };template <typename T>using safely_multipliable_t = typename safely_multipliable<T>::type;} // namespace suisen// ! type aliasesusing i128 = __int128_t;using u128 = __uint128_t;using ll = long long;using uint = unsigned int;using ull = unsigned long long;template <typename T> using vec = std::vector<T>;template <typename T> using vec2 = vec<vec <T>>;template <typename T> using vec3 = vec<vec2<T>>;template <typename T> using vec4 = vec<vec3<T>>;template <typename T>using pq_greater = std::priority_queue<T, std::vector<T>, std::greater<T>>;template <typename T, typename U>using umap = std::unordered_map<T, U>;// ! macros (capital: internal macro)#define OVERLOAD2(_1,_2,name,...) name#define OVERLOAD3(_1,_2,_3,name,...) name#define OVERLOAD4(_1,_2,_3,_4,name,...) name#define REP4(i,l,r,s) for(std::remove_reference_t<std::remove_const_t<decltype(r)>>i=(l);i<(r);i+=(s))#define REP3(i,l,r) REP4(i,l,r,1)#define REP2(i,n) REP3(i,0,n)#define REPINF3(i,l,s) for(std::remove_reference_t<std::remove_const_t<decltype(l)>>i=(l);;i+=(s))#define REPINF2(i,l) REPINF3(i,l,1)#define REPINF1(i) REPINF2(i,0)#define RREP4(i,l,r,s) for(std::remove_reference_t<std::remove_const_t<decltype(r)>>i=(l)+fld((r)-(l)-1,s)*(s);i>=(l);i-=(s))#define RREP3(i,l,r) RREP4(i,l,r,1)#define RREP2(i,n) RREP3(i,0,n)#define rep(...) OVERLOAD4(__VA_ARGS__, REP4 , REP3 , REP2 )(__VA_ARGS__)#define rrep(...) OVERLOAD4(__VA_ARGS__, RREP4 , RREP3 , RREP2 )(__VA_ARGS__)#define repinf(...) OVERLOAD3(__VA_ARGS__, REPINF3, REPINF2, REPINF1)(__VA_ARGS__)#define CAT_I(a, b) a##b#define CAT(a, b) CAT_I(a, b)#define UNIQVAR(tag) CAT(tag, __LINE__)#define loop(n) for (std::remove_reference_t<std::remove_const_t<decltype(n)>> UNIQVAR(loop_variable) = n; UNIQVAR(loop_variable) --> 0;)#define all(iterable) (iterable).begin(), (iterable).end()#define input(type, ...) type __VA_ARGS__; read(__VA_ARGS__)// ! I/O utilities// pairtemplate <typename T, typename U>std::ostream& operator<<(std::ostream& out, const std::pair<T, U> &a) {return out << a.first << ' ' << a.second;}// tupletemplate <unsigned int N = 0, typename ...Args>std::ostream& operator<<(std::ostream& out, const std::tuple<Args...> &a) {if constexpr (N >= std::tuple_size_v<std::tuple<Args...>>) {return out;} else {out << std::get<N>(a);if constexpr (N + 1 < std::tuple_size_v<std::tuple<Args...>>) {out << ' ';}return operator<<<N + 1>(out, a);}}// vectortemplate <typename T>std::ostream& operator<<(std::ostream& out, const std::vector<T> &a) {for (auto it = a.begin(); it != a.end();) {out << *it;if (++it != a.end()) out << ' ';}return out;}// arraytemplate <typename T, size_t N>std::ostream& operator<<(std::ostream& out, const std::array<T, N> &a) {for (auto it = a.begin(); it != a.end();) {out << *it;if (++it != a.end()) out << ' ';}return out;}inline void print() { std::cout << '\n'; }template <typename Head, typename... Tail>inline void print(const Head &head, const Tail &...tails) {std::cout << head;if (sizeof...(tails)) std::cout << ' ';print(tails...);}template <typename Iterable>auto print_all(const Iterable& v, std::string sep = " ", std::string end = "\n") -> decltype(std::cout << *v.begin(), void()) {for (auto it = v.begin(); it != v.end();) {std::cout << *it;if (++it != v.end()) std::cout << sep;}std::cout << end;}// pairtemplate <typename T, typename U>std::istream& operator>>(std::istream& in, std::pair<T, U> &a) {return in >> a.first >> a.second;}// tupletemplate <unsigned int N = 0, typename ...Args>std::istream& operator>>(std::istream& in, std::tuple<Args...> &a) {if constexpr (N >= std::tuple_size_v<std::tuple<Args...>>) {return in;} else {return operator>><N + 1>(in >> std::get<N>(a), a);}}// vectortemplate <typename T>std::istream& operator>>(std::istream& in, std::vector<T> &a) {for (auto it = a.begin(); it != a.end(); ++it) in >> *it;return in;}// arraytemplate <typename T, size_t N>std::istream& operator>>(std::istream& in, std::array<T, N> &a) {for (auto it = a.begin(); it != a.end(); ++it) in >> *it;return in;}template <typename ...Args>void read(Args &...args) {( std::cin >> ... >> args );}// ! integral utilities// Returns pow(-1, n)template <typename T>constexpr inline int pow_m1(T n) {return -(n & 1) | 1;}// Returns pow(-1, n)template <>constexpr inline int pow_m1<bool>(bool n) {return -int(n) | 1;}// Returns floor(x / y)template <typename T>constexpr inline T fld(const T x, const T y) {return (x ^ y) >= 0 ? x / y : (x - (y + pow_m1(y >= 0))) / y;}template <typename T>constexpr inline T cld(const T x, const T y) {return (x ^ y) <= 0 ? x / y : (x + (y + pow_m1(y >= 0))) / y;}template <typename T, suisen::constraints_t<suisen::is_nbit<T, 16>> = nullptr>constexpr inline int popcount(const T x) { return __builtin_popcount(x); }template <typename T, suisen::constraints_t<suisen::is_nbit<T, 32>> = nullptr>constexpr inline int popcount(const T x) { return __builtin_popcount(x); }template <typename T, suisen::constraints_t<suisen::is_nbit<T, 64>> = nullptr>constexpr inline int popcount(const T x) { return __builtin_popcountll(x); }template <typename T, suisen::constraints_t<suisen::is_nbit<T, 16>> = nullptr>constexpr inline int count_lz(const T x) { return x ? __builtin_clz(x) : suisen::bit_num<T>; }template <typename T, suisen::constraints_t<suisen::is_nbit<T, 32>> = nullptr>constexpr inline int count_lz(const T x) { return x ? __builtin_clz(x) : suisen::bit_num<T>; }template <typename T, suisen::constraints_t<suisen::is_nbit<T, 64>> = nullptr>constexpr inline int count_lz(const T x) { return x ? __builtin_clzll(x) : suisen::bit_num<T>; }template <typename T, suisen::constraints_t<suisen::is_nbit<T, 16>> = nullptr>constexpr inline int count_tz(const T x) { return x ? __builtin_ctz(x) : suisen::bit_num<T>; }template <typename T, suisen::constraints_t<suisen::is_nbit<T, 32>> = nullptr>constexpr inline int count_tz(const T x) { return x ? __builtin_ctz(x) : suisen::bit_num<T>; }template <typename T, suisen::constraints_t<suisen::is_nbit<T, 64>> = nullptr>constexpr inline int count_tz(const T x) { return x ? __builtin_ctzll(x) : suisen::bit_num<T>; }template <typename T>constexpr inline int floor_log2(const T x) { return suisen::bit_num<T> - 1 - count_lz(x); }template <typename T>constexpr inline int ceil_log2(const T x) { return floor_log2(x) + ((x & -x) != x); }template <typename T>constexpr inline int kth_bit(const T x, const unsigned int k) { return (x >> k) & 1; }template <typename T>constexpr inline int parity(const T x) { return popcount(x) & 1; }struct all_subset {struct all_subset_iter {const int s; int t;constexpr all_subset_iter(int s) : s(s), t(s + 1) {}constexpr auto operator*() const { return t; }constexpr auto operator++() {}constexpr auto operator!=(std::nullptr_t) { return t ? (--t &= s, true) : false; }};int s;constexpr all_subset(int s) : s(s) {}constexpr auto begin() { return all_subset_iter(s); }constexpr auto end() { return nullptr; }};// ! containertemplate <typename T, typename Comparator, suisen::constraints_t<suisen::is_comparator<Comparator, T>> = nullptr>auto priqueue_comp(const Comparator comparator) {return std::priority_queue<T, std::vector<T>, Comparator>(comparator);}template <typename Iterable>auto isize(const Iterable &iterable) -> decltype(int(iterable.size())) {return iterable.size();}template <typename T, typename Gen, suisen::constraints_t<suisen::is_same_as_invoke_result<T, Gen, int>> = nullptr>auto generate_vector(int n, Gen generator) {std::vector<T> v(n);for (int i = 0; i < n; ++i) v[i] = generator(i);return v;}template <typename T>auto generate_range_vector(T l, T r) {return generate_vector(r - l, [l](int i) { return l + i; });}template <typename T>auto generate_range_vector(T n) {return generate_range_vector(0, n);}template <typename T>void sort_unique_erase(std::vector<T> &a) {std::sort(a.begin(), a.end());a.erase(std::unique(a.begin(), a.end()), a.end());}template <typename InputIterator, typename BiConsumer>auto foreach_adjacent_values(InputIterator first, InputIterator last, BiConsumer f) -> decltype(f(*first++, *last), void()) {if (first != last) for (auto itr = first, itl = itr++; itr != last; itl = itr++) f(*itl, *itr);}template <typename Container, typename BiConsumer>auto foreach_adjacent_values(Container c, BiConsumer f) -> decltype(c.begin(), c.end(), void()){foreach_adjacent_values(c.begin(), c.end(), f);}// ! other utilities// x <- min(x, y). returns true iff `x` has chenged.template <typename T>inline bool chmin(T &x, const T &y) {if (y >= x) return false;x = y;return true;}// x <- max(x, y). returns true iff `x` has chenged.template <typename T>inline bool chmax(T &x, const T &y) {if (y <= x) return false;x = y;return true;}namespace suisen {}using namespace suisen;using namespace std;struct io_setup {io_setup(int precision = 20) {std::ios::sync_with_stdio(false);std::cin.tie(nullptr);std::cout << std::fixed << std::setprecision(precision);}} io_setup_ {};// ! code from here#include <cassert>#include <numeric>#ifdef _MSC_VER#include <intrin.h>#endif#include <utility>#ifdef _MSC_VER#endifnamespace atcoder {namespace internal {// @param m `1 <= m`// @return x mod mconstexpr long long safe_mod(long long x, long long m) {x %= m;if (x < 0) x += m;return x;}// Fast modular multiplication by barrett reduction// Reference: https://en.wikipedia.org/wiki/Barrett_reduction// NOTE: reconsider after Ice Lakestruct barrett {unsigned int _m;unsigned long long im;// @param m `1 <= m < 2^31`explicit barrett(unsigned int m) : _m(m), im((unsigned long long)(-1) / m + 1) {}// @return munsigned int umod() const { return _m; }// @param a `0 <= a < m`// @param b `0 <= b < m`// @return `a * b % m`unsigned int mul(unsigned int a, unsigned int b) const {// [1] m = 1// a = b = im = 0, so okay// [2] m >= 2// im = ceil(2^64 / m)// -> im * m = 2^64 + r (0 <= r < m)// let z = a*b = c*m + d (0 <= c, d < m)// a*b * im = (c*m + d) * im = c*(im*m) + d*im = c*2^64 + c*r + d*im// c*r + d*im < m * m + m * im < m * m + 2^64 + m <= 2^64 + m * (m + 1) < 2^64 * 2// ((ab * im) >> 64) == c or c + 1unsigned long long z = a;z *= b;#ifdef _MSC_VERunsigned long long x;_umul128(z, im, &x);#elseunsigned long long x =(unsigned long long)(((unsigned __int128)(z)*im) >> 64);#endifunsigned int v = (unsigned int)(z - x * _m);if (_m <= v) v += _m;return v;}};// @param n `0 <= n`// @param m `1 <= m`// @return `(x ** n) % m`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;}// Reference:// M. Forisek and J. Jancina,// Fast Primality Testing for Integers That Fit into a Machine Word// @param n `0 <= n`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 = is_prime_constexpr(n);// @param b `1 <= b`// @return pair(g, x) s.t. g = gcd(a, b), xa = g (mod b), 0 <= x < b/gconstexpr 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};// Contracts:// [1] s - m0 * a = 0 (mod b)// [2] t - m1 * a = 0 (mod b)// [3] s * |m1| + t * |m0| <= blong long s = b, t = a;long long m0 = 0, m1 = 1;while (t) {long long u = s / t;s -= t * u;m0 -= m1 * u; // |m1 * u| <= |m1| * s <= b// [3]:// (s - t * u) * |m1| + t * |m0 - m1 * u|// <= s * |m1| - t * u * |m1| + t * (|m0| + |m1| * u)// = s * |m1| + t * |m0| <= bauto tmp = s;s = t;t = tmp;tmp = m0;m0 = m1;m1 = tmp;}// by [3]: |m0| <= b/g// by g != b: |m0| < b/gif (m0 < 0) m0 += b / s;return {s, m0};}// Compile time primitive root// @param m must be prime// @return primitive root (and minimum in now)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 = primitive_root_constexpr(m);// @param n `n < 2^32`// @param m `1 <= m < 2^32`// @return sum_{i=0}^{n-1} floor((ai + b) / m) (mod 2^64)unsigned long long floor_sum_unsigned(unsigned long long n,unsigned long long m,unsigned long long a,unsigned long long b) {unsigned long long ans = 0;while (true) {if (a >= m) {ans += n * (n - 1) / 2 * (a / m);a %= m;}if (b >= m) {ans += n * (b / m);b %= m;}unsigned long long y_max = a * n + b;if (y_max < m) break;// y_max < m * (n + 1)// floor(y_max / m) <= nn = (unsigned long long)(y_max / m);b = (unsigned long long)(y_max % m);std::swap(m, a);}return ans;}} // namespace internal} // namespace atcodernamespace atcoder {namespace internal {#ifndef _MSC_VERtemplate <class T>using is_signed_int128 =typename std::conditional<std::is_same<T, __int128_t>::value ||std::is_same<T, __int128>::value,std::true_type,std::false_type>::type;template <class T>using is_unsigned_int128 =typename std::conditional<std::is_same<T, __uint128_t>::value ||std::is_same<T, unsigned __int128>::value,std::true_type,std::false_type>::type;template <class T>using make_unsigned_int128 =typename std::conditional<std::is_same<T, __int128_t>::value,__uint128_t,unsigned __int128>;template <class T>using is_integral = typename std::conditional<std::is_integral<T>::value ||is_signed_int128<T>::value ||is_unsigned_int128<T>::value,std::true_type,std::false_type>::type;template <class T>using is_signed_int = typename std::conditional<(is_integral<T>::value &&std::is_signed<T>::value) ||is_signed_int128<T>::value,std::true_type,std::false_type>::type;template <class T>using is_unsigned_int =typename std::conditional<(is_integral<T>::value &&std::is_unsigned<T>::value) ||is_unsigned_int128<T>::value,std::true_type,std::false_type>::type;template <class T>using to_unsigned = typename std::conditional<is_signed_int128<T>::value,make_unsigned_int128<T>,typename std::conditional<std::is_signed<T>::value,std::make_unsigned<T>,std::common_type<T>>::type>::type;#elsetemplate <class T> using is_integral = typename std::is_integral<T>;template <class T>using is_signed_int =typename std::conditional<is_integral<T>::value && std::is_signed<T>::value,std::true_type,std::false_type>::type;template <class T>using is_unsigned_int =typename std::conditional<is_integral<T>::value &&std::is_unsigned<T>::value,std::true_type,std::false_type>::type;template <class T>using to_unsigned = typename std::conditional<is_signed_int<T>::value,std::make_unsigned<T>,std::common_type<T>>::type;#endiftemplate <class T>using is_signed_int_t = std::enable_if_t<is_signed_int<T>::value>;template <class T>using is_unsigned_int_t = std::enable_if_t<is_unsigned_int<T>::value>;template <class T> using to_unsigned_t = typename to_unsigned<T>::type;} // namespace internal} // namespace atcodernamespace atcoder {namespace internal {struct modint_base {};struct static_modint_base : modint_base {};template <class T> using is_modint = std::is_base_of<modint_base, T>;template <class T> using is_modint_t = std::enable_if_t<is_modint<T>::value>;} // namespace internaltemplate <int m, std::enable_if_t<(1 <= m)>* = nullptr>struct static_modint : internal::static_modint_base {using mint = static_modint;public:static constexpr int mod() { return m; }static mint raw(int v) {mint x;x._v = v;return x;}static_modint() : _v(0) {}template <class T, internal::is_signed_int_t<T>* = nullptr>static_modint(T v) {long long x = (long long)(v % (long long)(umod()));if (x < 0) x += umod();_v = (unsigned int)(x);}template <class T, internal::is_unsigned_int_t<T>* = nullptr>static_modint(T v) {_v = (unsigned int)(v % umod());}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;}mint& operator+=(const mint& rhs) {_v += rhs._v;if (_v >= umod()) _v -= umod();return *this;}mint& operator-=(const mint& rhs) {_v -= rhs._v;if (_v >= umod()) _v += umod();return *this;}mint& operator*=(const mint& rhs) {unsigned long long z = _v;z *= rhs._v;_v = (unsigned int)(z % umod());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 {if (prime) {assert(_v);return pow(umod() - 2);} else {auto eg = internal::inv_gcd(_v, m);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;}private:unsigned int _v;static constexpr unsigned int umod() { return m; }static constexpr bool prime = internal::is_prime<m>;};template <int id> struct dynamic_modint : internal::modint_base {using mint = dynamic_modint;public:static int mod() { return (int)(bt.umod()); }static void set_mod(int m) {assert(1 <= m);bt = internal::barrett(m);}static mint raw(int v) {mint x;x._v = v;return x;}dynamic_modint() : _v(0) {}template <class T, internal::is_signed_int_t<T>* = nullptr>dynamic_modint(T v) {long long x = (long long)(v % (long long)(mod()));if (x < 0) x += mod();_v = (unsigned int)(x);}template <class T, internal::is_unsigned_int_t<T>* = nullptr>dynamic_modint(T v) {_v = (unsigned int)(v % mod());}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;}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 = internal::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;}private:unsigned int _v;static internal::barrett bt;static unsigned int umod() { return bt.umod(); }};template <int id> internal::barrett dynamic_modint<id>::bt(998244353);using modint998244353 = static_modint<998244353>;using modint1000000007 = static_modint<1000000007>;using modint = dynamic_modint<-1>;namespace internal {template <class T>using is_static_modint = std::is_base_of<internal::static_modint_base, T>;template <class T>using is_static_modint_t = std::enable_if_t<is_static_modint<T>::value>;template <class> struct is_dynamic_modint : public std::false_type {};template <int id>struct is_dynamic_modint<dynamic_modint<id>> : public std::true_type {};template <class T>using is_dynamic_modint_t = std::enable_if_t<is_dynamic_modint<T>::value>;} // namespace internal} // namespace atcoderusing mint = atcoder::modint998244353;std::istream& operator>>(std::istream& in, mint &a) {long long e; in >> e; a = e;return in;}std::ostream& operator<<(std::ostream& out, const mint &a) {out << a.val();return out;}#include <algorithm>#include <array>#include <vector>#ifdef _MSC_VER#endifnamespace atcoder {namespace internal {// @param n `0 <= n`// @return minimum non-negative `x` s.t. `n <= 2**x`int ceil_pow2(int n) {int x = 0;while ((1U << x) < (unsigned int)(n)) x++;return x;}// @param n `1 <= n`// @return minimum non-negative `x` s.t. `(n & (1 << x)) != 0`constexpr int bsf_constexpr(unsigned int n) {int x = 0;while (!(n & (1 << x))) x++;return x;}// @param n `1 <= n`// @return minimum non-negative `x` s.t. `(n & (1 << x)) != 0`int bsf(unsigned int n) {#ifdef _MSC_VERunsigned long index;_BitScanForward(&index, n);return index;#elsereturn __builtin_ctz(n);#endif}} // namespace internal} // namespace atcodernamespace atcoder {namespace internal {template <class mint,int g = internal::primitive_root<mint::mod()>,internal::is_static_modint_t<mint>* = nullptr>struct fft_info {static constexpr int rank2 = bsf_constexpr(mint::mod() - 1);std::array<mint, rank2 + 1> root; // root[i]^(2^i) == 1std::array<mint, rank2 + 1> iroot; // root[i] * iroot[i] == 1std::array<mint, std::max(0, rank2 - 2 + 1)> rate2;std::array<mint, std::max(0, rank2 - 2 + 1)> irate2;std::array<mint, std::max(0, rank2 - 3 + 1)> rate3;std::array<mint, std::max(0, rank2 - 3 + 1)> irate3;fft_info() {root[rank2] = mint(g).pow((mint::mod() - 1) >> rank2);iroot[rank2] = root[rank2].inv();for (int i = rank2 - 1; i >= 0; i--) {root[i] = root[i + 1] * root[i + 1];iroot[i] = iroot[i + 1] * iroot[i + 1];}{mint prod = 1, iprod = 1;for (int i = 0; i <= rank2 - 2; i++) {rate2[i] = root[i + 2] * prod;irate2[i] = iroot[i + 2] * iprod;prod *= iroot[i + 2];iprod *= root[i + 2];}}{mint prod = 1, iprod = 1;for (int i = 0; i <= rank2 - 3; i++) {rate3[i] = root[i + 3] * prod;irate3[i] = iroot[i + 3] * iprod;prod *= iroot[i + 3];iprod *= root[i + 3];}}}};template <class mint, internal::is_static_modint_t<mint>* = nullptr>void butterfly(std::vector<mint>& a) {int n = int(a.size());int h = internal::ceil_pow2(n);static const fft_info<mint> info;int len = 0; // a[i, i+(n>>len), i+2*(n>>len), ..] is transformedwhile (len < h) {if (h - len == 1) {int p = 1 << (h - len - 1);mint rot = 1;for (int s = 0; s < (1 << len); s++) {int offset = s << (h - len);for (int i = 0; i < p; i++) {auto l = a[i + offset];auto r = a[i + offset + p] * rot;a[i + offset] = l + r;a[i + offset + p] = l - r;}if (s + 1 != (1 << len))rot *= info.rate2[bsf(~(unsigned int)(s))];}len++;} else {// 4-baseint p = 1 << (h - len - 2);mint rot = 1, imag = info.root[2];for (int s = 0; s < (1 << len); s++) {mint rot2 = rot * rot;mint rot3 = rot2 * rot;int offset = s << (h - len);for (int i = 0; i < p; i++) {auto mod2 = 1ULL * mint::mod() * mint::mod();auto a0 = 1ULL * a[i + offset].val();auto a1 = 1ULL * a[i + offset + p].val() * rot.val();auto a2 = 1ULL * a[i + offset + 2 * p].val() * rot2.val();auto a3 = 1ULL * a[i + offset + 3 * p].val() * rot3.val();auto a1na3imag =1ULL * mint(a1 + mod2 - a3).val() * imag.val();auto na2 = mod2 - a2;a[i + offset] = a0 + a2 + a1 + a3;a[i + offset + 1 * p] = a0 + a2 + (2 * mod2 - (a1 + a3));a[i + offset + 2 * p] = a0 + na2 + a1na3imag;a[i + offset + 3 * p] = a0 + na2 + (mod2 - a1na3imag);}if (s + 1 != (1 << len))rot *= info.rate3[bsf(~(unsigned int)(s))];}len += 2;}}}template <class mint, internal::is_static_modint_t<mint>* = nullptr>void butterfly_inv(std::vector<mint>& a) {int n = int(a.size());int h = internal::ceil_pow2(n);static const fft_info<mint> info;int len = h; // a[i, i+(n>>len), i+2*(n>>len), ..] is transformedwhile (len) {if (len == 1) {int p = 1 << (h - len);mint irot = 1;for (int s = 0; s < (1 << (len - 1)); s++) {int offset = s << (h - len + 1);for (int i = 0; i < p; i++) {auto l = a[i + offset];auto r = a[i + offset + p];a[i + offset] = l + r;a[i + offset + p] =(unsigned long long)(mint::mod() + l.val() - r.val()) *irot.val();;}if (s + 1 != (1 << (len - 1)))irot *= info.irate2[bsf(~(unsigned int)(s))];}len--;} else {// 4-baseint p = 1 << (h - len);mint irot = 1, iimag = info.iroot[2];for (int s = 0; s < (1 << (len - 2)); s++) {mint irot2 = irot * irot;mint irot3 = irot2 * irot;int offset = s << (h - len + 2);for (int i = 0; i < p; i++) {auto a0 = 1ULL * a[i + offset + 0 * p].val();auto a1 = 1ULL * a[i + offset + 1 * p].val();auto a2 = 1ULL * a[i + offset + 2 * p].val();auto a3 = 1ULL * a[i + offset + 3 * p].val();auto a2na3iimag =1ULL *mint((mint::mod() + a2 - a3) * iimag.val()).val();a[i + offset] = a0 + a1 + a2 + a3;a[i + offset + 1 * p] =(a0 + (mint::mod() - a1) + a2na3iimag) * irot.val();a[i + offset + 2 * p] =(a0 + a1 + (mint::mod() - a2) + (mint::mod() - a3)) *irot2.val();a[i + offset + 3 * p] =(a0 + (mint::mod() - a1) + (mint::mod() - a2na3iimag)) *irot3.val();}if (s + 1 != (1 << (len - 2)))irot *= info.irate3[bsf(~(unsigned int)(s))];}len -= 2;}}}template <class mint, internal::is_static_modint_t<mint>* = nullptr>std::vector<mint> convolution_naive(const std::vector<mint>& a,const std::vector<mint>& b) {int n = int(a.size()), m = int(b.size());std::vector<mint> ans(n + m - 1);if (n < m) {for (int j = 0; j < m; j++) {for (int i = 0; i < n; i++) {ans[i + j] += a[i] * b[j];}}} else {for (int i = 0; i < n; i++) {for (int j = 0; j < m; j++) {ans[i + j] += a[i] * b[j];}}}return ans;}template <class mint, internal::is_static_modint_t<mint>* = nullptr>std::vector<mint> convolution_fft(std::vector<mint> a, std::vector<mint> b) {int n = int(a.size()), m = int(b.size());int z = 1 << internal::ceil_pow2(n + m - 1);a.resize(z);internal::butterfly(a);b.resize(z);internal::butterfly(b);for (int i = 0; i < z; i++) {a[i] *= b[i];}internal::butterfly_inv(a);a.resize(n + m - 1);mint iz = mint(z).inv();for (int i = 0; i < n + m - 1; i++) a[i] *= iz;return a;}} // namespace internaltemplate <class mint, internal::is_static_modint_t<mint>* = nullptr>std::vector<mint> convolution(std::vector<mint>&& a, std::vector<mint>&& b) {int n = int(a.size()), m = int(b.size());if (!n || !m) return {};if (std::min(n, m) <= 60) return convolution_naive(a, b);return internal::convolution_fft(a, b);}template <class mint, internal::is_static_modint_t<mint>* = nullptr>std::vector<mint> convolution(const std::vector<mint>& a,const std::vector<mint>& b) {int n = int(a.size()), m = int(b.size());if (!n || !m) return {};if (std::min(n, m) <= 60) return convolution_naive(a, b);return internal::convolution_fft(a, b);}template <unsigned int mod = 998244353,class T,std::enable_if_t<internal::is_integral<T>::value>* = nullptr>std::vector<T> convolution(const std::vector<T>& a, const std::vector<T>& b) {int n = int(a.size()), m = int(b.size());if (!n || !m) return {};using mint = static_modint<mod>;std::vector<mint> a2(n), b2(m);for (int i = 0; i < n; i++) {a2[i] = mint(a[i]);}for (int i = 0; i < m; i++) {b2[i] = mint(b[i]);}auto c2 = convolution(move(a2), move(b2));std::vector<T> c(n + m - 1);for (int i = 0; i < n + m - 1; i++) {c[i] = c2[i].val();}return c;}std::vector<long long> convolution_ll(const std::vector<long long>& a,const std::vector<long long>& b) {int n = int(a.size()), m = int(b.size());if (!n || !m) return {};static constexpr unsigned long long MOD1 = 754974721; // 2^24static constexpr unsigned long long MOD2 = 167772161; // 2^25static constexpr unsigned long long MOD3 = 469762049; // 2^26static constexpr unsigned long long M2M3 = MOD2 * MOD3;static constexpr unsigned long long M1M3 = MOD1 * MOD3;static constexpr unsigned long long M1M2 = MOD1 * MOD2;static constexpr unsigned long long M1M2M3 = MOD1 * MOD2 * MOD3;static constexpr unsigned long long i1 =internal::inv_gcd(MOD2 * MOD3, MOD1).second;static constexpr unsigned long long i2 =internal::inv_gcd(MOD1 * MOD3, MOD2).second;static constexpr unsigned long long i3 =internal::inv_gcd(MOD1 * MOD2, MOD3).second;auto c1 = convolution<MOD1>(a, b);auto c2 = convolution<MOD2>(a, b);auto c3 = convolution<MOD3>(a, b);std::vector<long long> c(n + m - 1);for (int i = 0; i < n + m - 1; i++) {unsigned long long x = 0;x += (c1[i] * i1) % MOD1 * M2M3;x += (c2[i] * i2) % MOD2 * M1M3;x += (c3[i] * i3) % MOD3 * M1M2;// B = 2^63, -B <= x, r(real value) < B// (x, x - M, x - 2M, or x - 3M) = r (mod 2B)// r = c1[i] (mod MOD1)// focus on MOD1// r = x, x - M', x - 2M', x - 3M' (M' = M % 2^64) (mod 2B)// r = x,// x - M' + (0 or 2B),// x - 2M' + (0, 2B or 4B),// x - 3M' + (0, 2B, 4B or 6B) (without mod!)// (r - x) = 0, (0)// - M' + (0 or 2B), (1)// -2M' + (0 or 2B or 4B), (2)// -3M' + (0 or 2B or 4B or 6B) (3) (mod MOD1)// we checked that// ((1) mod MOD1) mod 5 = 2// ((2) mod MOD1) mod 5 = 3// ((3) mod MOD1) mod 5 = 4long long diff =c1[i] - internal::safe_mod((long long)(x), (long long)(MOD1));if (diff < 0) diff += MOD1;static constexpr unsigned long long offset[5] = {0, 0, M1M2M3, 2 * M1M2M3, 3 * M1M2M3};x -= offset[diff % 5];c[i] = x;}return c;}} // namespace atcoder#include <iostream>namespace suisen {template <typename mint>class inv_mods {public:inv_mods() {}inv_mods(int n) { ensure(n); }const mint& operator[](int i) const {ensure(i);return invs[i];}static void ensure(int n) {int sz = invs.size();if (sz < 2) invs = {0, 1}, sz = 2;if (sz < n + 1) {invs.resize(n + 1);for (int i = sz; i <= n; ++i) invs[i] = mint(mod - mod / i) * invs[mod % i];}}private:static std::vector<mint> invs;static constexpr int mod = mint::mod();};template <typename mint>std::vector<mint> inv_mods<mint>::invs{};}namespace suisen {template <typename mint>using convolution_t = std::vector<mint> (*)(const std::vector<mint> &, const std::vector<mint> &);template <typename mint>class FPS : public std::vector<mint> {public:using std::vector<mint>::vector;FPS(const std::initializer_list<mint> l) : std::vector<mint>::vector(l) {}static void set_multiplication(convolution_t<mint> multiplication) {FPS<mint>::mult = multiplication;}inline FPS& operator=(const std::vector<mint> &&f) & noexcept {std::vector<mint>::operator=(std::move(f));return *this;}inline FPS& operator=(const std::vector<mint> &f) & {std::vector<mint>::operator=(f);return *this;}inline const mint operator[](int n) const noexcept { return n <= deg() ? unsafe_get(n) : 0; }inline mint& operator[](int n) noexcept { ensure_deg(n); return unsafe_get(n); }inline int size() const noexcept { return std::vector<mint>::size(); }inline int deg() const noexcept { return size() - 1; }inline int normalize() {while (this->size() and this->back() == 0) this->pop_back();return deg();}inline FPS& pre_inplace(int max_deg) noexcept {if (deg() > max_deg) this->resize(std::max(0, max_deg + 1));return *this;}inline FPS pre(int max_deg) const noexcept { return FPS(*this).pre_inplace(max_deg); }inline FPS operator+() const { return FPS(*this); }FPS operator-() const {FPS f(*this);for (auto &e : f) e = mint::mod() - e;return f;}inline FPS& operator++() { ++(*this)[0]; return *this; }inline FPS& operator--() { --(*this)[0]; return *this; }inline FPS& operator+=(const mint x) { (*this)[0] += x; return *this; }inline FPS& operator-=(const mint x) { (*this)[0] -= x; return *this; }FPS& operator+=(const FPS &g) {ensure_deg(g.deg());for (int i = 0; i <= g.deg(); ++i) unsafe_get(i) += g.unsafe_get(i);return *this;}FPS& operator-=(const FPS &g) {ensure_deg(g.deg());for (int i = 0; i <= g.deg(); ++i) unsafe_get(i) -= g.unsafe_get(i);return *this;}inline FPS& operator*=(const FPS &g) { return *this = FPS<mint>::mult(*this, g); }inline FPS& operator*=( FPS &&g) { return *this = FPS<mint>::mult(*this, g); }inline FPS& operator*=(const mint x) {for (auto &e : *this) e *= x;return *this;}FPS& operator/=(FPS &&g) {const int fd = normalize(), gd = g.normalize();assert(gd >= 0);if (fd < gd) { this->clear(); return *this; }if (gd == 0) return *this *= g.unsafe_get(0).inv();static constexpr int THRESHOLD_NAIVE_POLY_QUOTIENT = 256;if (gd <= THRESHOLD_NAIVE_POLY_QUOTIENT) {*this = std::move(naive_div_inplace(std::move(g), gd).first);return *this;}std::reverse(this->begin(), this->end()), std::reverse(g.begin(), g.end());const int k = fd - gd;*this *= g.inv_inplace(k), this->resize(k + 1);std::reverse(this->begin(), this->end());return *this;}FPS& operator%=(FPS &&g) {int fd = normalize(), gd = g.normalize();assert(gd >= 0);if (fd < gd) return *this;if (gd == 0) { this->clear(); return *this; }static constexpr int THRESHOLD_NAIVE_REMAINDER = 256;if (gd <= THRESHOLD_NAIVE_REMAINDER) return naive_div_inplace(std::move(g), gd).second;*this -= g * (*this / g);return pre_inplace(gd - 1);}inline FPS& operator/=(const FPS &g) { return *this /= FPS(g); }inline FPS& operator%=(const FPS &g) { return *this %= FPS(g); }FPS& operator<<=(const int shamt) {this->insert(this->begin(), shamt, 0);return *this;}FPS& operator>>=(const int shamt) {if (shamt > size()) this->clear();else this->erase(this->begin(), this->begin() + shamt);return *this;}inline FPS operator+(FPS &&g) const { return FPS(*this) += std::move(g); }inline FPS operator-(FPS &&g) const { return FPS(*this) -= std::move(g); }inline FPS operator*(FPS &&g) const { return FPS(*this) *= std::move(g); }inline FPS operator/(FPS &&g) const { return FPS(*this) /= std::move(g); }inline FPS operator%(FPS &&g) const { return FPS(*this) %= std::move(g); }inline FPS operator+(const FPS &g) const { return FPS(*this) += g; }inline FPS operator+(const mint x) const { return FPS(*this) += x; }inline FPS operator-(const FPS &g) const { return FPS(*this) -= g; }inline FPS operator-(const mint x) const { return FPS(*this) -= x; }inline FPS operator*(const FPS &g) const { return FPS(*this) *= g; }inline FPS operator*(const mint x) const { return FPS(*this) *= x; }inline FPS operator/(const FPS &g) const { return FPS(*this) /= g; }inline FPS operator%(const FPS &g) const { return FPS(*this) %= g; }inline friend FPS operator*(const mint x, const FPS &f) { return f * x; }inline friend FPS operator*(const mint x, FPS &&f) { return f *= x; }inline FPS operator<<(const int shamt) { return FPS(*this) <<= shamt; }inline FPS operator>>(const int shamt) { return FPS(*this) >>= shamt; }friend bool operator==(const FPS &f, const FPS &g) {int n = f.size(), m = g.size();if (n < m) return g == f;for (int i = 0; i < m; ++i) if (f.unsafe_get(i) != g.unsafe_get(i)) return false;for (int i = m; i < n; ++i) if (f.unsafe_get(i) != 0) return false;return true;}FPS& diff_inplace() {if (this->size() == 0) return *this;for (int i = 1; i <= deg(); ++i) unsafe_get(i - 1) = unsafe_get(i) * i;this->pop_back();return *this;}FPS& intg_inplace() {int d = deg();ensure_deg(d + 1);for (int i = d; i >= 0; --i) unsafe_get(i + 1) = unsafe_get(i) * invs[i + 1];unsafe_get(0) = 0;return *this;}FPS& inv_inplace(const int max_deg) {FPS res { unsafe_get(0).inv() };for (int k = 1; k <= max_deg; k *= 2) {FPS tmp(this->pre(k * 2) * (res * res));res *= 2, res -= tmp.pre_inplace(2 * k);}return *this = std::move(res), pre_inplace(max_deg);}FPS& log_inplace(const int max_deg) {FPS f_inv = inv(max_deg);diff_inplace(), *this *= f_inv, pre_inplace(max_deg - 1), intg_inplace();return *this;}FPS& exp_inplace(const int max_deg) {FPS res {1};for (int k = 1; k <= max_deg; k *= 2) res *= ++(pre(k * 2) - res.log(k * 2)), res.pre_inplace(k * 2);return *this = std::move(res), pre_inplace(max_deg);}FPS& pow_inplace(const long long k, const int max_deg) {int tlz = 0;while (tlz <= deg() and unsafe_get(tlz) == 0) ++tlz;if (tlz * k > max_deg) { this->clear(); return *this; }*this >>= tlz;mint base = (*this)[0];*this *= base.inv(), log_inplace(max_deg), *this *= k, exp_inplace(max_deg), *this *= base.pow(k);return *this <<= tlz * k, pre_inplace(max_deg);}inline FPS diff() const { return FPS(*this).diff_inplace(); }inline FPS intg() const { return FPS(*this).intg_inplace(); }inline FPS inv(const int max_deg) const { return FPS(*this).inv_inplace(max_deg); }inline FPS log(const int max_deg) const { return FPS(*this).log_inplace(max_deg); }inline FPS exp(const int max_deg) const { return FPS(*this).exp_inplace(max_deg); }inline FPS pow(const long long k, const int max_deg) const { return FPS(*this).pow_inplace(k, max_deg); }private:static inv_mods<mint> invs;static convolution_t<mint> mult;inline void ensure_deg(int d) { if (deg() < d) this->resize(d + 1, 0); }inline const mint& unsafe_get(int i) const { return std::vector<mint>::operator[](i); }inline mint& unsafe_get(int i) { return std::vector<mint>::operator[](i); }std::pair<FPS, FPS&> naive_div_inplace(FPS &&g, const int gd) {const int k = deg() - gd;mint head_inv = g.unsafe_get(gd).inv();FPS q(k + 1);for (int i = k; i >= 0; --i) {mint div = this->unsafe_get(i + gd) * head_inv;q.unsafe_get(i) = div;for (int j = 0; j <= gd; ++j) this->unsafe_get(i + j) -= div * g.unsafe_get(j);}return {q, pre_inplace(gd - 1)};}};template <typename mint>convolution_t<mint> FPS<mint>::mult = [](const auto &, const auto &) {std::cerr << "convolution function is not available." << std::endl;assert(false);return std::vector<mint>{};};} // namespace suisentemplate <typename mint>auto sqrt(suisen::FPS<mint> a) -> decltype(mint::mod(), suisen::FPS<mint>{}) {assert(false);}template <typename mint>auto log(suisen::FPS<mint> a) -> decltype(mint::mod(), suisen::FPS<mint>{}) {return a.log(a.deg());}template <typename mint>auto exp(suisen::FPS<mint> a) -> decltype(mint::mod(), mint()) {return a.exp(a.deg());}template <typename mint, typename T>auto pow(suisen::FPS<mint> a, T b) -> decltype(mint::mod(), mint()) {return a.pow(b, a.deg());}template <typename mint>auto inv(suisen::FPS<mint> a) -> decltype(mint::mod(), suisen::FPS<mint>{}) {return a.inv(a.deg());}int main() {suisen::FPS<mint>::set_multiplication([](const auto &a, const auto &b) { return atcoder::convolution(a, b); });input(int, n, m);FPS<mint> f(n + 1);rep(v, 2, m + 1) {rep(j, n / v + 1) {++f[j * v];}}rrep(i, n) f[i + 1] = f[i + 1] - f[i];f[0] = 1;print(mint(m).pow(n) - f.inv(n)[n]);return 0;}