結果
問題 |
No.42 貯金箱の溜息
|
ユーザー |
![]() |
提出日時 | 2025-07-23 22:13:10 |
言語 | C++23 (gcc 13.3.0 + boost 1.87.0) |
結果 |
AC
|
実行時間 | 16 ms / 5,000 ms |
コード長 | 18,863 bytes |
コンパイル時間 | 4,960 ms |
コンパイル使用メモリ | 322,916 KB |
実行使用メモリ | 7,716 KB |
最終ジャッジ日時 | 2025-07-23 22:13:16 |
合計ジャッジ時間 | 5,981 ms |
ジャッジサーバーID (参考情報) |
judge4 / judge2 |
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ファイルパターン | 結果 |
---|---|
other | AC * 3 |
ソースコード
#include <bits/stdc++.h> using namespace std; using 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 T1,typename T2,typename T3>istream &operator>>(istream &is,tuple<T1,T2,T3>&a){is>>std::get<0>(a)>>std::get<1>(a)>>std::get<2>(a);return is;} template<typename T,size_t n>istream &operator>>(istream &is,array<T,n>&a){for(auto&i:a)is>>i;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") #define uniq(x) sort(all(x)),x.erase(unique(all(x)),x.end()) template<typename T> inline int fkey(vector<T>&z,T key){return lower_bound(z.begin(),z.end(),key)-z.begin();} 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> #define SWITCH(a,b) (a) #else #define debug(...) static_cast<void>(0) #define debugg(...) static_cast<void>(0) #define SWITCH(a,b) (b) template<typename T1,typename T2>ostream &operator<<(ostream &os,const pair<T1,T2>&p){os<<p.first<<' '<<p.second;return os;} #endif struct 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> #include<optional> 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+=mint::raw(1); return ret; } inline mint operator--(int){ mint ret=*this; *this-=mint::raw(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=mod_int<1000000009>; template<typename T> std::vector<T>inverse_table(long long l,long long r){ assert(l<=r); if(l==r)return std::vector<T>{}; l=(l-1)%T::mod(); r=(r-1)%T::mod(); if(l<0)l+=T::mod(); if(r<0)r+=T::mod(); if(l>r){ int n=std::max(r,T::mod()-l); std::vector<T>fact(n+1),factinv(n+1); fact[0]=1; for(int i=1;i<=n;i++)fact[i]=fact[i-1]*T::raw(i); factinv[n]=fact[n].inv(); for(int i=n-1;i>=0;i--)factinv[i]=factinv[i+1]*T::raw(i+1); std::vector<T>ret; ret.reserve(r-l+T::mod()); for(int i=l+1;i<T::mod();i++)ret.push_back(-fact[T::mod()-i-1]*factinv[T::mod()-i]); ret.push_back(0); for(int i=1;i<=r;i++)ret.push_back(fact[i-1]*factinv[i]); return ret; } else{ int n=r-l; std::vector<T>ret(n); ret[0]=1; for(int i=1;i<n;i++)ret[i]=ret[i-1]*T::raw(l+i); T inv=(ret[n-1]*(n+l)).inv(); for(int i=n-1;i>=0;i--){ ret[i]*=inv; inv*=T::raw(i+1+l); } return ret; } } struct is_modint_impl{ template<typename T> static auto check(T&&x)->decltype(x.mod(),std::true_type{}); template<typename T> static auto check(...)->std::false_type; }; template<typename T> struct is_modint:public decltype(is_modint_impl::check<T>(std::declval<T>())){}; template<typename T> inline constexpr bool is_modint_v=is_modint<T>::value; struct is_dynamic_modint_impl{ template<typename T> static auto check(T&&x)->decltype(x.set_mod((typename T::value_type)0),std::true_type{}); template<typename T> static auto check(...)->std::false_type; }; template<typename T> struct is_dynamic_modint:public decltype(is_dynamic_modint_impl::check<T>(std::declval<T>())){}; template<typename T> inline constexpr bool is_dynamic_modint_v=is_dynamic_modint<T>::value; template<typename T> inline constexpr bool is_static_modint_v=is_modint_v<T>&&!is_dynamic_modint_v<T>; struct is_uso_modint_impl{ template<typename T> static auto check(T&&x)->decltype(x.uso(),std::true_type{}); template<typename T> static auto check(...)->std::false_type; }; template<typename T> struct is_uso_modint:public decltype(is_uso_modint_impl::check<T>(std::declval<T>())){}; template<typename T> inline constexpr bool is_uso_modint_v=is_uso_modint<T>::value; template<typename T,std::enable_if_t<is_modint_v<T>,std::nullptr_t> =nullptr> T interpolate(const std::vector<T>&y,T k){ int n=(int)y.size()-1; if(k.val()<=n)return y[k.val()]; T f=k,g=1; for(int i=1;i<=n;i++)f*=k-T::raw(i),g*=T::raw(i); if(n&1)g=-g; f/=g; std::vector<T>inv1=inverse_table<T>(1,n+1),inv2=inverse_table<T>(k.val()-n,k.val()+1); T res=y[0]*f*inv2[n]; for(int i=0;i<n;i++){ f=-(f*inv1[i]*T::raw(n-i)); res+=y[i+1]*f*inv2[n-i-1]; } return res; } template<typename T,typename Func> std::vector<T>arbitrary_fps_inv(const std::vector<T>&a,const Func&f,int deg=-1){ static_assert(std::is_convertible_v<Func,std::function<std::vector<T>(std::vector<T>,std::vector<T>)>>); int n=a.size(); if(deg==-1)deg=n; std::vector<T>b{a[0].inv()}; T two=2; for(int i=1;i<deg;i<<=1){ std::vector<T>h=f(b,b); h=f(h,std::vector<T>(a.begin(),a.begin()+std::min<int>(n,i*2))); b.resize(i*2); for(int j=0;j<i;j++)b[j]*=two; for(int j=0;j<i*2;j++)b[j]-=h[j]; } b.resize(deg); return b; } template<typename T,typename Func> std::vector<T>arbitrary_fps_log(const std::vector<T>&a,const Func&f,int deg=-1){ static_assert(std::is_convertible_v<Func,std::function<std::vector<T>(std::vector<T>,std::vector<T>)>>); int n=a.size(); if(deg==-1)deg=n; std::vector<T>inv=arbitrary_fps_inv(a,f,deg); std::vector<T>diff(n-1); for(int i=0;i<n-1;i++)diff[i]=T::raw(i+1)*a[i+1]; diff=f(diff,inv); diff.resize(deg); for(int i=deg-1;i>=1;i--)diff[i]=diff[i-1]/T::raw(i); diff[0]=0; return diff; } template<typename T,typename Func> std::vector<T>arbitrary_fps_exp(const std::vector<T>&a,const Func&f,int deg=-1){ static_assert(std::is_convertible_v<Func,std::function<std::vector<T>(std::vector<T>,std::vector<T>)>>); int n=a.size(); if(deg==-1)deg=n; std::vector<T>b{1}; for(int m=1;m<deg;m<<=1){ std::vector<T>nxt=arbitrary_fps_log(b,f,m*2); for(int i=0;i<m*2;i++)nxt[i]=-nxt[i]; for(int i=0;i<std::min(n,m*2);i++)nxt[i]+=a[i]; nxt[0]+=1; b=f(b,nxt); b.resize(m*2); } b.resize(deg); return b; } 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); } template<typename T,int p1,int p2,int p3> T crt3(int a1,int a2,int a3){ static_assert(p1<p2&&p2<p3); static constexpr long long x=pow_mod<int>(p1,p2-2,p2); static constexpr long long y=pow_mod<int>((long long)p1*p2%p3,p3-2,p3); long long c=(a2-a1+p2)*x%p2; long long c2=a1+c*p1; c=(a3-c2%p3+p3)*y%p3; return T(c2)+T(c)*T(p1)*T(p2); } 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; } } #include<concepts> 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<std::integral T> constexpr T safe_div(T a,T b){return a/b-(a%b&&(a^b)<0);} template<std::integral T> constexpr T safe_ceil(T a,T b){return a/b+(a%b&&(a^b)>0);} 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; 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> std::vector<T>anymod_convolution(const std::vector<T>&a,const std::vector<T>&b){ if(a.empty()||b.empty())return std::vector<T>{}; if(std::min(a.size(),b.size())<60){ std::vector<T>ret(a.size()+b.size()-1,0); for(int i=0;i<a.size();i++)for(int j=0;j<b.size();j++)ret[i+j]+=a[i]*b[j]; return ret; } using mint1=mod_int<167772161>; using mint2=mod_int<469762049>; using mint3=mod_int<998244353>; std::vector<mint1>a1(a.size()),b1(b.size()); std::vector<mint2>a2(a.size()),b2(b.size()); std::vector<mint3>a3(a.size()),b3(b.size()); for(int i=0;i<a.size();i++){ a1[i]=a[i].val(); a2[i]=a[i].val(); a3[i]=a[i].val(); } for(int i=0;i<b.size();i++){ b1[i]=b[i].val(); b2[i]=b[i].val(); b3[i]=b[i].val(); } a1=ntt_convolution(a1,b1),a2=ntt_convolution(a2,b2),a3=ntt_convolution(a3,b3); std::vector<T>ret(a.size()+b.size()-1); for(int i=0;i<ret.size();i++)ret[i]=crt3<T,mint1::mod(),mint2::mod(),mint3::mod()>(a1[i].val(),a2[i].val(),a3[i].val()); return ret; } void SOLVE(){ vector<mint>dp(3000); dp[0]=1; for(int i:{1,5,10,50,100,500}){ for(int j=3000;j-->i;)dp[j]-=dp[j-i]; } dp=arbitrary_fps_inv(dp,anymod_convolution<mint>); int q; cin>>q; while(q--){ ll x; cin>>x; vector<mint>y; y.reserve(6); int r=x%500; rep(i,6)y.push_back(dp[i*500+r]); cout<<interpolate(y,mint(x/500))<<'\n'; } }