結果

問題 No.2206 Popcount Sum 2
コンテスト
ユーザー Taiki0715
提出日時 2024-10-01 12:17:23
言語 C++23
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 342 ms / 4,000 ms
コード長 8,767 bytes
コンパイル時間 6,373 ms
コンパイル使用メモリ 318,244 KB
実行使用メモリ 6,932 KB
最終ジャッジ日時 2024-10-01 12:17:40
合計ジャッジ時間 14,330 ms
ジャッジサーバーID
（参考情報） 		judge1 / judge2
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 * 1
other AC * 18
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 # 

#include <bits/stdc++.h>
using namespace std;
#if __has_include(<atcoder/all>)
#include <atcoder/all>
#endif
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 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 reps(i,a,n) for(int i=(a);i<int(n);i++)
#define rep(i,n) reps(i,0,n)
#define all(x) x.begin(),x.end()
#define pcnt(x) __builtin_popcountll(x)
#define fin(x) return cout<<x<<'\n',static_cast<void>(0)
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;}
#endif
void SOLVE();
int main(){
  ios::sync_with_stdio(false);
  cin.tie(nullptr);
  cout<<fixed<<setprecision(16);
  #ifdef LOCAL
  clock_t start=clock();
  #endif
  int testcase=1;
  cin>>testcase;
  for(int i=0;i<testcase;i++){
    SOLVE();
  }
  #ifdef LOCAL
  cerr<<"time:";
  cerr<<(clock()-start)/1000;
  cerr<<"ms\n";
  #endif
}
template<int m>
struct mod_int{
private:
  using uint=unsigned int;
  using mint=mod_int;
  uint v;
  static_assert(m<uint(1)<<31);
public:
  mod_int():v(0){}
  mod_int(ll a){
    a%=m;
    if(a<0)v=a+m;
    else v=a;
  }
  static 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>=m)this->v-=m;
    return *this;
  }
  inline mint &operator-=(const mint &b){
    this->v-=b.v;
    if(this->v>=m)this->v+=m;
    return *this;
  }
  inline mint &operator*=(const mint &b){
    this->v=(uint64_t(this->v)*uint64_t(b.v))%m;
    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(ll n)const{
    mint ret=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(m-2);
  }
  mint sqrt()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);
    }
  }
  pair<bool,mint> safe_sqrt()const{
    if(this->pow((m-1)/2)==1)return make_pair(true,this->sqrt());
    else return make_pair(false,0);
  }
  friend istream &operator>>(istream &is,mint &b){
    ll a;
    is>>a;
    b=mint(a);
    return is;
  }
  friend ostream &operator<<(ostream &os,const mint &b){
    os<<b.val();
    return os;
  }
};
using mint998=mod_int<998244353>;
using mint107=mod_int<1000000007>;
template<typename T>
struct F{
private:
  static int capacity;
  static vector<T>fact,factinv,inv;
  static void resize(int n){
    fact.resize(n+1),factinv.resize(n+1),inv.resize(n+1);
    for(int i=capacity+1;i<=n;i++){
      fact[i]=fact[i-1]*i;
      inv[i]=-inv[T::mod()%i]*(T::mod()/i);
      factinv[i]=factinv[i-1]*inv[i];
    }
    capacity=n;
  }
public:
  static T C(int n,int k){
    if(n<k)return 0;
    if(k<0)return 0;
    if(capacity<n)resize(n);
    return fact[n]*factinv[k]*factinv[n-k];
  }
  static T P(int n,int k){
    if(n<k)return 0;
    if(k<0)return 0;
    if(capacity<n)resize(n);
    return fact[n]*factinv[n-k];
  }
  static T H(int n,int k){
    if(n==0&&k==0)return 1;
    return C(n+k-1,k);
  }
  static T factorial(int n){
    if(capacity<n)resize(n);
    return fact[n];
  }
  static T factorial_inv(int n){
    if(capacity<n)resize(n);
    return factinv[n];
  }
  static T S(ll n,int k){
    if(n<0)return 0;
    if(n<k)return 0;
    T ret=0;
    if(capacity<k)resize(k);
    rep(i,k+1){
      ret+=fact[k]*factinv[i]*factinv[k-i]*T::raw(i).pow(n)*((k-i)&1?-1:1);
    }
    return ret*factinv[k];
  }
  template<typename... INT>
  static T O(INT...k){
    int n=0;
    for(int i:initializer_list<int>{k...}){
      if(i<0)return 0;
      n+=i;
    }
    if(capacity<n)resize(n);
    T ret=fact[n];
    for(int i:initializer_list<int>{k...})ret*=factinv[i];
    return ret;
  }
};
template<typename T>int F<T>::capacity=1;
template<typename T>vector<T>F<T>::fact{1,1};
template<typename T>vector<T>F<T>::factinv{1,1};
template<typename T>vector<T>F<T>::inv{0,1};
using namespace std;
template<typename T>
struct BinomialPrefixSum{
private:
  static vector<vector<T>>table;
  static constexpr int b=256;
  static const T inv2;
  static void resize(int n){
    if(table.size()>n)return;
    int pre=table.size();
    table.resize(n+1);
    for(int i=pre;i<=n;i++){
      table[i].resize(i+1);
      table[i][0]=1;
      int half=i/2;
      T pow2i=table[i][i]=T::raw(2).pow(i*b);
      for(int j=1;j<=half;j++){
        T now=table[i][j-1];
        for(int k=1;k<b;k++)now+=F<T>::C(i*b,b*(j-1)+k);
        table[i][i-j]=pow2i-now;
        table[i][j]=now+=F<T>::C(i*b,j*b);
      }
    }
  }
public:
  static T get(int n,int k){
    if(n<k)k=n;
    if(k<0)return 0;
    int sn=n/b,sk=k/b;
    int sn2=sn*b,sk2=sk*b;
    if(n-sn2<sn2+b-n){
      if(k-sk2<sk2+b-k){
        if(n-sn2+k-sk2<n-k){
          resize(sn);
          T now=table[sn][sk];
          for(int i=sn2;i<n;i++)now=now*2-F<T>::C(i,sk2);
          for(int i=sk2+1;i<=k;i++)now+=F<T>::C(n,i);
          return now;
        }
      }
      else if(sn2!=sk2){
        sk2+=b;
        sk++;
        resize(sn);
        T now=table[sn][sk];
        for(int i=sk2;i>k;i--)now-=F<T>::C(sn2,i);
        for(int i=sn2;i<n;i++)now=now*2-F<T>::C(i,k);
        return now;
      }
    }
    else{
      sn2+=b;
      sn++;
      if(k-sk2<sk2+b-k){
        if(sn2-n+k-sk2<n-k){
          resize(sn);
          T now=table[sn][sk];
          for(int i=sk2+1;i<=k;i++)now+=F<T>::C(sn2,i);
          for(int i=sn2-1;i>=n;i--)now=(now+F<T>::C(i,k))*inv2;
          return now;
        }
      }
      else{
        if(sn2-n+sk2-k<n-k){
          resize(sn);
          sk2+=b;
          sk++;
          T now=table[sn][sk];
          for(int i=sk2;i>k;i--)now-=F<T>::C(sn2,i);
          for(int i=sn2-1;i>=n;i--)now=(now+F<T>::C(i,k))*inv2;
          return now;
        }
      }
    }
    T now=T::raw(2).pow(n);
    for(int i=n;i>k;i--)now-=F<T>::C(n,i);
    return now;
  }
  static inline T get(int n,int k1,int k2){
    return get(n,k2)-get(n,k1-1);
  }
};
template<typename T>vector<vector<T>>BinomialPrefixSum<T>::table;
template<typename T>const T BinomialPrefixSum<T>::inv2(T(2).inv());
using mint=mint998;
void SOLVE(){
  int n,m;
  cin>>n>>m;
  cout<<(mint(2).pow(n)-1)*BinomialPrefixSum<mint>::get(n-1,m-1)<<'\n';
}
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