結果

問題 No.1931 Fraction 2
ユーザー kiyoshi0205kiyoshi0205
提出日時 2022-05-06 22:54:39
言語 C++23
(gcc 12.3.0 + boost 1.83.0)
結果
WA  
実行時間 -
コード長 9,322 bytes
コンパイル時間 9,219 ms
コンパイル使用メモリ 351,936 KB
実行使用メモリ 38,304 KB
最終ジャッジ日時 2024-07-06 17:20:18
合計ジャッジ時間 23,839 ms
ジャッジサーバーID
（参考情報） 		judge2 / judge4
このコードへのチャレンジ
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テストケース

テストケース表示
入力 結果 実行時間
実行使用メモリ
testcase_00 AC 6 ms
8,916 KB
testcase_01 AC 7 ms
8,888 KB
testcase_02 AC 7 ms
8,948 KB
testcase_03 WA -
testcase_04 RE -
testcase_05 WA -
testcase_06 WA -
testcase_07 WA -
testcase_08 WA -
testcase_09 WA -
testcase_10 WA -
testcase_11 WA -
testcase_12 WA -
testcase_13 RE -
testcase_14 RE -
testcase_15 RE -
testcase_16 RE -
testcase_17 WA -
testcase_18 RE -
testcase_19 WA -
testcase_20 RE -
testcase_21 RE -
testcase_22 RE -
testcase_23 RE -
testcase_24 WA -
testcase_25 RE -
testcase_26 WA -
testcase_27 RE -
testcase_28 WA -
testcase_29 WA -
testcase_30 WA -
testcase_31 WA -
testcase_32 WA -
testcase_33 WA -
testcase_34 WA -
testcase_35 WA -
testcase_36 WA -
testcase_37 WA -
testcase_38 WA -
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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;}
struct unionfind{
  private:
  int maxN;
  vector<int> par,treesize;
  public:unionfind(int N) :maxN(N),par(N),treesize(N,1){
    for(int i=0;i<maxN;++i)par[i]=i;
  }
  int root(int x){
    while(par[x]!=x){
      x=par[x]=par[par[x]];
    }
    return x;
  }
  bool merge(int x,int y){
    x=root(x);
    y=root(y);
    if(x==y)return false;
    if(treesize[x]>treesize[y])swap(x,y);
    par[x]=y;
    treesize[y]+=treesize[x];
    return true;
  }
  bool merge(pair<int,int> v){
    return merge(v.first,v.second);
  }
  bool parcheck(int x,int y){
    return root(x)==root(y);
  }
  bool parcheck(pair<int,int> v){
    return parcheck(v.first,v.second);
  }
  int size(int x){
    return treesize[root(x)];
  }
  void clear(){
    treesize.assign(maxN,1);
    for(int i=0;i<maxN;++i)par[i]=i;
  }
  vector<vector<int>> groups(){
    vector<vector<int>> res(maxN);
    for(int i=0;i<maxN;++i)res[root(i)].emplace_back(i);
    // return res;
    vector<vector<int>> res2;
    for(vector<int> x:res){
      if(x.size())res2.emplace_back(x);
    }
    return res2;
  }
};
struct HLD{
private:
  //無向木であること!
  vector<vector<int>> g;
  int fdfs(int now,int p,int depth){
    int d=0;
    dep[now]=depth;
    par[now]=p;
    for(size_t i=0;i+1<g[now].size();++i){
      if(g[now][i]==p)swap(g[now][i],g[now].back());
      if(chmax(d,fdfs(g[now][i],now,depth+1)))swap(g[now][0],g[now][i]);
    }
    g[now].pop_back();
    return d+1;
  }
  void sdfs(int now){
    in[now]=ETlist.size();
    ETlist.emplace_back(now);
    for(size_t i=0;i<g[now].size();++i){
      nxt[g[now][i]]=i?g[now][i]:nxt[now];
      sdfs(g[now][i]);
    }
    out[now]=ETlist.size();
  }
public:
  // nxt[i]:iのheavy root
  // Heavy edge i = [in[nxt[i]],in[i]]
  // sub tree i = [in[i],out[i])
  vector<int> par,nxt,in,out,ETlist,dep;
  HLD(vector<vector<int>> G,int first=0):g(G),par(G.size()),nxt(G.size()),in(G.size()),out(G.size()){
    ETlist.reserve(G.size());
    init(first);
  };
  HLD(int N):g(N),par(N),nxt(N),in(N),out(N),dep(N){ETlist.reserve(N);};
  void add_edge(int a,int b){
    g[a].emplace_back(b);
    g[b].emplace_back(a);
  }
  void init(int first=0){
    {
      int d=0;par[first]=-1;
      for(auto& x:g[first])if(chmax(d,fdfs(x,first,1)))swap(x,g[first][0]);
    }
    nxt[first]=first;
    sdfs(first);
  }
  int la(int x,int k){
    int y=nxt[x];
    if(in[x]-in[y]>=k)return ETlist[in[x]-k];
    if(y==0)return 0;
    return la(par[y],k-(in[x]-in[y])-1);
  }
  int lca(int a,int b){
    if(in[a]>in[b])swap(a,b);
    if(nxt[a]==nxt[b])return a;
    return lca(a,par[nxt[b]]);
  }
};

#include<atcoder/all>
using mint=atcoder::modint998244353;
ostream& operator<<(ostream& os,const mint& v){
  return os<<v.val();
}
template<class Edge,class Ver>
pair<Edge,vector<Ver>> diameter(const vector<vector<pair<Edge,Ver>>>& g){
  int N=g.size();
  Edge *dist,LIM=numeric_limits<Edge>::max();
  dist=new Edge[N];
  fill(dist,dist+N,LIM);
  queue<Ver> que;
  que.emplace(dist[0]=0);
  while(!que.empty()){
    auto now=que.front();
    for(auto x:g[now]){
      if(dist[x.second]==LIM){
        dist[x.second]=dist[now]+x.first;
        que.emplace(x.second);
      }
    }
    que.pop();
  }
  Ver f=max_element(dist,dist+N)-dist;
  fill(dist,dist+N,LIM);
  dist[f]=0;
  que.emplace(f);
  Ver *par=new Ver[N];
  while(!que.empty()){
    auto now=que.front();
    for(auto x:g[now]){
      if(dist[x.second]==LIM){
        par[x.second]=now;
        dist[x.second]=dist[now]+x.first;
        que.emplace(x.second);
      }
    }
    que.pop();
  }
  Ver s=max_element(dist,dist+N)-dist;
  Edge ans=dist[s];
  vector<Ver> res(1,s);
  while(s!=f)res.emplace_back(s=par[s]);
  delete[] par;
  delete[] dist;
  return pair<Edge,vector<Ver>>(ans,res);
}
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);
  mat bp(N);
  rep(i,N){
    cin>>a[i]>>b[i];
    map<ll,ll> mp;
    j=b[i];
    while(j>1){
      bp[i].emplace_back(lpf[j]);
      mp[lpf[j]]++;
      j/=lpf[j];
    }
    uniq(bp[i]);
    for(auto[p,cnt]:mp){
      g[p].emplace_back(modpow(p,cnt),i);
    }
  }
  mint allprod=1;
  rep(i,200001){
    if(g[i].size()){
      vrsort(g[i]);
      allprod*=g[i][0].first;
    }
  }
  debug(allprod);
  mint ans;
  rep(i,N){
    auto res=allprod*a[i];
    for(auto p:bp[i])res/=gcd(b[i],g[p][0].first);
    ans+=res;
  }
  debug(ans,allprod);
  rep1(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])l.emplace_back(b[id]/val%p);
    auto r=l;
    rep1(j,l.size())(l[j]*=l[j-1])%=p;
    brep1(j,r.size())(r[j-1]*=r[j])%=p;
    for(auto x:g[i]){
      auto id=x.second;
      ll tmp=a[id]%p;
      if(id)(tmp*=l[id-1])%=p;
      if(id+1<ll(r.size()))(tmp*=r[id+1])%=p;
      s+=tmp;
      if(s>=p)s-=p;
    }
    debug(s,p);
    ans/=gcd(s,p);
    allprod/=gcd(s,p);
  }
  print(ans<<" "<<allprod);
}
0