結果

問題 No.1931 Fraction 2
コンテスト
ユーザー kiyoshi0205
提出日時 2022-05-06 23:26:46
言語 C++23
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 231 ms / 2,000 ms
コード長 5,610 bytes
コンパイル時間 9,055 ms
コンパイル使用メモリ 352,712 KB
実行使用メモリ 23,740 KB
最終ジャッジ日時 2024-07-06 17:24:41
合計ジャッジ時間 14,204 ms
ジャッジサーバーID
（参考情報） 		judge2 / judge3
このコードへのチャレンジ
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ファイルパターン 結果
sample AC * 3
other AC * 36
権限があれば一括ダウンロードができます

ソースコード

diff # 

#pragma GCC target("avx")
#pragma GCC optimize("O3")
#pragma GCC optimize("unroll-loops")
#include<bits/stdc++.h>
// #include<ext/pb_ds/assoc_container.hpp>
// #include<ext/pb_ds/tree_policy.hpp>
// #include<ext/pb_ds/tag_and_trait.hpp>
// using namespace __gnu_pbds;
// #include<boost/multiprecision/cpp_int.hpp>
// namespace multiprecisioninteger = boost::multiprecision;
// using cint=multiprecisioninteger::cpp_int;
using namespace std;
using ll=long long;
using datas=pair<ll,ll>;
using ddatas=pair<long double,long double>;
using tdata=pair<ll,datas>;
using vec=vector<ll>;
using mat=vector<vec>;
using pvec=vector<datas>;
using pmat=vector<pvec>;
// using llset=tree<ll,null_type,less<ll>,rb_tree_tag,tree_order_statistics_node_update>;
#define For(i,a,b) for(i=a;i<(ll)b;++i)
#define bFor(i,b,a) for(i=b,--i;i>=(ll)a;--i)
#define rep(i,N) For(i,0,N)
#define rep1(i,N) For(i,1,N)
#define brep(i,N) bFor(i,N,0)
#define brep1(i,N) bFor(i,N,1)
#define all(v) (v).begin(),(v).end()
#define allr(v) (v).rbegin(),(v).rend()
#define vsort(v) sort(all(v))
#define vrsort(v) sort(allr(v))
#define uniq(v) vsort(v),(v).erase(unique(all(v)),(v).end())
#define endl "\n"
#define popcount __builtin_popcountll
#define eb emplace_back
#define print(x) cout<<x<<endl
#define printyes print("Yes")
#define printno print("No")
#define printYES print("YES")
#define printNO print("NO")
#define output(v) do{bool f=0;for(auto outi:v){cout<<(f?" ":"")<<outi;f=1;}cout<<endl;}while(0)
#define matoutput(v) do{for(auto outimat:v)output(outimat);}while(0)
// constexpr ll mod=1000000007;
constexpr ll mod=998244353;
constexpr ll inf=1LL<<60;
constexpr long double eps=1e-9;
const long double PI=acosl(-1);
template<class T,class E> ostream& operator<<(ostream& os,const pair<T,E>& p){return os<<"("<<p.first<<","<<p.second<<")";}
template<class T> ostream& operator<<(ostream& os,const vector<T>& v){
  os<<"{";bool f=false;
  for(auto& x:v){if(f)os<<",";os<<x;f=true;}
  os<<"}";
  return os;
}
template<class T> ostream& operator<<(ostream& os,const set<T>& v){
  os<<"{";bool f=false;
  for(auto& x:v){if(f)os<<",";os<<x;f=true;}
  os<<"}";
  return os;
}
template<class T> ostream& operator<<(ostream& os,const multiset<T>& v){
  os<<"{";bool f=false;
  for(auto& x:v){if(f)os<<",";os<<x;f=true;}
  os<<"}";
  return os;
}
template<class T,class E> ostream& operator<<(ostream& os,const map<T,E>& v){
  os<<"{";bool f=false;
  for(auto& x:v){if(f)os<<",";os<<x;f=true;}
  os<<"}";
  return os;
}
template<class T> inline bool chmax(T& a,const T b){bool x=a<b;if(x)a=b;return x;}
template<class T> inline bool chmin(T& a,const T b){bool x=a>b;if(x)a=b;return x;}
#ifdef DEBUG
void debugg(){cout<<endl;}
template<class T,class... Args>void debugg(const T& x,const Args&... args){cout<<" "<<x;debugg(args...);}
#define debug(...) cout<<__LINE__<<" ["<<#__VA_ARGS__<<"]:",debugg(__VA_ARGS__)
#else
#define debug(...) (void(0))
#endif

inline void startupcpp(void) noexcept{
  cin.tie(0)->sync_with_stdio(0);
  cout<<fixed<<setprecision(15);
}

ll modinv(ll a,const ll m=mod) noexcept{
  ll b=m,u=1,v=0,t;
  while(b){
    t=a/b;
    a-=t*b; swap(a,b);
    u-=t*v; swap(u,v);
  }
  return (u+m)%m;
}

ll moddevide(const ll a,const ll b) noexcept{return (a*modinv(b))%mod;}

vec modncrlistp,modncrlistm;

ll modncr(const ll n,const ll r) noexcept{
  if(n<r||r<0)return 0;
  ll i,size=modncrlistp.size();
  if(size<=n){
    modncrlistp.resize(n+1);
    modncrlistm.resize(n+1);
    if(!size){
      modncrlistp[0]=modncrlistm[0]=1;
      size++;
    }
    For(i,size,n+1)modncrlistp[i]=modncrlistp[i-1]*i%mod;
    modncrlistm[n]=modinv(modncrlistp[n]);
    for(i=n;i>size;--i)modncrlistm[i-1]=modncrlistm[i]*i%mod;
  }
  return modncrlistp[n]*modncrlistm[r]%mod*modncrlistm[n-r]%mod;
}

ll modpow(ll a,ll n,const ll m=mod){
  if(n<0)return 0;
  ll res=1;
  while(n>0){
    if(n&1)res=res*a%m;
    a=a*a%m;
    n>>=1;
  }
  return res;
}

constexpr ll gcd(const ll a,const ll b) noexcept{return (!b)?abs(a):(a%b==0)?abs(b):gcd(b,a%b);}
constexpr ll lcm(const ll a,const ll b) noexcept{return a/gcd(a,b)*b;}

#include<atcoder/all>
using mint=atcoder::modint998244353;
ostream& operator<<(ostream& os,const mint& v){
  return os<<v.val();
}
vector<int> linear_sieve(int N){
  vector<int> p,lpf(N+1,0);
  for(int i=2;i<=N;++i){
    if(lpf[i]==0){
      p.emplace_back(i);
      lpf[i]=i;
    }
    for(auto x:p){
      if(x>lpf[i]||i*x>N)break;
      lpf[i*x]=x;
    }
  }
  return lpf;
}
ll N,M,K,H,W,A,B,C,D;
string s,t;
int main(){
  startupcpp();
  auto lpf=linear_sieve(200000);
  pmat g(200001);
  ll i,j;
  cin>>N;
  vec a(N),b(N);
  rep(i,N){
    cin>>a[i]>>b[i];
    map<ll,ll> mp;
    j=b[i];
    while(j>1){
      mp[lpf[j]]++;
      j/=lpf[j];
    }
    for(auto[p,cnt]:mp){
      g[p].emplace_back(modpow(p,cnt),i);
    }
  }
  mint alllcm=1;
  rep(i,200001){
    if(g[i].size()){
      vrsort(g[i]);
      alllcm*=g[i][0].first;
    }
  }
  mint ans;
  rep(i,N)ans+=a[i]*alllcm/b[i];
  debug(ans,alllcm);
  rep(i,200001){
    if(g[i].empty())continue;
    ll p=g[i][0].first,s=0;
    vec l;
    l.reserve(g[i].size());
    for(auto [val,id]:g[i]){
      debug(val,id);
      l.emplace_back(b[id]/val%p);
    }
    debug(l);
    auto r=l;
    rep1(j,l.size())(l[j]*=l[j-1])%=p;
    brep1(j,r.size())(r[j-1]*=r[j])%=p;
    debug(l,r);
    rep(j,g[i].size()){
      auto[val,id]=g[i][j];
      ll tmp=p/val*a[id]%p;
      if(j)(tmp*=l[j-1])%=p;
      if(j+1<ll(r.size()))(tmp*=r[j+1])%=p;
      debug(val,id,tmp);
      s+=tmp;
    }
    debug(s,p);
    ans/=gcd(s,p);
    alllcm/=gcd(s,p);
  }
  print(ans<<" "<<alllcm);
}
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