結果
問題 | No.2670 Sum of Products of Interval Lengths |
ユーザー | 👑 potato167 |
提出日時 | 2024-03-08 22:47:07 |
言語 | C++17(gcc12) (gcc 12.3.0 + boost 1.87.0) |
結果 |
AC
|
実行時間 | 548 ms / 2,000 ms |
コード長 | 34,812 bytes |
コンパイル時間 | 4,257 ms |
コンパイル使用メモリ | 254,848 KB |
実行使用メモリ | 21,816 KB |
最終ジャッジ日時 | 2024-09-29 20:16:41 |
合計ジャッジ時間 | 10,606 ms |
ジャッジサーバーID (参考情報) |
judge2 / judge1 |
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ファイルパターン | 結果 |
---|---|
other | AC * 17 |
ソースコード
#include <bits/stdc++.h>#pragma GCC optimize("unroll-loops")using namespace std;using std::cout;using std::cin;using std::endl;using ll=long long;using ld=long double;const ll ILL=2167167167167167167;const int INF=1050000000;const int mod=998244353;#define rep(i,a,b) for (int i=(int)(a);i<(int)(b);i++)#define all(p) p.begin(),p.end()template<class T> using _pq = priority_queue<T, vector<T>, greater<T>>;template<class T> ll LB(vector<T> &v,T a){return lower_bound(v.begin(),v.end(),a)-v.begin();}template<class T> ll UB(vector<T> &v,T a){return upper_bound(v.begin(),v.end(),a)-v.begin();}template<class T> bool chmin(T &a,T b){if(a>b){a=b;return 1;}else return 0;}template<class T> bool chmax(T &a,T b){if(a<b){a=b;return 1;}else return 0;}template<class T> void So(vector<T> &v) {sort(v.begin(),v.end());}template<class T> void Sore(vector<T> &v) {sort(v.begin(),v.end(),[](T x,T y){return x>y;});}void yneos(bool a,bool upp=0){if(a) cout<<(upp?"YES\n":"Yes\n"); else cout<<(upp?"NO\n":"No\n");}template<class T> void vec_out(vector<T> &p,int ty=0){if(ty==2){cout<<'{';for(int i=0;i<(int)p.size();i++){if(i){cout<<",";}cout<<'"'<<p[i]<<'"';}cout<<"}\n";}else{if(ty==1){cout<<p.size()<<"\n";}for(int i=0;i<(int)(p.size());i++){if(i) cout<<" ";cout<<p[i];}cout<<"\n";}}template<class T> T vec_min(vector<T> &a){assert(!a.empty());T ans=a[0];for(auto &x:a) chmin(ans,x);return ans;}template<class T> T vec_max(vector<T> &a){assert(!a.empty());T ans=a[0];for(auto &x:a) chmax(ans,x);return ans;}template<class T> T vec_sum(vector<T> &a){T ans=T(0);for(auto &x:a) ans+=x;return ans;}int pop_count(long long a){int res=0;while(a){res+=(a&1),a>>=1;}return res;}namespace 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`int bsf(unsigned int n) {#ifdef _MSC_VERunsigned long index;_BitScanForward(&index, n);return index;#elsereturn __builtin_ctz(n);#endif}} // namespace internalnamespace 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`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);} // namespace internalnamespace 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 internalnamespace 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());}static_modint(bool 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());}dynamic_modint(bool 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 internalnamespace internal {template <class mint, internal::is_static_modint_t<mint>* = nullptr>void butterfly(std::vector<mint>& a) {static constexpr int g = internal::primitive_root<mint::mod()>;int n = int(a.size());int h = internal::ceil_pow2(n);static bool first = true;static mint sum_e[30]; // sum_e[i] = ies[0] * ... * ies[i - 1] * es[i]if (first) {first = false;mint es[30], ies[30]; // es[i]^(2^(2+i)) == 1int cnt2 = bsf(mint::mod() - 1);mint e = mint(g).pow((mint::mod() - 1) >> cnt2), ie = e.inv();for (int i = cnt2; i >= 2; i--) {// e^(2^i) == 1es[i - 2] = e;ies[i - 2] = ie;e *= e;ie *= ie;}mint now = 1;for (int i = 0; i <= cnt2 - 2; i++) {sum_e[i] = es[i] * now;now *= ies[i];}}for (int ph = 1; ph <= h; ph++) {int w = 1 << (ph - 1), p = 1 << (h - ph);mint now = 1;for (int s = 0; s < w; s++) {int offset = s << (h - ph + 1);for (int i = 0; i < p; i++) {auto l = a[i + offset];auto r = a[i + offset + p] * now;a[i + offset] = l + r;a[i + offset + p] = l - r;}now *= sum_e[bsf(~(unsigned int)(s))];}}}template <class mint, internal::is_static_modint_t<mint>* = nullptr>void butterfly_inv(std::vector<mint>& a) {static constexpr int g = internal::primitive_root<mint::mod()>;int n = int(a.size());int h = internal::ceil_pow2(n);static bool first = true;static mint sum_ie[30]; // sum_ie[i] = es[0] * ... * es[i - 1] * ies[i]if (first) {first = false;mint es[30], ies[30]; // es[i]^(2^(2+i)) == 1int cnt2 = bsf(mint::mod() - 1);mint e = mint(g).pow((mint::mod() - 1) >> cnt2), ie = e.inv();for (int i = cnt2; i >= 2; i--) {// e^(2^i) == 1es[i - 2] = e;ies[i - 2] = ie;e *= e;ie *= ie;}mint now = 1;for (int i = 0; i <= cnt2 - 2; i++) {sum_ie[i] = ies[i] * now;now *= es[i];}}for (int ph = h; ph >= 1; ph--) {int w = 1 << (ph - 1), p = 1 << (h - ph);mint inow = 1;for (int s = 0; s < w; s++) {int offset = s << (h - ph + 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()) *inow.val();}inow *= sum_ie[bsf(~(unsigned int)(s))];}}}} // 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) {if (n < m) {std::swap(n, m);std::swap(a, b);}std::vector<mint> ans(n + m - 1);for (int i = 0; i < n; i++) {for (int j = 0; j < m; j++) {ans[i + j] += a[i] * b[j];}}return ans;}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;}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 atcoderusing namespace atcoder;//参考 https://nyaannyaan.github.io/library/fps/formal-power-series.hpp.htmlnamespace po167{long long rev(long long a,long long MOD){long long D=1,C=MOD-2;while(C){if(C&1) D=(D*a)%MOD;C>>=1;a=(a*a)%MOD;}return D;}template <unsigned int mod = 998244353>std::vector<long long> add_Polynomial(std::vector<long long> &p,std::vector<long long> &q){std::vector<long long> r(std::max(p.size(),q.size()));for(int i=0;i<(int)r.size();i++){if((int)p.size()>i) r[i]=p[i];if((int)q.size()>i) r[i]=(r[i]+q[i])%mod;}return r;}template <unsigned int mod = 998244353>std::vector<long long> sub_Polynomial(std::vector<long long> &p,std::vector<long long> &q){std::vector<long long> r(std::max(p.size(),q.size()));for(int i=0;i<(int)r.size();i++){if((int)p.size()>i) r[i]=p[i];if((int)q.size()>i) r[i]=(r[i]-q[i]);if(r[i]<0) r[i]=(r[i]%mod+mod)%mod;}return r;}template <unsigned int mod = 998244353>long long substitution_Polynomial(std::vector<long long> &p,long long x){long long ans=0;long long D=1;for(int i=0;i<p.size();i++){ans=(ans+(D*p[i])%mod)%mod;D=(D*x)%mod;}return ans;}template <unsigned int mod = 998244353>std::vector<long long> differential_Polynomial(std::vector<long long> &p){int N=p.size();std::vector<long long> r(N);for(int i=1;i<N;i++){r[i-1]=((long long)(i)*p[i])%mod;}return r;}template <unsigned int mod = 998244353>std::vector<long long> Integral_Polynomial(std::vector<long long> &p){int N=p.size();std::vector<long long> r(1+N);std::vector<long long> rev(N+1,1);for(int i=0;i<N;i++){if(i+1>1){rev[i+1]=(mod-((mod/(i+1))*rev[mod%(i+1)])%mod)%mod;}r[i+1]=(rev[i+1]*p[i])%mod;}return r;}template <class T>std::vector<T> slice_vec(std::vector<T> &p,int S){if(S>=(int)(p.size())) return p;std::vector<T> r(S);for(int i=0;i<S;i++) r[i]=p[i];return r;}// return f^{-1} mod x^{L}// https://judge.yosupo.jp/submission/79004template <unsigned int mod = 998244353>std::vector<long long> inv_FPS(std::vector<long long> &p,int L){int N=p.size();assert(0<N);assert(p[0]%mod!=0);std::vector<long long> q={1},tmp,tmp2;long long D=p[0];long long C=mod-2;while(C){if(C&1){q[0]=(q[0]*D)%mod;}C>>=1;D=(D*D)%mod;}int S=1;while(S<L){S*=2;tmp.assign(S,0);for(int i=0;i<std::min((int)(p.size()),S);i++) tmp[i]=p[i];tmp2=convolution<mod>(tmp,convolution<mod>(q,q));for(int i=0;i<S;i++){if(i*2<S) tmp[i]=(2ll*q[i]-tmp2[i]+mod)%mod;else tmp[i]=(-tmp2[i]+mod)%mod;}swap(tmp,q);}std::vector<long long> ans(S);for(int i=0;i<S;i++) ans[i]=q[i];return ans;}// return log f(x)// https://judge.yosupo.jp/submission/79008template <unsigned int mod = 998244353>std::vector<long long> log_FPS(int N,int L,std::vector<long long> &p){assert(p[0]==1);auto tmp=convolution<mod>(differential_Polynomial<mod>(p),inv_FPS<mod>(p,L));auto tmp3=Integral_Polynomial<mod>(tmp);return slice_vec(tmp3,L);}// return e^{f(x)}template <unsigned int mod = 998244353>std::vector<long long> exp_FPS(int N,int L,std::vector<long long> &p){assert((int)p.size()==N);assert(0<N);assert(p[0]%mod==0);std::vector<long long> q={1},tmp,tmp2,tmp3;int S=1;while(S<L){S*=2;tmp=slice_vec(p,S);tmp2=log_FPS<mod>(S/2,S,q);tmp3=sub_Polynomial<mod>(tmp,tmp2);tmp3[0]++;tmp=convolution<mod>(q,tmp3);for(int i=0;i<S;i++){if(i==(int)(q.size())) q.push_back(tmp[i]);else q[i]=tmp[i];}}std::vector<long long> ans(S);for(int i=0;i<S;i++) ans[i]=q[i];return ans;}//if all zero:// return {0}std::vector<long long> zero_cut(std::vector<long long> &p){int ind=0;for(int i=0;i<(int)(p.size());i++){if(p[i]!=0) ind=i;}return slice_vec(p,ind+1);}//return {a,b} (p=aq+b)//https://judge.yosupo.jp/submission/79020template <unsigned int mod = 998244353>std::pair<std::vector<long long>,std::vector<long long>> div_FPS(std::vector<long long> &p,std::vector<long long> &q){int N=p.size(),M=q.size();if(N<M){return {{0},p};}auto f=p,g=q;std::reverse(f.begin(),f.end());std::reverse(g.begin(),g.end());auto tmp=convolution<mod>(f,inv_FPS(g,N-M+1));auto ans1=slice_vec(tmp,N-M+1);std::reverse(ans1.begin(),ans1.end());tmp=convolution(ans1,q);std::vector<long long> ans2(M-1);for(int i=0;i<M-1;i++) ans2[i]=(p[i]-tmp[i]+mod)%mod;return std::make_pair(zero_cut(ans1),zero_cut(ans2));}//return [f(p[0]),f(p[1])...f(p[M-1])]//https://judge.yosupo.jp/submission/79035template <unsigned int mod = 998244353>std::vector<long long> Multipoint_Evaluation(std::vector<long long> f,std::vector<long long>p){int M=p.size();if(M==0){return {};}std::vector<int> size={M};int ind=0;while(size[ind]!=1){size.push_back((size[ind]+1)/2);ind++;}ind++;std::vector<std::vector<std::vector<long long>>> divisor(ind),remain(ind);for(int i=0;i<ind;i++){divisor[i].resize(size[i]);if(i==0){for(int j=0;j<M;j++){divisor[i][j]={mod-p[j],1};}}else{for(int j=0;j<size[i];j++){if(j!=size[i]-1||size[i-1]%2==0){divisor[i][j]=convolution<mod>(divisor[i-1][j*2],divisor[i-1][j*2+1]);}else{divisor[i][j]=divisor[i-1][size[i-1]-1];}}}}for(int i=ind-1;i>=0;i--){remain[i].resize(size[i]);if(i==ind-1){remain[i][0]=div_FPS<mod>(f,divisor[ind-1][0]).second;}else{for(int j=0;j<size[i];j++){if(j!=size[i]-1||size[i]%2==0){remain[i][j]=div_FPS(remain[i+1][j/2],divisor[i][j]).second;}else{remain[i][j]=remain[i+1][j/2];}}}}std::vector<long long> ans(M);for(int i=0;i<M;i++) ans[i]=remain[0][i][0];return ans;}template <unsigned int mod = 998244353>std::vector<long long> multiplication_FPS(std::vector<std::vector<long long>> &p){std::queue<std::vector<long long>> pq;int N=p.size();for(int i=0;i<N;i++) pq.push(p[i]);for(int i=1;i<N;i++){auto l=pq.front();pq.pop();auto r=pq.front();pq.pop();pq.push(convolution<mod>(l,r));}return pq.front();}struct frac_fps{std::vector<long long> ch;std::vector<long long> mo;};template <unsigned int mod = 998244353>frac_fps add_frac_fps(frac_fps &l,frac_fps &r){auto tmp1=convolution<mod>(l.ch,r.mo);auto tmp2=convolution<mod>(l.mo,r.ch);return {add_Polynomial<mod>(tmp1,tmp2),convolution<mod>(l.mo,r.mo)};}template <unsigned int mod = 998244353>std::vector<long long> Polynomial_Interpolation(std::vector<long long> &x,std::vector<long long> &y){int N=x.size();assert(x.size()==y.size());std::vector<std::vector<long long>> p(N);for(int i=0;i<N;i++){p[i]={(mod-x[i])%mod,1};}auto tmp1=multiplication_FPS<mod>(p);auto div=differential_Polynomial<mod>(tmp1);auto val=Multipoint_Evaluation<mod>(div,x);std::queue<frac_fps> q;for(int i=0;i<N;i++) q.push({{y[i]},{(mod-(val[i]*x[i])%mod)%mod,val[i]}});for(int i=1;i<N;i++){frac_fps l=q.front();q.pop();frac_fps r=q.front();q.pop();q.push(add_frac_fps<mod>(l,r));}long long D=1;auto ans=q.front().ch;for(int i=0;i<N;i++){D=(D*val[i])%mod;}D=rev(D,mod);for(int i=0;i<N;i++) ans[i]=(ans[i]*D)%mod;return ans;}//https://kopricky.github.io/code/Computation_Advanced/garner.htmltemplate<typename T>T mod_add(const T a, const T b, const T mod){return (a + b) % mod;}template<typename T>T mod_mul(const T a, const T b, const T mod){return a * b % mod;}template<typename T>T mod_inv(T a, T mod){T u[] = {a, 1, 0}, v[] = {mod, 0, 1}, t;while(*v){t = *u / *v;swap(u[0] -= t * v[0], v[0]);swap(u[1] -= t * v[1], v[1]);swap(u[2] -= t * v[2], v[2]);}u[1] %= mod;return (u[1] < 0) ? (u[1] + mod) : u[1];}template<typename T>T garner(const vector<T>& a, vector<T> p, const T mod){const unsigned int sz = a.size();vector<T> kp(sz + 1, 0), rmult(sz + 1, 1);p.push_back(mod);for(unsigned int i = 0; i < sz; ++i){T x = mod_mul(a[i] - kp[i], mod_inv(rmult[i], p[i]), p[i]);x = (x < 0) ? (x + p[i]) : x;for(unsigned int j = i + 1; j < sz + 1; ++j){kp[j] = mod_add(kp[j], rmult[j] * x, p[j]);rmult[j] = mod_mul(rmult[j], p[i], p[j]);}}return kp[sz];}const long long _mod0=754974721;const long long _mod1=167772161;const long long _mod2=469762049;std::vector<long long> _MOD={_mod0,_mod1,_mod2};std::vector<long long> convolution_any_mod(std::vector<long long> a,std::vector<long long> b,long long pmod){for(auto &x:a) x=(x%pmod+pmod)%pmod;for(auto &x:b) x=(x%pmod+pmod)%pmod;std::vector<vector<long long>> res(3);res[0]=convolution<_mod0>(a,b);res[1]=convolution<_mod1>(a,b);res[2]=convolution<_mod2>(a,b);for(int i=0;i<(int)res[0].size();i++){std::vector<long long> q(3);for(int j=0;j<3;j++) q[j]=res[j][i];res[0][i]=garner(q,_MOD,pmod);}return res[0];}//retrun [x^ind](a(x)/b(x))template <unsigned int mod = 998244353>long long boston_mori(std::vector<long long> a,std::vector<long long> b,long long ind){assert(ind>=0);while(ind){std::vector<long long> n_a,n_b,c=b;for(int i=0;i<(int)(c.size());i++) if(i&1) c[i]*=-1;a=convolution<mod>(c,a);b=convolution<mod>(c,b);for(int i=0;i<(int)(b.size());i++) if((i+1)&1) n_b.push_back(b[i]);for(int i=0;i<(int)(a.size());i++) if((i+1+ind)&1) n_a.push_back(a[i]);std::swap(a,n_a);std::swap(b,n_b);ind>>=1;}return (mod+(a[0]*rev(b[0],mod))%mod)%mod;}}void solve();// oddloopint main() {ios::sync_with_stdio(false);cin.tie(nullptr);int t=1;//cin>>t;rep(i,0,t) solve();}void solve(){ll N,M;cin>>N>>M;vector<ll> p(N+1);rep(i,0,N) p[i+1]=i+1;p[0]=1;p=po167::inv_FPS(p,N+1);rep(i,0,N+1) p[i]=p[i]*(max(0ll,M+1-i)%mod)%mod;p[0]=1;p=po167::inv_FPS(p,N+1);cout<<(p[N]+mod)%mod<<"\n";}