結果
問題 | No.2670 Sum of Products of Interval Lengths |
ユーザー | hitonanode |
提出日時 | 2024-03-10 00:35:32 |
言語 | C++23 (gcc 13.3.0 + boost 1.87.0) |
結果 |
AC
|
実行時間 | 271 ms / 2,000 ms |
コード長 | 26,084 bytes |
コンパイル時間 | 3,767 ms |
コンパイル使用メモリ | 229,856 KB |
実行使用メモリ | 30,096 KB |
最終ジャッジ日時 | 2024-09-29 21:24:26 |
合計ジャッジ時間 | 7,143 ms |
ジャッジサーバーID (参考情報) |
judge3 / judge5 |
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ファイルパターン | 結果 |
---|---|
other | AC * 17 |
ソースコード
#include <algorithm>#include <array>#include <bitset>#include <cassert>#include <chrono>#include <cmath>#include <complex>#include <deque>#include <forward_list>#include <fstream>#include <functional>#include <iomanip>#include <ios>#include <iostream>#include <limits>#include <list>#include <map>#include <memory>#include <numeric>#include <optional>#include <queue>#include <random>#include <set>#include <sstream>#include <stack>#include <string>#include <tuple>#include <type_traits>#include <unordered_map>#include <unordered_set>#include <utility>#include <vector>using namespace std;using lint = long long;using pint = pair<int, int>;using plint = pair<lint, lint>;struct fast_ios { fast_ios(){ cin.tie(nullptr), ios::sync_with_stdio(false), cout << fixed << setprecision(20); }; } fast_ios_;#define ALL(x) (x).begin(), (x).end()#define FOR(i, begin, end) for(int i=(begin),i##_end_=(end);i<i##_end_;i++)#define IFOR(i, begin, end) for(int i=(end)-1,i##_begin_=(begin);i>=i##_begin_;i--)#define REP(i, n) FOR(i,0,n)#define IREP(i, n) IFOR(i,0,n)template <typename T> bool chmax(T &m, const T q) { return m < q ? (m = q, true) : false; }template <typename T> bool chmin(T &m, const T q) { return m > q ? (m = q, true) : false; }const std::vector<std::pair<int, int>> grid_dxs{{1, 0}, {-1, 0}, {0, 1}, {0, -1}};int floor_lg(long long x) { return x <= 0 ? -1 : 63 - __builtin_clzll(x); }template <class T1, class T2> T1 floor_div(T1 num, T2 den) { return (num > 0 ? num / den : -((-num + den - 1) / den)); }template <class T1, class T2> std::pair<T1, T2> operator+(const std::pair<T1, T2> &l, const std::pair<T1, T2> &r) { return std::make_pair(l.first + r.first, l.second + r.second); }template <class T1, class T2> std::pair<T1, T2> operator-(const std::pair<T1, T2> &l, const std::pair<T1, T2> &r) { return std::make_pair(l.first - r.first, l.second - r.second); }template <class T> std::vector<T> sort_unique(std::vector<T> vec) { sort(vec.begin(), vec.end()), vec.erase(unique(vec.begin(), vec.end()), vec.end()); return vec; }template <class T> int arglb(const std::vector<T> &v, const T &x) { return std::distance(v.begin(), std::lower_bound(v.begin(), v.end(), x)); }template <class T> int argub(const std::vector<T> &v, const T &x) { return std::distance(v.begin(), std::upper_bound(v.begin(), v.end(), x)); }template <class IStream, class T> IStream &operator>>(IStream &is, std::vector<T> &vec) { for (auto &v : vec) is >> v; return is; }template <class OStream, class T> OStream &operator<<(OStream &os, const std::vector<T> &vec);template <class OStream, class T, size_t sz> OStream &operator<<(OStream &os, const std::array<T, sz> &arr);template <class OStream, class T, class TH> OStream &operator<<(OStream &os, const std::unordered_set<T, TH> &vec);template <class OStream, class T, class U> OStream &operator<<(OStream &os, const pair<T, U> &pa);template <class OStream, class T> OStream &operator<<(OStream &os, const std::deque<T> &vec);template <class OStream, class T> OStream &operator<<(OStream &os, const std::set<T> &vec);template <class OStream, class T> OStream &operator<<(OStream &os, const std::multiset<T> &vec);template <class OStream, class T> OStream &operator<<(OStream &os, const std::unordered_multiset<T> &vec);template <class OStream, class T, class U> OStream &operator<<(OStream &os, const std::pair<T, U> &pa);template <class OStream, class TK, class TV> OStream &operator<<(OStream &os, const std::map<TK, TV> &mp);template <class OStream, class TK, class TV, class TH> OStream &operator<<(OStream &os, const std::unordered_map<TK, TV, TH> &mp);template <class OStream, class... T> OStream &operator<<(OStream &os, const std::tuple<T...> &tpl);template <class OStream, class T> OStream &operator<<(OStream &os, const std::vector<T> &vec) { os << '['; for (auto v : vec) os << v << ','; os <<']'; return os; }template <class OStream, class T, size_t sz> OStream &operator<<(OStream &os, const std::array<T, sz> &arr) { os << '['; for (auto v : arr) os << v<< ','; os << ']'; return os; }template <class... T> std::istream &operator>>(std::istream &is, std::tuple<T...> &tpl) { std::apply([&is](auto &&... args) { ((is >> args), ...);},tpl); return is; }template <class OStream, class... T> OStream &operator<<(OStream &os, const std::tuple<T...> &tpl) { os << '('; std::apply([&os](auto &&... args) {((os << args << ','), ...);}, tpl); return os << ')'; }template <class OStream, class T, class TH> OStream &operator<<(OStream &os, const std::unordered_set<T, TH> &vec) { os << '{'; for (auto v : vec) os<< v << ','; os << '}'; return os; }template <class OStream, class T> OStream &operator<<(OStream &os, const std::deque<T> &vec) { os << "deq["; for (auto v : vec) os << v << ','; os <<']'; return os; }template <class OStream, class T> OStream &operator<<(OStream &os, const std::set<T> &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}';return os; }template <class OStream, class T> OStream &operator<<(OStream &os, const std::multiset<T> &vec) { os << '{'; for (auto v : vec) os << v << ','; os <<'}'; return os; }template <class OStream, class T> OStream &operator<<(OStream &os, const std::unordered_multiset<T> &vec) { os << '{'; for (auto v : vec) os << v <<','; os << '}'; return os; }template <class OStream, class T, class U> OStream &operator<<(OStream &os, const std::pair<T, U> &pa) { return os << '(' << pa.first << ',' << pa.second << ')'; }template <class OStream, class TK, class TV> OStream &operator<<(OStream &os, const std::map<TK, TV> &mp) { os << '{'; for (auto v : mp) os << v.first << "=>" << v.second << ','; os << '}'; return os; }template <class OStream, class TK, class TV, class TH> OStream &operator<<(OStream &os, const std::unordered_map<TK, TV, TH> &mp) { os << '{'; for(auto v : mp) os << v.first << "=>" << v.second << ','; os << '}'; return os; }#ifdef HITONANODE_LOCALconst string COLOR_RESET = "\033[0m", BRIGHT_GREEN = "\033[1;32m", BRIGHT_RED = "\033[1;31m", BRIGHT_CYAN = "\033[1;36m", NORMAL_CROSSED = "\033[0;9;37m", RED_BACKGROUND = "\033[1;41m", NORMAL_FAINT = "\033[0;2m";#define dbg(x) std::cerr << BRIGHT_CYAN << #x << COLOR_RESET << " = " << (x) << NORMAL_FAINT << " (L" << __LINE__ << ") " << __FILE__ << COLOR_RESET<< std::endl#define dbgif(cond, x) ((cond) ? std::cerr << BRIGHT_CYAN << #x << COLOR_RESET << " = " << (x) << NORMAL_FAINT << " (L" << __LINE__ << ") " <<__FILE__ << COLOR_RESET << std::endl : std::cerr)#else#define dbg(x) ((void)0)#define dbgif(cond, x) ((void)0)#endif#include <cassert>#include <iostream>#include <set>#include <vector>template <int md> struct ModInt {using lint = long long;constexpr static int mod() { return md; }static int get_primitive_root() {static int primitive_root = 0;if (!primitive_root) {primitive_root = [&]() {std::set<int> fac;int v = md - 1;for (lint i = 2; i * i <= v; i++)while (v % i == 0) fac.insert(i), v /= i;if (v > 1) fac.insert(v);for (int g = 1; g < md; g++) {bool ok = true;for (auto i : fac)if (ModInt(g).pow((md - 1) / i) == 1) {ok = false;break;}if (ok) return g;}return -1;}();}return primitive_root;}int val_;int val() const noexcept { return val_; }constexpr ModInt() : val_(0) {}constexpr ModInt &_setval(lint v) { return val_ = (v >= md ? v - md : v), *this; }constexpr ModInt(lint v) { _setval(v % md + md); }constexpr explicit operator bool() const { return val_ != 0; }constexpr ModInt operator+(const ModInt &x) const {return ModInt()._setval((lint)val_ + x.val_);}constexpr ModInt operator-(const ModInt &x) const {return ModInt()._setval((lint)val_ - x.val_ + md);}constexpr ModInt operator*(const ModInt &x) const {return ModInt()._setval((lint)val_ * x.val_ % md);}constexpr ModInt operator/(const ModInt &x) const {return ModInt()._setval((lint)val_ * x.inv().val() % md);}constexpr ModInt operator-() const { return ModInt()._setval(md - val_); }constexpr ModInt &operator+=(const ModInt &x) { return *this = *this + x; }constexpr ModInt &operator-=(const ModInt &x) { return *this = *this - x; }constexpr ModInt &operator*=(const ModInt &x) { return *this = *this * x; }constexpr ModInt &operator/=(const ModInt &x) { return *this = *this / x; }friend constexpr ModInt operator+(lint a, const ModInt &x) { return ModInt(a) + x; }friend constexpr ModInt operator-(lint a, const ModInt &x) { return ModInt(a) - x; }friend constexpr ModInt operator*(lint a, const ModInt &x) { return ModInt(a) * x; }friend constexpr ModInt operator/(lint a, const ModInt &x) { return ModInt(a) / x; }constexpr bool operator==(const ModInt &x) const { return val_ == x.val_; }constexpr bool operator!=(const ModInt &x) const { return val_ != x.val_; }constexpr bool operator<(const ModInt &x) const {return val_ < x.val_;} // To use std::map<ModInt, T>friend std::istream &operator>>(std::istream &is, ModInt &x) {lint t;return is >> t, x = ModInt(t), is;}constexpr friend std::ostream &operator<<(std::ostream &os, const ModInt &x) {return os << x.val_;}constexpr ModInt pow(lint n) const {ModInt ans = 1, tmp = *this;while (n) {if (n & 1) ans *= tmp;tmp *= tmp, n >>= 1;}return ans;}static constexpr int cache_limit = std::min(md, 1 << 21);static std::vector<ModInt> facs, facinvs, invs;constexpr static void _precalculation(int N) {const int l0 = facs.size();if (N > md) N = md;if (N <= l0) return;facs.resize(N), facinvs.resize(N), invs.resize(N);for (int i = l0; i < N; i++) facs[i] = facs[i - 1] * i;facinvs[N - 1] = facs.back().pow(md - 2);for (int i = N - 2; i >= l0; i--) facinvs[i] = facinvs[i + 1] * (i + 1);for (int i = N - 1; i >= l0; i--) invs[i] = facinvs[i] * facs[i - 1];}constexpr ModInt inv() const {if (this->val_ < cache_limit) {if (facs.empty()) facs = {1}, facinvs = {1}, invs = {0};while (this->val_ >= int(facs.size())) _precalculation(facs.size() * 2);return invs[this->val_];} else {return this->pow(md - 2);}}constexpr ModInt fac() const {while (this->val_ >= int(facs.size())) _precalculation(facs.size() * 2);return facs[this->val_];}constexpr ModInt facinv() const {while (this->val_ >= int(facs.size())) _precalculation(facs.size() * 2);return facinvs[this->val_];}constexpr ModInt doublefac() const {lint k = (this->val_ + 1) / 2;return (this->val_ & 1) ? ModInt(k * 2).fac() / (ModInt(2).pow(k) * ModInt(k).fac()): ModInt(k).fac() * ModInt(2).pow(k);}constexpr ModInt nCr(int r) const {if (r < 0 or this->val_ < r) return ModInt(0);return this->fac() * (*this - r).facinv() * ModInt(r).facinv();}constexpr ModInt nPr(int r) const {if (r < 0 or this->val_ < r) return ModInt(0);return this->fac() * (*this - r).facinv();}static ModInt binom(int n, int r) {static long long bruteforce_times = 0;if (r < 0 or n < r) return ModInt(0);if (n <= bruteforce_times or n < (int)facs.size()) return ModInt(n).nCr(r);r = std::min(r, n - r);ModInt ret = ModInt(r).facinv();for (int i = 0; i < r; ++i) ret *= n - i;bruteforce_times += r;return ret;}// Multinomial coefficient, (k_1 + k_2 + ... + k_m)! / (k_1! k_2! ... k_m!)// Complexity: O(sum(ks))template <class Vec> static ModInt multinomial(const Vec &ks) {ModInt ret{1};int sum = 0;for (int k : ks) {assert(k >= 0);ret *= ModInt(k).facinv(), sum += k;}return ret * ModInt(sum).fac();}// Catalan number, C_n = binom(2n, n) / (n + 1)// C_0 = 1, C_1 = 1, C_2 = 2, C_3 = 5, C_4 = 14, ...// https://oeis.org/A000108// Complexity: O(n)static ModInt catalan(int n) {if (n < 0) return ModInt(0);return ModInt(n * 2).fac() * ModInt(n + 1).facinv() * ModInt(n).facinv();}ModInt sqrt() const {if (val_ == 0) return 0;if (md == 2) return val_;if (pow((md - 1) / 2) != 1) return 0;ModInt b = 1;while (b.pow((md - 1) / 2) == 1) b += 1;int e = 0, m = md - 1;while (m % 2 == 0) m >>= 1, e++;ModInt x = pow((m - 1) / 2), y = (*this) * x * x;x *= (*this);ModInt z = b.pow(m);while (y != 1) {int j = 0;ModInt t = y;while (t != 1) j++, t *= t;z = z.pow(1LL << (e - j - 1));x *= z, z *= z, y *= z;e = j;}return ModInt(std::min(x.val_, md - x.val_));}};template <int md> std::vector<ModInt<md>> ModInt<md>::facs = {1};template <int md> std::vector<ModInt<md>> ModInt<md>::facinvs = {1};template <int md> std::vector<ModInt<md>> ModInt<md>::invs = {0};using mint = ModInt<998244353>;// Integer convolution for arbitrary mod// with NTT (and Garner's algorithm) for ModInt / ModIntRuntime class.// We skip Garner's algorithm if `skip_garner` is true or mod is in `nttprimes`.// input: a (size: n), b (size: m)// return: vector (size: n + m - 1)template <typename MODINT>std::vector<MODINT> nttconv(std::vector<MODINT> a, std::vector<MODINT> b, bool skip_garner);constexpr int nttprimes[3] = {998244353, 167772161, 469762049};// Integer FFT (Fast Fourier Transform) for ModInt class// (Also known as Number Theoretic Transform, NTT)// is_inverse: inverse transform// ** Input size must be 2^n **template <typename MODINT> void ntt(std::vector<MODINT> &a, bool is_inverse = false) {int n = a.size();if (n == 1) return;static const int mod = MODINT::mod();static const MODINT root = MODINT::get_primitive_root();assert(__builtin_popcount(n) == 1 and (mod - 1) % n == 0);static std::vector<MODINT> w{1}, iw{1};for (int m = w.size(); m < n / 2; m *= 2) {MODINT dw = root.pow((mod - 1) / (4 * m)), dwinv = 1 / dw;w.resize(m * 2), iw.resize(m * 2);for (int i = 0; i < m; i++) w[m + i] = w[i] * dw, iw[m + i] = iw[i] * dwinv;}if (!is_inverse) {for (int m = n; m >>= 1;) {for (int s = 0, k = 0; s < n; s += 2 * m, k++) {for (int i = s; i < s + m; i++) {MODINT x = a[i], y = a[i + m] * w[k];a[i] = x + y, a[i + m] = x - y;}}}} else {for (int m = 1; m < n; m *= 2) {for (int s = 0, k = 0; s < n; s += 2 * m, k++) {for (int i = s; i < s + m; i++) {MODINT x = a[i], y = a[i + m];a[i] = x + y, a[i + m] = (x - y) * iw[k];}}}int n_inv = MODINT(n).inv().val();for (auto &v : a) v *= n_inv;}}template <int MOD>std::vector<ModInt<MOD>> nttconv_(const std::vector<int> &a, const std::vector<int> &b) {int sz = a.size();assert(a.size() == b.size() and __builtin_popcount(sz) == 1);std::vector<ModInt<MOD>> ap(sz), bp(sz);for (int i = 0; i < sz; i++) ap[i] = a[i], bp[i] = b[i];ntt(ap, false);if (a == b)bp = ap;elsentt(bp, false);for (int i = 0; i < sz; i++) ap[i] *= bp[i];ntt(ap, true);return ap;}long long garner_ntt_(int r0, int r1, int r2, int mod) {using mint2 = ModInt<nttprimes[2]>;static const long long m01 = 1LL * nttprimes[0] * nttprimes[1];static const long long m0_inv_m1 = ModInt<nttprimes[1]>(nttprimes[0]).inv().val();static const long long m01_inv_m2 = mint2(m01).inv().val();int v1 = (m0_inv_m1 * (r1 + nttprimes[1] - r0)) % nttprimes[1];auto v2 = (mint2(r2) - r0 - mint2(nttprimes[0]) * v1) * m01_inv_m2;return (r0 + 1LL * nttprimes[0] * v1 + m01 % mod * v2.val()) % mod;}template <typename MODINT>std::vector<MODINT> nttconv(std::vector<MODINT> a, std::vector<MODINT> b, bool skip_garner) {if (a.empty() or b.empty()) return {};int sz = 1, n = a.size(), m = b.size();while (sz < n + m) sz <<= 1;if (sz <= 16) {std::vector<MODINT> ret(n + m - 1);for (int i = 0; i < n; i++) {for (int j = 0; j < m; j++) ret[i + j] += a[i] * b[j];}return ret;}int mod = MODINT::mod();if (skip_garner orstd::find(std::begin(nttprimes), std::end(nttprimes), mod) != std::end(nttprimes)) {a.resize(sz), b.resize(sz);if (a == b) {ntt(a, false);b = a;} else {ntt(a, false), ntt(b, false);}for (int i = 0; i < sz; i++) a[i] *= b[i];ntt(a, true);a.resize(n + m - 1);} else {std::vector<int> ai(sz), bi(sz);for (int i = 0; i < n; i++) ai[i] = a[i].val();for (int i = 0; i < m; i++) bi[i] = b[i].val();auto ntt0 = nttconv_<nttprimes[0]>(ai, bi);auto ntt1 = nttconv_<nttprimes[1]>(ai, bi);auto ntt2 = nttconv_<nttprimes[2]>(ai, bi);a.resize(n + m - 1);for (int i = 0; i < n + m - 1; i++)a[i] = garner_ntt_(ntt0[i].val(), ntt1[i].val(), ntt2[i].val(), mod);}return a;}template <typename MODINT>std::vector<MODINT> nttconv(const std::vector<MODINT> &a, const std::vector<MODINT> &b) {return nttconv<MODINT>(a, b, false);}// Formal Power Series (形式的冪級数) based on ModInt<mod> / ModIntRuntime// Reference: https://ei1333.github.io/luzhiled/snippets/math/formal-power-series.htmltemplate <typename T> struct FormalPowerSeries : std::vector<T> {using std::vector<T>::vector;using P = FormalPowerSeries;void shrink() {while (this->size() and this->back() == T(0)) this->pop_back();}P operator+(const P &r) const { return P(*this) += r; }P operator+(const T &v) const { return P(*this) += v; }P operator-(const P &r) const { return P(*this) -= r; }P operator-(const T &v) const { return P(*this) -= v; }P operator*(const P &r) const { return P(*this) *= r; }P operator*(const T &v) const { return P(*this) *= v; }P operator/(const P &r) const { return P(*this) /= r; }P operator/(const T &v) const { return P(*this) /= v; }P operator%(const P &r) const { return P(*this) %= r; }P &operator+=(const P &r) {if (r.size() > this->size()) this->resize(r.size());for (int i = 0; i < (int)r.size(); i++) (*this)[i] += r[i];return *this;}P &operator+=(const T &v) {if (this->empty()) this->resize(1);(*this)[0] += v;return *this;}P &operator-=(const P &r) {if (r.size() > this->size()) this->resize(r.size());for (int i = 0; i < (int)r.size(); i++) (*this)[i] -= r[i];return *this;}P &operator-=(const T &v) {if (this->empty()) this->resize(1);(*this)[0] -= v;return *this;}P &operator*=(const T &v) {for (auto &x : (*this)) x *= v;return *this;}P &operator*=(const P &r) {if (this->empty() || r.empty())this->clear();else {auto ret = nttconv(*this, r);*this = P(ret.begin(), ret.end());}return *this;}P &operator%=(const P &r) {*this -= *this / r * r;return *this;}P operator-() const {P ret = *this;for (auto &v : ret) v = -v;return ret;}P &operator/=(const T &v) {assert(v != T(0));for (auto &x : (*this)) x /= v;return *this;}P &operator/=(const P &r) {if (this->size() < r.size()) {this->clear();return *this;}int n = (int)this->size() - r.size() + 1;return *this = (reversed().pre(n) * r.reversed().inv(n)).pre(n).reversed(n);}P pre(int sz) const {P ret(this->begin(), this->begin() + std::min((int)this->size(), sz));return ret;}P operator>>(int sz) const {if ((int)this->size() <= sz) return {};return P(this->begin() + sz, this->end());}P operator<<(int sz) const {if (this->empty()) return {};P ret(*this);ret.insert(ret.begin(), sz, T(0));return ret;}P reversed(int sz = -1) const {assert(sz >= -1);P ret(*this);if (sz != -1) ret.resize(sz, T());std::reverse(ret.begin(), ret.end());return ret;}P differential() const { // formal derivative (differential) of f.p.s.const int n = (int)this->size();P ret(std::max(0, n - 1));for (int i = 1; i < n; i++) ret[i - 1] = (*this)[i] * T(i);return ret;}P integral() const {const int n = (int)this->size();P ret(n + 1);ret[0] = T(0);for (int i = 0; i < n; i++) ret[i + 1] = (*this)[i] / T(i + 1);return ret;}/*** @brief f(x)g(x) = 1 (mod x^deg)** @param deg* @return P ret.size() == deg*/P inv(int deg) const {assert(deg >= -1);if (deg == 0) return {};assert(this->size() and this->at(0) != T()); // Requirement: F(0) != 0const int n = this->size();if (deg == -1) deg = n;P ret({T(1) / this->at(0)});for (int i = 1; i < deg; i <<= 1) {auto h = (pre(i << 1) * ret).pre(i << 1) >> i;auto tmp = (-h * ret).pre(i);ret.insert(ret.end(), tmp.cbegin(), tmp.cend());ret.resize(i << 1);}return ret.pre(deg);}P log(int len = -1) const {assert(len >= -1);if (len == 0) return {};assert(this->size() and ((*this)[0]) == T(1)); // Requirement: F(0) = 1const int n = (int)this->size();if (len == 0) return {};if (len == -1) len = n;return (this->differential() * this->inv(len)).pre(len - 1).integral();}P sqrt(int deg = -1) const {assert(deg >= -1);const int n = (int)this->size();if (deg == -1) deg = n;if (this->empty()) return {};if ((*this)[0] == T(0)) {for (int i = 1; i < n; i++)if ((*this)[i] != T(0)) {if ((i & 1) or deg - i / 2 <= 0) return {};return (*this >> i).sqrt(deg - i / 2) << (i / 2);}return {};}T sqrtf0 = (*this)[0].sqrt();if (sqrtf0 == T(0)) return {};P y = (*this) / (*this)[0], ret({T(1)});T inv2 = T(1) / T(2);for (int i = 1; i < deg; i <<= 1) ret = (ret + y.pre(i << 1) * ret.inv(i << 1)) * inv2;return ret.pre(deg) * sqrtf0;}P exp(int deg = -1) const {assert(deg >= -1);assert(this->empty() or ((*this)[0]) == T(0)); // Requirement: F(0) = 0const int n = (int)this->size();if (deg == -1) deg = n;P ret({T(1)});for (int i = 1; i < deg; i <<= 1) {ret = (ret * (pre(i << 1) + T(1) - ret.log(i << 1))).pre(i << 1);}return ret.pre(deg);}P pow(long long k, int deg = -1) const {assert(deg >= -1);const int n = (int)this->size();if (deg == -1) deg = n;if (k == 0) {P ret(deg);if (deg >= 1) ret[0] = T(1);ret.shrink();return ret;}for (int i = 0; i < n; i++) {if ((*this)[i] != T(0)) {T rev = T(1) / (*this)[i];P C = (*this) * rev, D(n - i);for (int j = i; j < n; j++) D[j - i] = C.coeff(j);D = (D.log(deg) * T(k)).exp(deg) * (*this)[i].pow(k);if (__int128(k) * i > deg) return {};P E(deg);long long S = i * k;for (int j = 0; j + S < deg and j < (int)D.size(); j++) E[j + S] = D[j];E.shrink();return E;}}return *this;}// Calculate f(X + c) from f(X), O(NlogN)P shift(T c) const {const int n = (int)this->size();P ret = *this;for (int i = 0; i < n; i++) ret[i] *= T(i).fac();std::reverse(ret.begin(), ret.end());P exp_cx(n, 1);for (int i = 1; i < n; i++) exp_cx[i] = exp_cx[i - 1] * c * T(i).inv();ret = ret * exp_cx;ret.resize(n);std::reverse(ret.begin(), ret.end());for (int i = 0; i < n; i++) ret[i] *= T(i).facinv();return ret;}T coeff(int i) const {if ((int)this->size() <= i or i < 0) return T(0);return (*this)[i];}T eval(T x) const {T ret = 0, w = 1;for (auto &v : *this) ret += w * v, w *= x;return ret;}};using fps = FormalPowerSeries<mint>;int main() {int N;lint M;cin >> N >> M;dbg(make_tuple(N, M));fps f{1, -1, 1};dbg(f);f = f.inv(N + 5);f.insert(f.begin(), 0);FOR(len, 1, N + 1) {// if (len > M) break;f.at(len) *= max(0LL, M - len + 1);}f = (fps{1} - f).inv(N + 1);cout << f.coeff(N) << endl;}