#line 2 "cpplib/util/template.hpp" #pragma GCC optimize("Ofast") #pragma GCC optimize("unroll-loops") #pragma GCC target("avx2") #include using namespace std; struct __INIT__{__INIT__(){cin.tie(0);ios::sync_with_stdio(false);cout< vec; typedef vector> mat; typedef vector>> mat3; typedef vector svec; typedef vector> smat; templateusing V=vector; templateusing VV=V>; templateinline void output(T t){bool f=0;for(auto i:t){cout<<(f?" ":"")<inline void output2(T t){for(auto i:t)output(i);} templateinline void debug(T t){bool f=0;for(auto i:t){cerr<<(f?" ":"")<inline void debug2(T t){for(auto i:t)debug(i);} #define loop(n) for(long long _=0;_<(long long)(n);++_) #define _overload4(_1,_2,_3,_4,name,...) name #define __rep(i,a) repi(i,0,a,1) #define _rep(i,a,b) repi(i,a,b,1) #define repi(i,a,b,c) for(long long i=(long long)(a);i<(long long)(b);i+=c) #define rep(...) _overload4(__VA_ARGS__,repi,_rep,__rep)(__VA_ARGS__) #define _overload3_rev(_1,_2,_3,name,...) name #define _rep_rev(i,a) repi_rev(i,0,a) #define repi_rev(i,a,b) for(long long i=(long long)(b)-1;i>=(long long)(a);--i) #define rrep(...) _overload3_rev(__VA_ARGS__,repi_rev,_rep_rev)(__VA_ARGS__) // #define rep(i,...) for(auto i:range(__VA_ARGS__)) // #define rrep(i,...) for(auto i:reversed(range(__VA_ARGS__))) // #define repi(i,a,b) for(lint i=lint(a);i<(lint)(b);++i) // #define rrepi(i,a,b) for(lint i=lint(b)-1;i>=lint(a);--i) // #define irep(i) for(lint i=0;;++i) // inline vector range(long long n){if(n<=0)return vector();vectorv(n);iota(v.begin(),v.end(),0LL);return v;} // inline vector range(long long a,long long b){if(b<=a)return vector();vectorv(b-a);iota(v.begin(),v.end(),a);return v;} // inline vector range(long long a,long long b,long long c){if((b-a+c-1)/c<=0)return vector();vectorv((b-a+c-1)/c);for(int i=0;i<(int)v.size();++i)v[i]=i?v[i-1]+c:a;return v;} // templateinline T reversed(T v){reverse(v.begin(),v.end());return v;} #define all(n) begin(n),end(n) templatebool chmin(T& s,const E& t){bool res=s>t;s=min(s,t);return res;} templatebool chmax(T& s,const E& t){bool res=s(s,t);return res;} const string ds="DRUL"; const vector dx={1,0,-1,0,1,1,-1,-1}; const vector dy={0,1,0,-1,1,-1,1,-1}; #define SUM(v) accumulate(all(v),0LL) #if __cplusplus>=201703L templateauto make_vector(T x,int arg,Args ...args){if constexpr(sizeof...(args)==0)return vector(arg,x);else return vector(arg,make_vector(x,args...));} #endif #define extrep(v,...) for(auto v:__MAKE_MAT__({__VA_ARGS__})) #define bit(n,a) ((n>>a)&1) vector> __MAKE_MAT__(vector v){if(v.empty())return vector>(1,vector());long long n=v.back();v.pop_back();vector> ret;vector> tmp=__MAKE_MAT__(v);for(auto e:tmp)for(long long i=0;i>; templateusing graph_w=vector>>; templateostream& operator<<(ostream& out,pairv){out<<"("<=201703L constexpr inline long long powll(long long a,long long b){long long res=1;while(b--)res*=a;return res;} #endif templatepair& operator+=(pair&s,const pair&t){s.first+=t.first;s.second+=t.second;return s;} templatepair& operator-=(pair&s,const pair&t){s.first-=t.first;s.second-=t.second;return s;} templatepair operator+(const pair&s,const pair&t){auto res=s;return res+=t;} templatepair operator-(const pair&s,const pair&t){auto res=s;return res-=t;} #define BEGIN_STACK_EXTEND(size) void * stack_extend_memory_ = malloc(size);void * stack_extend_origin_memory_;char * stack_extend_dummy_memory_ = (char*)alloca((1+(int)(((long long)stack_extend_memory_)&127))*16);*stack_extend_dummy_memory_ = 0;asm volatile("mov %%rsp, %%rbx\nmov %%rax, %%rsp":"=b"(stack_extend_origin_memory_):"a"((char*)stack_extend_memory_+(size)-1024)); #define END_STACK_EXTEND asm volatile("mov %%rax, %%rsp"::"a"(stack_extend_origin_memory_));free(stack_extend_memory_); #line 5 "cpplib/math/mod_int.hpp" /** * @brief ModInt */ template struct mod_int { using mint=mod_int; using u64 = std::uint_fast64_t; u64 a; constexpr mod_int(const long long x = 0)noexcept:a(x>=0?x%get_mod():get_mod()-(-x)%get_mod()){} constexpr u64 &value()noexcept{return a;} constexpr const u64 &value() const noexcept {return a;} constexpr mint operator+(const mint rhs)const noexcept{return mint(*this) += rhs;} constexpr mint operator-(const mint rhs)const noexcept{return mint(*this)-=rhs;} constexpr mint operator*(const mint rhs) const noexcept {return mint(*this) *= rhs;} constexpr mint operator/(const mint rhs) const noexcept {return mint(*this) /= rhs;} constexpr mint &operator+=(const mint rhs) noexcept { a += rhs.a; if (a >= get_mod())a -= get_mod(); return *this; } constexpr mint &operator-=(const mint rhs) noexcept { if (a= get_mod())a -= get_mod(); return *this; } constexpr mint operator--(int) noexcept { if (a<1)a += get_mod(); a -= 1; return *this; } constexpr mint &operator/=(mint rhs) noexcept { u64 exp=get_mod()-2; while (exp) { if (exp % 2) { *this *= rhs; } rhs *= rhs; exp /= 2; } return *this; } constexpr bool operator==(mint x) const{ return a==x.a; } constexpr bool operator!=(mint x) const{ return a!=x.a; } constexpr bool operator<(mint x) const{ return a(mint x) const{ return a>x.a; } constexpr bool operator<=(mint x) const{ return a<=x.a; } constexpr bool operator>=(mint x) const{ return a>=x.a; } constexpr static int root(){ mint root = 2; while(root.pow((get_mod()-1)>>1).a==1)root++; return root.a; } constexpr mint pow(long long n)const{ long long x=a; mint ret = 1; while(n>0) { if(n&1)(ret*=x); (x*=x)%=get_mod(); n>>=1; } return ret; } constexpr mint inv(){ return pow(get_mod()-2); } static std::vector fac; static std::vector ifac; static bool init; constexpr static int mx=10000001; void build()const{ init=0; fac.resize(mx); ifac.resize(mx); fac[0]=1,ifac[0]=1; for(int i=1;i=0;i--)ifac[i]=ifac[i+1]*(i+1); } mint comb(long long b){ if(init)build(); if(a<0||b<0)return 0; if(a==0&&b==0)return 1; if((long long)a>(std::istream& lhs,mint& rhs) noexcept { lhs >> rhs.a; return lhs; } constexpr static bool is_static=true; constexpr static u64 get_mod(){ return MOD; } }; templatestd::vector> mod_int::fac; templatestd::vector> mod_int::ifac; templatebool mod_int::init=1; #line 3 "cpplib/math/mod_int998244353.hpp" using mint=mod_int<998'244'353>; /** * @brief ModInt(998'244'353) */ #line 6 "cpplib/math/FPS_base.hpp" #include #line 8 "cpplib/math/FPS_base.hpp" /** * @brief 形式的冪級数(BASE) */ template struct FPS_BASE:std::vector{ using std::vector::vector; using P=FPS_BASE; F fft; FPS_BASE(){} inline P operator +(T x)const noexcept{return P(*this)+=x;} inline P operator -(T x)const noexcept{return P(*this)-=x;} inline P operator *(T x)const noexcept{return P(*this)*=x;} inline P operator /(T x)const noexcept{return P(*this)/=x;} inline P operator <<(int x)noexcept{return P(*this)<<=x;} inline P operator >>(int x)noexcept{return P(*this)>>=x;} inline P operator +(const P& x)const noexcept{return P(*this)+=x;} inline P operator -(const P& x)const noexcept{return P(*this)-=x;} inline P operator -()const noexcept{return P(1,T(0))-=P(*this);} inline P operator *(const P& x)const noexcept{return P(*this)*=x;} inline P operator /(const P& x)const noexcept{return P(*this)/=x;} inline P operator %(const P& x)const noexcept{return P(*this)%=x;} bool operator ==(P x){ for(int i=0;i<(int)max((*this).size(),x.size());++i){ if(i>=(int)(*this).size()&&x[i]!=T())return 0; if(i>=(int)x.size()&&(*this)[i]!=T())return 0; if(i<(int)min((*this).size(),x.size()))if((*this)[i]!=x[i])return 0; } return 1; } P &operator +=(T x){ if(this->size()==0)this->resize(1,T(0)); (*this)[0]+=x; return (*this); } P &operator -=(T x){ if(this->size()==0)this->resize(1,T(0)); (*this)[0]-=x; return (*this); } P &operator *=(T x){ for(int i=0;i<(int)this->size();++i){ (*this)[i]*=x; } return (*this); } P &operator /=(T x){ if(std::is_same::value){ for(int i=0;i<(int)this->size();++i){ (*this)[i]/=x; } return (*this); } return (*this)*=(T(1)/x); } P &operator <<=(int x){ P ret(x,T(0)); this->insert(begin(*this),ret.begin(),ret.end()); return (*this); } P &operator >>=(int x){ if((int)(*this).size()<=x)return (*this)=P(); P ret; ret.insert(ret.end(),begin(*this)+x,end(*this)); return (*this)=ret; } P &operator +=(const P& x){ if(this->size()resize(x.size(),T(0)); for(int i=0;i<(int)x.size();++i){ (*this)[i]+=x[i]; } return (*this); } P &operator -=(const P& x){ if(this->size()resize(x.size(),T(0)); for(int i=0;i<(int)x.size();++i){ (*this)[i]-=x[i]; } return (*this); } P &operator *=(const P& x){ return (*this)=F()(*this,x); } P &operator /=(P x){ if(this->size()clear(); return (*this); } const int n=this->size()-x.size()+1; return (*this) = (rev().pre(n)*x.rev().inv(n)).pre(n).rev(n); } P &operator %=(const P& x){ return ((*this)-=(*this)/x*x); } inline void print(){ for(int i=0;i<(int)(*this).size();++i)std::cerr<<(*this)[i]<<" \n"[i==(int)(*this).size()-1]; if((int)(*this).size()==0)std::cerr<<'\n'; } inline P& shrink(){while((int)(*this).size()!=1&&(*this).back()==0)(*this).pop_back();return (*this);} inline P pre(int sz)const{ return P(begin(*this),begin(*this)+std::min((int)this->size(),sz)); } P rev(int deg=-1){ P ret(*this); if(deg!=-1)ret.resize(deg,T(0)); reverse(begin(ret),end(ret)); return ret; } P inv(int deg=-1){ assert((*this)[0]!=T(0)); const int n=deg==-1?this->size():deg; P ret({T(1)/(*this)[0]}); for(int i=1;isize(),x.size()));++i){ ret[i]*=x[i]; } return ret; } P diff(){ if((int)(*this).size()<=1)return P(); P ret(*this); for(int i=0;i<(int)ret.size();i++){ ret[i]*=i; } return ret>>1; } P integral(){ P ret(*this); for(int i=0;i<(int)ret.size();i++){ ret[i]/=i+1; } return ret<<1; } P log(int deg=-1){ assert((*this)[0]==T(1)); const int n=deg==-1?this->size():deg; return (diff()*inv(n)).pre(n-1).integral(); } P exp(int deg=-1){ assert((*this)[0]==T(0)); const int n=deg==-1?this->size():deg; P ret({T(1)}); for(int i=1;isize():deg; // long long i=0; // P ret(*static_cast(this)); // while(i!=(int)this->size()&&ret[i]==0)i++; // if(i==(int)this->size())return P(n,0); // if(i*c>=n)return P(n,0); // T k=ret[i]; // return ((((ret>>i)/k).log(n)*c).exp(n)*(k.pow(c))<<(i*c)).pre(n); P x(*this); P ret(1,1); while(c) { if(c&1){ ret*=x; if(~deg)ret=ret.pre(deg); } x*=x; if(~deg)x=x.pre(deg); c>>=1; } return ret; } P sqrt(int deg=-1){ const int n=deg==-1?this->size():deg; if((*this)[0]==T(0)) { for(int i=1;i<(int)this->size();i++) { if((*this)[i]!=T(0)) { if(i&1)return{}; if(n-i/2<=0)break; auto ret=(*this>>i).sqrt(n-i/2)<<(i/2); if((int)ret.size()size(); P f(*this),g(n,0); for(int i=0;i>=n-1; for(int i=0;isize()-1;i>=0;--i){ res*=x; res+=(*this)[i]; } return res; } P mul(const std::vector>& x){ int mx=0; for(auto [s,t]:x){ if(mxsize()+mx); for(int i=0;i<(int)this->size();++i){ for(auto [s,t]:x){ res[i+s]+=(*this)[i]*t; } } return res; } P div(const std::vector>& x){ P res(*this); T cnt=0; for(auto [s,t]:x){ if(s==0)cnt+=t; } cnt=cnt.inv(); for(int i=0;i<(int)this->size();++i){ for(auto [s,t]:x){ if(s==0)continue; if(i>=s)res[i]-=res[i-s]*t*cnt; } } res*=cnt; return res; } static P interpolation(const std::vector&x,const std::vector& y){ const int n=x.size(); std::vector>a(n*2-1); std::vector

b(n*2-1); for(int i=0;i=0;--i)a[i]={a[2*i+1].first*a[2*i+2].second+a[2*i+2].first*a[2*i+1].second,a[2*i+1].second*a[2*i+2].second}; auto d=(a[0].first).multipoint_eval(x); for(int i=0;i=0;--i)b[i]=b[2*i+1]*a[2*i+2].second+b[2*i+2]*a[2*i+1].second; return b[0]; } static P interpolation(const std::vector& y){ const int n=y.size(); std::vector>a(n*2-1); std::vector

b(n*2-1); for(int i=0;i=0;--i)a[i]={a[2*i+1].first*a[2*i+2].second+a[2*i+2].first*a[2*i+1].second,a[2*i+1].second*a[2*i+2].second}; for(int i=0;i=0;--i)b[i]=b[2*i+1]*a[2*i+2].second+b[2*i+2]*a[2*i+1].second; return b[0]; } std::vector multipoint_eval(const std::vector&x){ const int n=x.size(); P* v=new P[2*n-1]; for(int i=0;i=0;i--){v[i]=v[i*2+1]*v[i*2+2];} v[0]=P(*this)%v[0];v[0].shrink(); for(int i=1;ires(n); for(int i=0;isize()); return q.nth_term(p,x); } P gcd(P q){ return *this==P()?q:(q%(*this).shrink()).gcd(*this); } //(*this)(t(x)) P manipulate(P t,int deg){ P s=P(*this); if(deg==0)return P(); if((int)t.size()==1)return P{s.eval(t[0])}; int k=std::min((int)::sqrt(deg/(::log2(deg)+1))+1,(int)t.size()); int b=deg/k+1; P t2=t.pre(k); std::vector

table(s.size()/2+1,P{1}); for(int i=1;i<(int)table.size();i++){ table[i]=((table[i-1])*t2).pre(deg); } auto f=[&](auto f,auto l,auto r,int deg)->P{ if(r-l==1)return P{*l}; auto m=l+(r-l)/2; return f(f,l,m,deg)+(table[m-l]*f(f,m,r,deg)).pre(deg); }; P ans=P(); P tmp=f(f,s.begin(),s.end(),deg); P tmp2=P{1}; T tmp3=T(1); int tmp5=-1; P tmp6=t2.diff(); if(tmp6==P()){ for(int i=0;i>(tmp5-1)).inv(deg); for(int i=0;i>(tmp5-1))*tmp4).pre(deg); tmp2=(tmp2*(t-t2)).pre(deg); tmp3*=T(i+1); } } return ans; } //(*this)(t(x)) P manipulate2(P t,int deg){ P ans=P(); P s=(*this).rev(); for(int i=0;i<(int)s.size();++i){ ans=(ans*t+s[i]).pre(deg); } return ans; } P find_linear_recurrence()const{ const int n=this->size(); P b={T(-1)},c={T(-1)}; T y=T(1); for(int i=1;i<=n;++i){ int l=c.size(),m=b.size(); T x=0; for(int j=0;j sum_of_fractional(const vector>&v){ auto f=[&](const auto& s,const auto& t){ return s.second>t.second; }; priority_queue,vector>,decltype(f)>que(f); for(auto& e:v){ que.emplace(e); } while(que.size()>=2){ auto [s,t]=move(que.top()); que.pop(); auto [u,r]=move(que.top()); que.pop(); que.emplace(s*r+t*u,t*r); } return que.top(); } static P sum_of_exp(const vector&v){ vector>tmp(v.size()); for(int i=0;i<(int)v.size();++i){ tmp[i]=make_pair(P{T(1)},P{T(1),T(v[i])*(-1)}); } auto [s,t]=sum_of_fractional(tmp); auto res=s*t.inv(); res.ord_to_exp(); return res; } void ord_to_exp(){ for(int i=0;isize();++i){ (*this)[i]/=F().fact(T(i)); } } void exp_to_ord(){ for(int i=0;isize();++i){ (*this)[i]*=F().fact(T(i)); } } void debug(){ for(int i=0;i<(int)(*this).size();++i)std::cerr<<(*this)[i]<<" \n"[i==(int)(*this).size()-1]; } }; #line 3 "cpplib/math/FPS_mint.hpp" #include #include #include #include #include #ifdef _MSC_VER #include #endif namespace atcoder { namespace internal { int ceil_pow2(int n) { int x = 0; while ((1U << x) < (unsigned int)(n)) x++; return x; } constexpr int bsf_constexpr(unsigned int n) { int x = 0; while (!(n & (1 << x))) x++; return x; } int bsf(unsigned int n) { #ifdef _MSC_VER unsigned long index; _BitScanForward(&index, n); return index; #else return __builtin_ctz(n); #endif } } // namespace internal } // namespace atcoder #include #include #include #ifdef _MSC_VER #include #endif #include #ifdef _MSC_VER #include #endif namespace atcoder { namespace internal { constexpr long long safe_mod(long long x, long long m) { x %= m; if (x < 0) x += m; return x; } struct barrett { unsigned int _m; unsigned long long im; explicit barrett(unsigned int m) : _m(m), im((unsigned long long)(-1) / m + 1) {} unsigned int umod() const { return _m; } unsigned int mul(unsigned int a, unsigned int b) const { unsigned long long z = a; z *= b; #ifdef _MSC_VER unsigned long long x; _umul128(z, im, &x); #else unsigned long long x = (unsigned long long)(((unsigned __int128)(z)*im) >> 64); #endif unsigned int v = (unsigned int)(z - x * _m); if (_m <= v) v += _m; return v; } }; constexpr long long pow_mod_constexpr(long long x, long long n, int m) { if (m == 1) return 0; unsigned int _m = (unsigned int)(m); unsigned long long r = 1; unsigned long long y = safe_mod(x, m); while (n) { if (n & 1) r = (r * y) % _m; y = (y * y) % _m; n >>= 1; } return r; } constexpr bool is_prime_constexpr(int n) { if (n <= 1) return false; if (n == 2 || n == 7 || n == 61) return true; if (n % 2 == 0) return false; long long d = n - 1; while (d % 2 == 0) d /= 2; constexpr long long bases[3] = {2, 7, 61}; for (long long a : bases) { long long t = d; long long y = pow_mod_constexpr(a, t, n); while (t != n - 1 && y != 1 && y != n - 1) { y = y * y % n; t <<= 1; } if (y != n - 1 && t % 2 == 0) { return false; } } return true; } template constexpr bool is_prime = is_prime_constexpr(n); constexpr std::pair inv_gcd(long long a, long long b) { a = safe_mod(a, b); if (a == 0) return {b, 0}; long long s = b, t = a; long long m0 = 0, m1 = 1; while (t) { long long u = s / t; s -= t * u; m0 -= m1 * u; // |m1 * u| <= |m1| * s <= b auto tmp = s; s = t; t = tmp; tmp = m0; m0 = m1; m1 = tmp; } if (m0 < 0) m0 += b / s; return {s, m0}; } constexpr int primitive_root_constexpr(int m) { if (m == 2) return 1; if (m == 167772161) return 3; if (m == 469762049) return 3; if (m == 754974721) return 11; if (m == 998244353) return 3; int divs[20] = {}; divs[0] = 2; int cnt = 1; int x = (m - 1) / 2; while (x % 2 == 0) x /= 2; for (int i = 3; (long long)(i)*i <= x; i += 2) { if (x % i == 0) { divs[cnt++] = i; while (x % i == 0) { x /= i; } } } if (x > 1) { divs[cnt++] = x; } for (int g = 2;; g++) { bool ok = true; for (int i = 0; i < cnt; i++) { if (pow_mod_constexpr(g, (m - 1) / divs[i], m) == 1) { ok = false; break; } } if (ok) return g; } } template constexpr int primitive_root = primitive_root_constexpr(m); 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; n = (unsigned long long)(y_max / m); b = (unsigned long long)(y_max % m); std::swap(m, a); } return ans; } } // namespace internal } // namespace atcoder #include #include #include namespace atcoder { namespace internal { #ifndef _MSC_VER template using is_signed_int128 = typename std::conditional::value || std::is_same::value, std::true_type, std::false_type>::type; template using is_unsigned_int128 = typename std::conditional::value || std::is_same::value, std::true_type, std::false_type>::type; template using make_unsigned_int128 = typename std::conditional::value, __uint128_t, unsigned __int128>; template using is_integral = typename std::conditional::value || is_signed_int128::value || is_unsigned_int128::value, std::true_type, std::false_type>::type; template using is_signed_int = typename std::conditional<(is_integral::value && std::is_signed::value) || is_signed_int128::value, std::true_type, std::false_type>::type; template using is_unsigned_int = typename std::conditional<(is_integral::value && std::is_unsigned::value) || is_unsigned_int128::value, std::true_type, std::false_type>::type; template using to_unsigned = typename std::conditional< is_signed_int128::value, make_unsigned_int128, typename std::conditional::value, std::make_unsigned, std::common_type>::type>::type; #else template using is_integral = typename std::is_integral; template using is_signed_int = typename std::conditional::value && std::is_signed::value, std::true_type, std::false_type>::type; template using is_unsigned_int = typename std::conditional::value && std::is_unsigned::value, std::true_type, std::false_type>::type; template using to_unsigned = typename std::conditional::value, std::make_unsigned, std::common_type>::type; #endif template using is_signed_int_t = std::enable_if_t::value>; template using is_unsigned_int_t = std::enable_if_t::value>; template using to_unsigned_t = typename to_unsigned::type; } // namespace internal } // namespace atcoder namespace atcoder { namespace internal { struct modint_base {}; struct static_modint_base : modint_base {}; template using is_modint = std::is_base_of; template using is_modint_t = std::enable_if_t::value>; } // namespace internal template * = 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 * = nullptr> static_modint(T v) { long long x = (long long)(v % (long long)(umod())); if (x < 0) x += umod(); _v = (unsigned int)(x); } template * = 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; }; template 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 * = nullptr> dynamic_modint(T v) { long long x = (long long)(v % (long long)(mod())); if (x < 0) x += mod(); _v = (unsigned int)(x); } template * = 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 internal::barrett dynamic_modint::bt(998244353); using modint998244353 = static_modint<998244353>; using modint1000000007 = static_modint<1000000007>; using modint = dynamic_modint<-1>; namespace internal { template using is_static_modint = std::is_base_of; template using is_static_modint_t = std::enable_if_t::value>; template struct is_dynamic_modint : public std::false_type {}; template struct is_dynamic_modint> : public std::true_type {}; template using is_dynamic_modint_t = std::enable_if_t::value>; } // namespace internal } // namespace atcoder namespace atcoder { namespace internal { template , internal::is_static_modint_t* = nullptr> struct fft_info { static constexpr int rank2 = bsf_constexpr(mint::mod() - 1); std::array root; // root[i]^(2^i) == 1 std::array iroot; // root[i] * iroot[i] == 1 std::array rate2; std::array irate2; std::array rate3; std::array 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 * = nullptr> void butterfly(std::vector& a) { int n = int(a.size()); int h = internal::ceil_pow2(n); static const fft_info info; int len = 0; // a[i, i+(n>>len), i+2*(n>>len), ..] is transformed while (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 { int 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 * = nullptr> void butterfly_inv(std::vector& a) { int n = int(a.size()); int h = internal::ceil_pow2(n); static const fft_info info; int len = h; // a[i, i+(n>>len), i+2*(n>>len), ..] is transformed while (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 { int 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 * = nullptr> std::vector convolution_naive(const std::vector& a, const std::vector& b) { int n = int(a.size()), m = int(b.size()); std::vector 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 * = nullptr> std::vector convolution_fft(std::vector a, std::vector 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 internal template * = nullptr> std::vector convolution(std::vector&& a, std::vector&& 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 * = nullptr> std::vector convolution(const std::vector& a, const std::vector& 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 ::value>* = nullptr> std::vector convolution(const std::vector& a, const std::vector& b) { int n = int(a.size()), m = int(b.size()); if (!n || !m) return {}; using mint = static_modint; std::vector 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 c(n + m - 1); for (int i = 0; i < n + m - 1; i++) { c[i] = c2[i].val(); } return c; } std::vector convolution_ll(const std::vector& a, const std::vector& b) { int n = int(a.size()), m = int(b.size()); if (!n || !m) return {}; static constexpr unsigned long long MOD1 = 754974721; // 2^24 static constexpr unsigned long long MOD2 = 167772161; // 2^25 static constexpr unsigned long long MOD3 = 469762049; // 2^26 static 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(a, b); auto c2 = convolution(a, b); auto c3 = convolution(a, b); std::vector 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; long 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 #line 1 "cpplib/math/ceil_pow2.hpp" int ceil_pow2(int n) { int x = 0; while ((1U << x) < (unsigned int)(n)) x++; return x; } #line 2 "cpplib/math/mod_pow.hpp" /** * @brief (x^y)%mod */ long long mod_pow(long long x,long long y,long long mod){ long long ret=1; while(y>0) { if(y&1)(ret*=x)%=mod; (x*=x)%=mod; y>>=1; } return ret; } #line 4 "cpplib/math/garner.hpp" /** * * @brief ガーナーのアルゴリズム * */ long long garner(const std::vector&a,const std::vector&mods){ const int sz=a.size(); long long coeffs[sz+1]={1,1,1,1}; long long constants[sz+1]={}; for(int i=0;i struct _FPS{ template T operator()(const T& _s,const T& _t){ if(_s.size()==0||_t.size()==0)return T(); const size_t sz=_s.size()+_t.size()-1; if((Mint::get_mod()&((1<>s(_s.size()),t(_t.size()); for(size_t i=0;i<_s.size();++i)s[i]=_s[i].value(); for(size_t i=0;i<_t.size();++i)t[i]=_t[i].value(); std::vector> _v=atcoder::convolution(s,t); T v(_v.size()); for (size_t i=0;i<_v.size();++i)v[i]=_v[i].val(); return v; }else{ std::vector>s1(_s.size()),t1(_t.size()); std::vector>s2(_s.size()),t2(_t.size()); std::vector>s3(_s.size()),t3(_t.size()); for(size_t i=0;i<_s.size();++i){ s1[i]=_s[i].value(); s2[i]=_s[i].value(); s3[i]=_s[i].value(); } for(size_t i=0;i<_t.size();++i){ t1[i]=_t[i].value(); t2[i]=_t[i].value(); t3[i]=_t[i].value(); } auto v1=atcoder::convolution(s1,t1); auto v2=atcoder::convolution(s2,t2); auto v3=atcoder::convolution(s3,t3); T v(sz); for(size_t i=0;i{v1[i].val(),v2[i].val(),v3[i].val()},std::vector{1224736769,1045430273,1007681537,(long long)Mint::get_mod()}); } return v; } } template T fact(const T& s){ return s.fact(); } template T pow(const T& s,long long i){ return s.pow(i); } }; templateusing fps=FPS_BASE>; #line 4 "main.cpp" int main(){ lint n,m; cin>>n>>m; lint k=min(n,m)+1; tuple,fps> res={{1},{1,-1}},tmp={{1,2},{0,1,-1}}; // lint k2=k-1; // while(k2){ // if(k2%2)res=f(res,tmp); // tmp=f(tmp,tmp); // k2/=2; // } // debug(fps{1,2}.pow(n-k+1,n)); if(m{1,2}*fps{1,-1}.inv(n+1)).pow(k,n+1)).div({{0,1},{1,1},{2,1}}); p.resize(n+1); // debug(p); auto ans=(fps{1,2}*fps{1,-1}.inv(n+1)).pow(max(n,m)+1-k,n+1)*p; cout<