#1081381 (C++23) No.2120 場合の数の下８桁

• 問題: No.2120 場合の数の下８桁
• ユーザー: eQe
• 提出日時: 2025-05-02 02:41:04
• 言語: C++23 (gcc 13.3.0 + boost 1.87.0)
• 結果: AC
• 実行時間: 20 ms / 2,000 ms
• コード長: 12,004 bytes
• コンパイル時間: 6,813 ms
• コンパイル使用メモリ: 334,768 KB
• 実行使用メモリ: 9,472 KB
• 最終ジャッジ日時: 2025-05-02 02:41:12
• 合計ジャッジ時間: 8,036 ms
• ジャッジサーバーID （参考情報）: judge3 / judge1

ファイルパターン	結果
other	AC * 20

ソースコード

#include<bits/stdc++.h>
#include<atcoder/all>
using namespace std;
namespace my{
#define eb emplace_back
#define LL(...) ll __VA_ARGS__;lin(__VA_ARGS__)
#define jo(a,b) a##b
#define FO_IMPL(n,c) for(ll jo(_i,c)=n;jo(_i,c)-->0;)
#define FO(n) FO_IMPL(n,__COUNTER__)
#define FOR(i,...) for(auto[i,i##stop,i##step]=range(0,__VA_ARGS__);i<i##stop;i+=i##step)
#define fo(i,...) FO##__VA_OPT__(R)(i __VA_OPT__(,__VA_ARGS__))
#define of(i,...) for(auto[i,i##stop,i##step]=range(1,__VA_ARGS__);i>=i##stop;i+=i##step)
#define fe(a,e,...) for(auto&&__VA_OPT__([)e __VA_OPT__(,__VA_ARGS__]):a)
#define maybe(p,c) (p?c:remove_cvref_t<decltype(c)>{})
#define base_operator(op,type) auto operator op(const type&v)const{auto copy=*this;return copy op##=v;}
#define entry void solve();void solve2();}int main(){my::io();my::solve();}namespace my{
void io(){cin.tie(nullptr)->sync_with_stdio(0);cout<<fixed<<setprecision(15);}
using ll=long long;
using ull=unsigned long long;
using i64=int64_t;
using ui64=uint64_t;
using ui128=__uint128_t;
constexpr auto range(ll s,ll b){ll a=0;if(s)swap(a,b);return array{a-s,b,1-s*2};}
constexpr auto range(ll s,ll a,ll b,ll c=1){return array{a-s,b,(1-s*2)*c};}
const string newline{char(10)};
const string space{char(32)};
constexpr auto abs(auto x){return x<0?-x:x;}
constexpr auto pow(auto x,auto n,auto e){assert(n>=0);decltype(x)r=e;for(;n;x*=x,n>>=1)if(n&1)r*=x;return r;}
constexpr auto pow(auto x,auto n){return pow(x,n,1);}
auto min(auto...a){return min(initializer_list<common_type_t<decltype(a)...>>{a...});}
template<class T,class U>common_type_t<T,U>gcd(T a,U b){return b?gcd(b,a%b):abs(a);}
auto gcd(auto...a){common_type_t<decltype(a)...>r=0;((r=gcd(r,a)),...);return r;}
auto mod(auto a,auto b){return(a%=b)<0?a+b:a;}
auto inv_mod(auto x,auto m){assert(gcd(x,m)==1);decltype(x)a=mod(x,m),b=m,u=1,v=0;while(b)swap(u-=a/b*v,v),swap(a-=a/b*b,b);return mod(u,m);}
ll rand(){static ll x=495;x^=x<<7;x^=x>>9;return x;}
ll rand(ll l,ll r=0){if(l>r)swap(l,r);return rand()%(r-l)+l;}

template<class A,class B>struct pair{
  A a;B b;
  pair()=default;
  pair(A a,B b):a(a),b(b){}
  pair(const std::pair<A,B>&p):a(p.first),b(p.second){}
  auto operator<=>(const pair&)const=default;
  pair operator+(const pair&p)const{return{a+p.a,b+p.b};}
  friend istream&operator>>(istream&i,pair&p){return i>>p.a>>p.b;}
  friend ostream&operator<<(ostream&o,const pair&p){return o<<p.a<<space<<p.b;}
};

template<class F=less<>>auto&sort(auto&a,F f={}){ranges::sort(a,f);return a;}

template<class...A>using pack_back_t=tuple_element_t<sizeof...(A)-1,tuple<A...>>;

template<class V>concept vectorial=is_base_of_v<vector<typename remove_cvref_t<V>::value_type>,remove_cvref_t<V>>;
template<class V>constexpr int rank(){if constexpr(vectorial<V>)return rank<typename V::value_type>()+1;else return 0;}
template<class T>struct core_t_helper{using core_t=T;};
template<vectorial V>struct core_t_helper<V>{using core_t=typename core_t_helper<typename V::value_type>::core_t;};
template<class T>using core_t=core_t_helper<T>::core_t;
template<class V>istream&operator>>(istream&i,vector<V>&v){fe(v,e)i>>e;return i;}
template<class T>ostream&operator<<(ostream&o,const vector<T>&v){ll n=v.size();fo(i,n)o<<v[i]<<maybe(i<n-1,space);return o;}
template<vectorial V>ostream&operator<<(ostream&o,const vector<V>&v){ll n=v.size();fo(i,n)o<<v[i]<<maybe(i<n-1,newline);return o;}

template<class V>struct vec;
template<int rank,class T>struct hvec_helper{using type=vec<typename hvec_helper<rank-1,T>::type>;};
template<class T>struct hvec_helper<0,T>{using type=T;};
template<int rank,class T>using hvec=typename hvec_helper<rank,T>::type;

template<class V>struct vec:vector<V>{
  static constexpr int R=rank<vec<V>>();
  using C=core_t<V>;
  using vector<V>::vector;
  vec(const vector<V>&v){vector<V>::operator=(v);}
  vec(const auto&...a)requires(sizeof...(a)>=3){resizes(a...);}
  void resizes(const auto&...a){*this=make(a...);}
  static auto make(ll n,const auto&...a){
    if constexpr(sizeof...(a)==1)return vec<C>(n,array{a...}[0]);
    else return vec<decltype(make(a...))>(n,make(a...));
  }

  vec&operator^=(const vec&u){this->insert(this->end(),u.begin(),u.end());return*this;}
  vec&operator+=(const vec&u){vec&v=*this;assert(v.size()==u.size());fo(i,v.size())v[i]+=u[i];return v;}
  vec&operator-=(const vec&u){vec&v=*this;assert(v.size()==u.size());fo(i,v.size())v[i]-=u[i];return v;}
  vec&operator+=(const C&c){fe(*this,e)e+=c;return*this;}
  vec&operator*=(const C&c){fe(*this,e)e*=c;return*this;}
  base_operator(^,vec)
  base_operator(+,vec)
  base_operator(-,vec)
  base_operator(+,C);
  base_operator(*,C);

  vec&operator++(){fe(*this,e)++e;return*this;}
  vec&operator--(){fe(*this,e)--e;return*this;}

  ll size()const{return vector<V>::size();}

  auto&emplace_back(auto&&...a){vector<V>::emplace_back(std::forward<decltype(a)>(a)...);return*this;}
  auto pop_back(){auto r=this->back();vector<V>::pop_back();return r;}

  auto scan(const auto&f)const{
    pair<C,bool>r{};
    fe(*this,e)if constexpr(!vectorial<V>)r.b?f(r.a,e),r:r={e,1};else if(auto s=e.scan(f);s.b)r.b?f(r.a,s.a),r:r=s;
    return r;
  }
  auto min()const{return scan([](auto&a,auto b){if(b<a)a=b;}).a;}

  template<class F=less<>>auto sort(F f={})const{vec v=*this;ranges::sort(v,f);return v;}

  auto transform(const auto&f)const{
    hvec<R,decltype(f(C()))>res(size());
    if constexpr(vectorial<V>)fo(i,size())res[i]=(*this)[i].transform(f);
    else std::transform(this->begin(),this->end(),res.begin(),f);
    return res;
  }

  auto rle()const{vec<pair<V,ll>>r;fe(*this,e)if(r.size()&&e==r.back().a)++r.back().b;else r.eb(e,1);return r;}
  auto rce()const{return sort().rle();}

  auto as()const{return transform([](const auto&e){return e.a;});}
};
template<class...A>requires(sizeof...(A)>=2)vec(const A&...a)->vec<hvec<sizeof...(A)-2,pack_back_t<A...>>>;
vec(ll)->vec<ll>;

void lin(auto&...a){(cin>>...>>a);}

void pp(const auto&...a){ll n=sizeof...(a);((cout<<a<<maybe(--n>0,space)),...);cout<<newline;}

template<class T>concept modulary=requires(T t){t.mod();};

template<class T>T fac(ll n){static vec<T>v{1};if(ll m=v.size();m<=n){v.resize(n+1);fo(i,m,n+1)v[i]=v[i-1]*i;}return v[n];}

template<class T>T fac_inv(ll n){
  static vec<T>v{1};
  if(ll m=v.size();m<=n){
    v.resize(n+1);
    v[n]=fac<T>(n).inv();
    of(i,n,m)v[i]=v[i+1]*(i+1);
  }
  return v[n];
}

template<class T>T comb(ll n,ll k){
  if(n<0||k<0||n<k)return 0;
  if constexpr(modulary<T>)return fac<T>(n)*fac_inv<T>(k)*fac_inv<T>(n-k);
  else return fac<T>(n)/fac<T>(k)/fac<T>(n-k);
}

template<int tag=-1>struct montgomery64{
  using modular=montgomery64;
  static inline ui64 N=998244353;
  static inline ui64 N_inv=996491785301655553ull;
  static inline ui64 R2=299560064;

  static int set_mod(ui64 N){
    if(modular::N==N)return 0;
    assert(N<(1ull<<63));
    assert(N&1);
    modular::N=N;
    R2=-ui128(N)%N;
    N_inv=N;
    fo(5)N_inv*=2-N*N_inv;
    assert(N*N_inv==1);
    return 0;
  }

  static ui64 mod(){return N;}

  ui64 a;
  montgomery64(const i64&a=0):a(reduce((ui128)(a%(i64)N+N)*R2)){}

  static ui64 reduce(const ui128&T){ui128 r=(T+ui128(ui64(T)*-N_inv)*N)>>64;return r>=N?r-N:r;}

  auto&operator+=(const modular&b){if((a+=b.a)>=N)a-=N;return*this;}
  auto&operator-=(const modular&b){if(i64(a-=b.a)<0)a+=N;return*this;}
  auto&operator*=(const modular&b){a=reduce(ui128(a)*b.a);return*this;}
  auto&operator/=(const modular&b){*this*=b.inv();return*this;}

  friend auto operator+(const modular&a,const modular&b){return modular{a}+=b;}
  friend auto operator-(const modular&a,const modular&b){return modular{a}-=b;}
  friend auto operator*(const modular&a,const modular&b){return modular{a}*=b;}
  friend auto operator/(const modular&a,const modular&b){return modular{a}/=b;}
  friend bool operator==(const modular&a,const modular&b){return a.a==b.a;}
  auto operator-()const{return modular{}-modular{*this};}

  modular pow(ui128 n)const{return my::pow(*this,n);}

  modular inv()const{ui64 a=val(),b=N,u=1,v=0;assert(gcd(a,b)==1);while(b)swap(u-=a/b*v,v),swap(a-=a/b*b,b);return u;}
  ui64 val()const{return reduce(a);}

  friend istream&operator>>(istream&i,montgomery64<tag>&b){ll t;i>>t;b=t;return i;}
  friend ostream&operator<<(ostream&o,const montgomery64<tag>&b){return o<<b.val();}
};

template<class T>T one(T n){return n>0;}

auto zerofill(ll x,ll L){string s=to_string(x);return string(L-s.size(),'0')+s;}

bool miller_rabin(ll n,vec<ll>as){
  ll d=n-1;
  while(~d&1)d>>=1;

  using modular=montgomery64<1>;
  modular::set_mod(n);

  modular one=1,minus_one=n-1;
  fe(as,a){
    if(a%n==0)continue;
    ll t=d;
    modular y=modular(a).pow(t);
    while(t!=n-1&&y!=one&&y!=minus_one)y*=y,t<<=1;
    if(y!=minus_one&&~t&1)return 0;
  }
  return 1;
}

bool is_prime(ll n){
  if(~n&1)return n==2;
  if(n<=1)return 0;
  if(n<4759123141LL)return miller_rabin(n,{2,7,61});
  return miller_rabin(n,{2,325,9375,28178,450775,9780504,1795265022});
}

ll pollard_rho(ll n){
  if(~n&1)return 2;
  if(is_prime(n))return n;

  using modular=montgomery64<2>;
  modular::set_mod(n);

  modular R,one=1;
  auto f=[&](const modular&x){return x*x+R;};
  while(1){
    modular x,y,ys,q=one;
    R=rand(2,n),y=rand(2,n);
    ll g=1;
    constexpr ll m=128;
    for(ll r=1;g==1;r<<=1){
      x=y;
      fo(r)y=f(y);
      for(ll k=0;g==1&&k<r;k+=m){
        ys=y;
        for(ll i=0;i<m&&i<r-k;++i)q*=x-(y=f(y));
        g=std::gcd(q.val(),n);
      }
    }
    if(g==n)do g=std::gcd((x-(ys=f(ys))).val(),n);while(g==1);
    if(g!=n)return g;
  }
}

auto factorize(ll n){
  assert(n>0);
  vec<ll>res;
  auto f=[&](auto&f,ll m){
    if(m==1)return;
    auto d=pollard_rho(m);
    if(d==m)res.eb(d);
    else f(f,d),f(f,m/d);
  };
  f(f,n);
  return res.rce();
}

template<class T>T chinese_remainder_theorem_coprime(const vec<T>&a,vec<T>&m,T M=0){
  ll K=a.size();
  m.eb(M);
  vec<T>t(K),S(K+1),P(K+1,1);
  fo(i,K){
    t[i]=mod((a[i]-S[i])*inv_mod(P[i],m[i]),m[i]);
    fo(j,i+1,K+1){
      S[j]+=t[i]*P[j];
      P[j]*=m[i];
      if(m[j])S[j]%=m[j],P[j]%=m[j];
    }
  }
  m.pop_back();
  return S.back();
}

template<class T>T chinese_remainder_theorem(const vec<T>&a,const vec<T>&m,T M=0){
  ll K=a.size();
  fo(i,K)fo(j,i+1,K)if((a[i]-a[j])%gcd(m[i],m[j]))return-1;

  unordered_map<T,pair<T,T>>exponent_max_congruence;
  fo(i,K)fe(factorize(m[i]),p,b)if(exponent_max_congruence[p].b<b)exponent_max_congruence[p]={a[i],b};

  vec<T>a_mod_prime_pow,m_mod_prime_pow;
  fe(exponent_max_congruence,p,v){
    T pq=pow(p,v.b);
    a_mod_prime_pow.eb(v.a%pq);
    m_mod_prime_pow.eb(pq);
  }
  return chinese_remainder_theorem_coprime(a_mod_prime_pow,m_mod_prime_pow,M);
}

struct comb_mod_prime_pow{
  ll p,q;
  ll pq;
  ll delta;
  vec<ll>fac_p;
  vec<ll>fac_inv_p;
  comb_mod_prime_pow(ll N,ll p,ll q):p(p),q(q),pq(pow(p,q)),delta(p==2&&q>=3?1:-1){
    N=min(N+1,pq);
    fac_p.resize(N);
    fac_inv_p.resize(N);
    fac_p[0]=1;
    fo(i,1,N)fac_p[i]=fac_p[i-1]*(i%p?i:1)%pq;
    fac_inv_p.back()=inv_mod(fac_p.back(),pq);
    of(i,N-1)fac_inv_p[i]=fac_inv_p[i+1]*((i+1)%p?i+1:1)%pq;
  }

  inline ll operator()(ll n,ll k)const{return c(n,k);}
  ll c(ll n,ll m)const{
    ll r=n-m;
    ll Nj=n,Mj=m,Rj=r;
    ll e0=0,eq1=0;
    ll res=1;
    for(ll i=1;Nj>0;++i){
      (res*=fac_p[Nj%pq])%=pq;
      (res*=fac_inv_p[Mj%pq])%=pq;
      (res*=fac_inv_p[Rj%pq])%=pq;
      Nj/=p;
      Mj/=p;
      Rj/=p;

      ll eps=Nj-Mj-Rj;
      e0+=eps;
      if(i>=q)eq1+=eps;
    }
    if(delta==-1&&eq1&1)res=pq-res;
    if(e0>=q)res=0;
    return res*pow(p,e0)%pq;
  }
};

struct comb_mod{
  vec<comb_mod_prime_pow>v;
  comb_mod(ll N,ll M){fe(factorize(M),p,q)v.eb(N,p,q);}

  inline ll operator()(ll n,ll k)const{return c(n,k);}
  ll c(ll n,ll k)const{
    if(n<0||k<0||n<k)return 0;

    vec<ll>r,m;
    fe(v,e){
      r.eb(e.c(n,k));
      m.eb(e.pq);
    }
    return chinese_remainder_theorem(r,m);
  }
};

entry
void solve(){
  LL(N,K);
  comb_mod comb(N,1e8);
  pp(zerofill(comb(N,K),8));
}}