結果
問題 | No.1962 Not Divide |
ユーザー |
![]() |
提出日時 | 2024-12-04 16:39:18 |
言語 | C++23 (gcc 13.3.0 + boost 1.87.0) |
結果 |
AC
|
実行時間 | 26 ms / 2,000 ms |
コード長 | 19,185 bytes |
コンパイル時間 | 5,667 ms |
コンパイル使用メモリ | 333,856 KB |
実行使用メモリ | 5,248 KB |
最終ジャッジ日時 | 2024-12-04 16:39:26 |
合計ジャッジ時間 | 7,112 ms |
ジャッジサーバーID (参考情報) |
judge5 / judge2 |
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ファイルパターン | 結果 |
---|---|
sample | AC * 3 |
other | AC * 21 |
ソースコード
#include <bits/stdc++.h>using namespace std;#if __has_include(<atcoder/all>)#include <atcoder/all>#endifusing ll=long long;using ull=unsigned long long;using P=pair<ll,ll>;template<typename T>using minque=priority_queue<T,vector<T>,greater<T>>;template<typename T>bool chmax(T &a,const T &b){return (a<b?(a=b,true):false);}template<typename T>bool chmin(T &a,const T &b){return (a>b?(a=b,true):false);}template<typename T1,typename T2>istream &operator>>(istream &is,pair<T1,T2>&p){is>>p.first>>p.second;return is;}template<typename T>istream &operator>>(istream &is,vector<T> &a){for(auto &i:a)is>>i;return is;}template<typename T1,typename T2>void operator++(pair<T1,T2>&a,int n){a.first++,a.second++;}template<typename T1,typename T2>void operator--(pair<T1,T2>&a,int n){a.first--,a.second--;}template<typename T>void operator++(vector<T>&a,int n){for(auto &i:a)i++;}template<typename T>void operator--(vector<T>&a,int n){for(auto &i:a)i--;}#define overload3(_1,_2,_3,name,...) name#define rep1(i,n) for(int i=0;i<(int)(n);i++)#define rep2(i,l,r) for(int i=(int)(l);i<(int)(r);i++)#define rep(...) overload3(__VA_ARGS__,rep2,rep1)(__VA_ARGS__)#define reps(i,l,r) rep2(i,l,r)#define all(x) x.begin(),x.end()#define pcnt(x) __builtin_popcountll(x)#define fin(x) return cout<<(x)<<'\n',static_cast<void>(0)#define yn(x) cout<<((x)?"Yes\n":"No\n")ll myceil(ll a,ll b){return (a+b-1)/b;}template<typename T,size_t n,size_t id=0>auto vec(const int (&d)[n],const T &init=T()){if constexpr (id<n)return vector(d[id],vec<T,n,id+1>(d,init));else return init;}#ifdef LOCAL#include<debug.h>#else#define debug(...) static_cast<void>(0)#define debugg(...) static_cast<void>(0)template<typename T1,typename T2>ostream &operator<<(ostream &os,const pair<T1,T2>&p){os<<p.first<<' '<<p.second;return os;}#endifstruct Timer{clock_t start;Timer(){start=clock();ios::sync_with_stdio(false);cin.tie(nullptr);cout<<fixed<<setprecision(16);}inline double now(){return (double)(clock()-start)/1000;}#ifdef LOCAL~Timer(){cerr<<"time:";cerr<<now();cerr<<"ms\n";}#endif}timer;void SOLVE();int main(){int testcase=1;//cin>>testcase;for(int i=0;i<testcase;i++){SOLVE();}}#include<type_traits>template<typename T>constexpr std::enable_if_t<(std::numeric_limits<T>::digits<=32),T>pow_mod(T a,T n,T mod){using u64=unsigned long long;u64 res=1;while(n>0){if(n&1)res=((u64)res*a)%mod;a=((u64)a*a)%mod;n>>=1;}return T(res);}template<typename T>constexpr std::enable_if_t<(std::numeric_limits<T>::digits>32),T>pow_mod(T a,T n,T mod){using u128=__uint128_t;u128 res=1;while(n>0){if(n&1)res=((u128)res*a)%mod;a=((u128)a*a)%mod;n>>=1;}return T(res);}constexpr int primitive_root_constexpr(int x){if(x==167772161)return 3;if(x==469762049)return 3;if(x==754974721)return 11;if(x==880803841)return 26;if(x==998244353)return 3;if(x==2)return 1;int x2=x;int p[20];int c=0;x--;for(int i=2;i*i<=x;i++){if(x%i==0){p[c++]=i;while(x%i==0)x/=i;}}if(x!=1)p[c++]=x;x=x2;for(int g=2;;g++){bool ok=true;for(int i=0;i<c;i++)if(pow_mod(g,(x-1)/p[i],x)==1){ok=false;break;}if(ok)return g;}}template<typename T>constexpr std::enable_if_t<std::numeric_limits<T>::digits<=32,int>msb(T n){return n==0?-1:31-__builtin_clz(n);}template<typename T>constexpr std::enable_if_t<(std::numeric_limits<T>::digits>32),int>msb(T n){return n==0?-1:63-__builtin_clzll(n);}template<typename T>constexpr std::enable_if_t<std::numeric_limits<T>::digits<=32,int>lsb(T n){return n==0?-1:__builtin_ctz(n);}template<typename T>constexpr std::enable_if_t<(std::numeric_limits<T>::digits>32),int>lsb(T n){return n==0?-1:__builtin_ctzll(n);}template<typename T>constexpr std::enable_if_t<std::is_integral_v<T>,T>floor_pow2(T n){return n==0?0:T(1)<<msb(n);}template<typename T>constexpr std::enable_if_t<std::is_integral_v<T>,T>ceil_pow2(T n){return n<=1?1:T(1)<<(msb(n-1)+1);}template<int m>struct ntt_root{static constexpr int rank2=lsb(m-1);static constexpr int g=primitive_root_constexpr(m);std::array<int,rank2+1>root,invroot;std::array<int,std::max(0,rank2-1)>rate2,invrate2;std::array<int,std::max(0,rank2-2)>rate3,invrate3;constexpr ntt_root(){root[rank2]=pow_mod(g,m>>rank2,m);invroot[rank2]=pow_mod(root[rank2],m-2,m);for(int i=rank2-1;i>=0;i--){root[i]=(long long)root[i+1]*root[i+1]%m;invroot[i]=(long long)invroot[i+1]*invroot[i+1]%m;}int prod=1,invprod=1;for(int i=0;i<rank2-1;i++){rate2[i]=(long long)root[i+2]*prod%m;invrate2[i]=(long long)invroot[i+2]*invprod%m;prod=(long long)prod*invroot[i+2]%m;invprod=(long long)invprod*root[i+2]%m;}prod=invprod=1;for(int i=0;i<rank2-2;i++){rate3[i]=(long long)root[i+3]*prod%m;invrate3[i]=(long long)invroot[i+3]*invprod%m;prod=(long long)prod*invroot[i+3]%m;invprod=(long long)invprod*root[i+3]%m;}}};template<typename T>void dft(std::vector<T>&a){static constexpr ntt_root<T::mod()>r;static constexpr unsigned long long mod2=(unsigned long long)T::mod()*T::mod();int n=a.size();int h=lsb(n);int len=0;while(len<h){if(h-len==1){T rot=T::raw(1);for(int s=0;s<(1<<len);s++){int of=s*2;T u=a[of],v=a[of+1]*rot;a[of]=u+v;a[of+1]=u-v;rot*=T::raw(r.rate2[lsb(~(unsigned int)s)]);}len++;}else{int p=1<<(h-len-2);T rot=T::raw(1),imag=T::raw(r.root[2]);for(int s=0;s<(1<<len);s++){const unsigned long long rot1=rot.val(),rot2=rot1*rot1%T::mod(),rot3=rot1*rot2%T::mod();int of=s<<(h-len);for(int i=0;i<p;i++){const unsigned long long a0=a[i+of].val(),a1=(unsigned long long)a[i+of+p].val()*rot1,a2=(unsigned long long)a[i+of+p*2].val()*rot2,a3=(unsigned long long)a[i+of+p*3].val()*rot3;const unsigned long long m=(unsigned long long)T(a1+mod2-a3).val()*imag.val();const unsigned long long k=mod2-a2;a[i+of]=a0+a2+a1+a3;a[i+of+p]=a0+a2+(mod2*2-a1-a3);a[i+of+p*2]=a0+k+m;a[i+of+p*3]=a0+k+(mod2-m);}rot*=T::raw(r.rate3[lsb(~(unsigned int)s)]);}len+=2;}}}template<typename T>void idft(std::vector<T>&a){static constexpr ntt_root<T::mod()>r;static constexpr unsigned long long mod2=(unsigned long long)T::mod()*T::mod();int n=a.size();int h=lsb(n);int len=h;while(len){if(len==1){int p=1<<(h-1);for(int i=0;i<p;i++){T u=a[i],v=a[i+p];a[i]=u+v;a[i+p]=u-v;}len--;}else{int p=1<<(h-len);T rot=T::raw(1),imag=T::raw(r.invroot[2]);for(int s=0;s<(1<<(len-2));s++){const unsigned long long rot1=rot.val(),rot2=rot1*rot1%T::mod(),rot3=rot1*rot2%T::mod();int of=s<<(h-len+2);for(int i=0;i<p;i++){const unsigned long long a0=a[i+of].val(),a1=a[i+of+p].val(),a2=a[i+of+p*2].val(),a3=a[i+of+p*3].val();const unsigned long long k=T((T::mod()+a2-a3)*imag.val()).val();a[i+of]=a0+a1+a2+a3;a[i+of+p]=(a0+T::mod()-a1+k)*rot1;a[i+of+p*2]=(a0+a1+T::mod()*2-a2-a3)*rot2;a[i+of+p*3]=(a0+T::mod()*2-a1-k)*rot3;}rot*=T::raw(r.invrate3[lsb(~(unsigned int)s)]);}len-=2;}}}template<typename T>std::vector<T>ntt_convolution(std::vector<T> a,std::vector<T> b){int n=a.size(),m=b.size(),s=n+m-1;if(std::min(n,m)<60){std::vector<T>ret(s,0);if(n<m)for(int i=0;i<m;i++)for(int j=0;j<n;j++)ret[i+j]+=a[j]*b[i];else for(int i=0;i<n;i++)for(int j=0;j<m;j++)ret[i+j]+=a[i]*b[j];return ret;}int z=ceil_pow2(s);a.resize(z,0);b.resize(z,0);dft(a),dft(b);std::vector<T>c(z);for(int i=0;i<z;i++)c[i]=a[i]*b[i];idft(c);T g=T::raw(z).inv();for(int i=0;i<s;i++)c[i]*=g;return {c.begin(),c.begin()+s};}template<typename T>void ntt_doubling(std::vector<T>&a){static constexpr ntt_root<T::mod()>r;int n=a.size()/2;std::vector<T>b(a.begin(),a.begin()+n);idft(b);T now=T::raw(n).inv(),zeta=T::raw(r.root[msb(n)+1]);for(int i=0;i<n;i++){b[i]*=now;now*=zeta;}dft(b);std::copy(b.begin(),b.end(),a.begin()+n);}template<typename T>T bostan_mori(std::vector<T> p,std::vector<T> q,long long k){assert(p.size()<q.size());static constexpr ntt_root<T::mod()>r;int n=ceil_pow2((int)q.size()*2-1);p.resize(n,T::raw(0));q.resize(n,T::raw(0));dft(p),dft(q);T inv2=T::raw(2).inv();int n2=n/2;while(k){for(int i=0;i<n;i++)p[i]*=q[i^1];if(k&1){T prod=T::raw(1);for(int i=0;i<n2;i++){p[i]=(p[i*2]-p[i*2+1])*inv2*prod;prod*=r.invrate2[lsb(~i)];}}else{for(int i=0;i<n2;i++){p[i]=(p[i*2]+p[i*2+1])*inv2;}}for(int i=0;i<n2;i++)q[i]=q[i*2]*q[i*2+1];ntt_doubling(p),ntt_doubling(q);k>>=1;}idft(p);return p[0]/T::raw(n);}#include<optional>unsigned long long binary_gcd(unsigned long long a,unsigned long long b){if(a==0||b==0||a==b)return a<b?b:a;int n=lsb(a),m=lsb(b);while(a!=b){if(a>b)a=(a-b)>>lsb(a-b);else b=(b-a)>>lsb(b-a);}return a<<(n<m?n:m);}struct BarrettReduction{private:using i64=long long;using u64=unsigned long long;using u32=unsigned int;using u128=__uint128_t;u32 m;u64 im;public:BarrettReduction():m(0),im(0){}BarrettReduction(u32 n):m(n),im(u64(-1)/n+1){}inline i64 quo(u64 x)const{if(m==1)return x;u64 y=u64((u128(x)*im)>>64);u32 r=x-y*m;return m<=r?y-1:y;}inline u32 rem(u64 x)const{if(m==1)return 0;u64 y=u64((u128(x)*im)>>64);u32 r=x-y*m;return m<=r?r+m:r;}inline std::pair<u64,u32>quo_rem(u64 x)const{if(m==0)return std::make_pair(x,0);u64 y=u64((u128(x)*im)>>64);u32 r=x-y*m;return m<=r?std::make_pair(y-1,r+m):std::make_pair(y,r);}inline u32 pow(u32 a,u64 p)const{u32 res=m!=1;while(p){if(p&1)res=rem(u64(res)*a);a=rem(u64(a)*a);p>>=1;}return res;}};namespace prime_impl{constexpr int table_size=1<<16;bool table[table_size];struct prime_table_init{prime_table_init(){table[0]=table[1]=true;for(int i=2;i<table_size;i++)if(!table[i]){for(int j=i*2;j<table_size;j+=i)table[j]=true;}}}dummy;}bool isprime(unsigned long long n)noexcept{if(n<prime_impl::table_size)return !prime_impl::table[n];if(n%2==0)return false;if(n<(1ull<<31)){BarrettReduction br(n);unsigned long long d=n-1;while(!(d&1))d>>=1;for(unsigned long long base:{2,7,61}){unsigned long long t=d;unsigned long long y=1;while(t>0){if(t&1)y=br.rem(y*base);base=br.rem(base*base);t>>=1;}t=d;while(t!=n-1&&y!=1&&y!=n-1){y=br.rem(y*y);t<<=1;}if(y!=n-1&&t%2==0)return false;}return true;}unsigned long long d=n-1;int s=0;while(!(d&1))d>>=1,s++;int q=63;while(!(d>>q))q--;unsigned long long r=n;for(int i=0;i<5;i++)r*=2-r*n;auto redc=[&r,&n](__uint128_t x)->unsigned long long {x=(x+__uint128_t((unsigned long long)x*-r)*n)>>64;return x>=n?x-n:x;};__uint128_t r2=-__uint128_t(n)%n;unsigned long long one=redc(r2);for(unsigned long long base:{2,325,9375,28178,450775,9780504,1795265022}){if(base%n==0)continue;unsigned long long a=base=redc((base%n)*r2);for(int i=q-1;i>=0;i--){a=redc(__uint128_t(a)*a);if(d>>i&1)a=redc(__uint128_t(a)*base);}if(a==one)continue;for(int i=1;a!=n-one;i++){if(i>=s)return false;a=redc(__uint128_t(a)*a);}}return true;}std::vector<unsigned long long>factorize(unsigned long long n)noexcept{std::vector<unsigned long long>ret;auto div=[](unsigned long long x)noexcept->unsigned long long {unsigned long long r=x;for(int i=0;i<5;i++)r*=2-r*x;unsigned long long r2=-__uint128_t(x)%x;auto redc=[&r,&x](__uint128_t t)->unsigned long long {t=(t+__uint128_t((unsigned long long)t*-r)*x)>>64;return t>=x?t-x:t;};unsigned long long a=0,b=0;const unsigned long long one=redc(r2);unsigned long long e=one;unsigned long long m=1ll<<((63-__builtin_clzll(x))>>3);while(true){unsigned long long ca=a,cb=b;unsigned long long sk=one;for(int i=0;i<m;i++){a=redc(__uint128_t(a)*a+e);b=redc(__uint128_t(b)*b+e);b=redc(__uint128_t(b)*b+e);unsigned long long c=redc(a),d=redc(b);sk=redc(__uint128_t(sk)*(c>d?c-d:d-c));}unsigned long long g=binary_gcd(redc(sk),x);if(g>1){if(g<x)return g;for(int i=0;i<m;i++){ca=redc(__uint128_t(ca)*ca+e);cb=redc(__uint128_t(cb)*cb+e);cb=redc(__uint128_t(cb)*cb+e);unsigned long long c=redc(ca),d=redc(cb);unsigned long long cg=binary_gcd(c>d?c-d:d-c,x);if(cg>1){if(cg<x)return cg;else{e+=one;a=b=0;break;}}}}}};static unsigned long long st[64];int p=0;while(!(n&1)){n>>=1;ret.push_back(2);}if(n==1)return ret;st[p++]=n;while(p){unsigned long long now=st[--p];if(isprime(now)){ret.push_back(now);continue;}unsigned long long d=div(now);st[p++]=d;now/=d;if(now!=1)st[p++]=now;}return ret;}template<typename T>std::enable_if_t<std::is_integral_v<T>,T>carmichael(T n){auto f=factorize(n);std::sort(f.begin(),f.end());T res=1;for(int l=0,r=0;l<f.size();l=r){while(r<f.size()&&f[l]==f[r])r++;if(f[l]==2){if(r-l==2)res=2;else if(r-l>=3)res=T(1)<<(r-l-2);}else{T prod=f[l]-1;for(int i=0;i<r-l-1;i++)prod*=f[l];res=std::lcm(res,prod);}}return res;}constexpr int carmichael_constexpr(int n){if(n==998244353)return 998244352;if(n==1000000007)return 1000000006;if(n<=1)return n;int res=1;int t=0;while(n%2==0){n/=2;t++;}if(t==2)res=2;else if(t>=3)res=1<<(t-2);for(int i=3;i*i<=n;i++)if(n%i==0){int c=0;while(n%i==0){n/=i;c++;}int prod=i-1;for(int j=0;j<c-1;j++)prod*=i;res=std::lcm(res,prod);}if(n!=1)res=std::lcm(res,n-1);return res;}template<int m>struct mod_int{private:static constexpr unsigned int umod=static_cast<unsigned int>(m);static constexpr unsigned int car=carmichael_constexpr(m);using uint=unsigned int;using mint=mod_int;uint v;static_assert(m<uint(1)<<31);mint sqrt_impl()const{if(this->val()<=1)return *this;if constexpr(m%8==1){mint b=2;while(b.pow((m-1)/2).val()==1)b++;int m2=m-1,e=0;while(m2%2==0)m2>>=1,e++;mint x=this->pow((m2-1)/2);mint y=(*this)*x*x;x*=*this;mint z=b.pow(m2);while(y.val()!=1){int j=0;mint t=y;while(t.val()!=1)t*=t,j++;z=z.pow(1<<(e-j-1));x*=z;z*=z;y*=z;e=j;}return x;}else if constexpr(m%8==5){mint ret=this->pow((m+3)/8);if((ret*ret).val()==this->val())return ret;else return ret*mint::raw(2).pow((m-1)/4);}else{return this->pow((m+1)/4);}}public:using value_type=uint;mod_int():v(0){}template<typename T,std::enable_if_t<std::is_signed_v<T>,std::nullptr_t> =nullptr>mod_int(T a){a%=m;if(a<0)v=a+umod;else v=a;}template<typename T,std::enable_if_t<std::is_unsigned_v<T>,std::nullptr_t> =nullptr>mod_int(T a):v(a%umod){}static constexpr mint raw(int a){mint ret;ret.v=a;return ret;}inline uint val()const{return this->v;}static constexpr int mod(){return m;}inline mint &operator+=(const mint &b){this->v+=b.v;if(this->v>=umod)this->v-=umod;return *this;}inline mint &operator-=(const mint &b){this->v-=b.v;if(this->v>=umod)this->v+=umod;return *this;}inline mint &operator*=(const mint &b){this->v=((unsigned long long)this->v*b.v)%umod;return *this;}inline mint &operator/=(const mint &b){*this*=b.inv();return *this;}inline mint operator+()const{return *this;}inline mint operator-()const{return mint()-*this;}friend inline mint operator+(const mint &a,const mint &b){return mint(a)+=b;}friend inline mint operator-(const mint &a,const mint &b){return mint(a)-=b;}friend inline mint operator*(const mint &a,const mint &b){return mint(a)*=b;}friend inline mint operator/(const mint &a,const mint &b){return mint(a)/=b;}friend inline bool operator==(const mint &a,const mint &b){return a.val()==b.val();}friend inline bool operator!=(const mint &a,const mint &b){return !(a==b);}inline mint operator++(int){mint ret=*this;*this+=1;return ret;}inline mint operator--(int){mint ret=*this;*this-=1;return ret;}mint pow(long long n)const{mint ret=mint::raw(1),a(*this);while(n){if(n&1)ret*=a;a*=a;n>>=1;}return ret;}inline mint inv()const{assert(this->v!=0);return pow(car-1);}std::optional<mint>sqrt()const{if(this->val()<=1||this->pow((m-1)/2)==1)return std::make_optional(this->sqrt_impl());else return std::nullopt;}static constexpr unsigned int order(){return car;}friend std::istream &operator>>(std::istream &is,mint &b){long long a;is>>a;b=mint(a);return is;}friend std::ostream &operator<<(std::ostream &os,const mint &b){os<<b.val();return os;}};template<int m>struct std::hash<mod_int<m>>{std::size_t operator()(mod_int<m>x)const{return std::hash<unsigned int>()(x.val());}};using mint998=mod_int<998244353>;using mint107=mod_int<1000000007>;using mint=mint998;void SOLVE(){int n,m;cin>>n>>m;vector<pair<vector<mint>,vector<mint>>>poly(m);rep(i,1,m+1){vector<mint>a(i+1),b(i+2);a[1]++;a[i]--;b[0]++;b[i]-=2;b[i+1]++;poly[i-1]={a,b};}auto add=[](const pair<vector<mint>,vector<mint>>&lhs,const pair<vector<mint>,vector<mint>>&rhs)->pair<vector<mint>,vector<mint>> {vector<mint>a=ntt_convolution(lhs.second,rhs.second);vector<mint>b=ntt_convolution(lhs.first,rhs.second);vector<mint>c=ntt_convolution(lhs.second,rhs.first);if(b.size()>c.size())swap(b,c);rep(i,b.size())c[i]+=b[i];return {c,a};};for(int i=poly.size();--i;)poly[i/2]=add(poly[i/2],poly[i]);auto [a,b]=poly[0];vector<mint>p(b);if(a.size()>b.size())b.resize(a.size());rep(i,a.size())b[i]-=a[i];if(p.size()>=b.size())b.resize(p.size()+1);cout<<bostan_mori(p,b,n)<<endl;}