結果

問題 No.1918 Simple Math ?
ユーザー ytqm3ytqm3
提出日時 2022-04-29 22:46:19
言語 C++17
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 573 ms / 2,000 ms
コード長 6,135 bytes
コンパイル時間 4,301 ms
コンパイル使用メモリ 262,664 KB
最終ジャッジ日時 2025-01-28 23:32:52
ジャッジサーバーID
(参考情報)
judge3 / judge5
このコードへのチャレンジ
(要ログイン)
ファイルパターン 結果
sample AC * 1
other AC * 33
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 #
プレゼンテーションモードにする

#include<bits/stdc++.h>
#include<atcoder/all>
using i64=int64_t;
using u64=uint64_t;
using namespace std;
namespace ttl{
template<typename T> using Vec=vector<T>;
template<typename T> using Vec2D=vector<vector<T>>;
template<typename T> using Vec3D=vector<vector<vector<T>>>;
template<typename T> using Vec4D=vector<vector<vector<vector<T>>>>;
template<typename T> void Scan_(T& a){
cin>>a;
}
template<typename T,typename U> void Scan_(pair<T,U>& a){
Scan_(a.first),Scan_(a.second);
}
template<typename T> void Scan_(Vec<T>& a){
for(auto& v:a){
Scan_(v);
}
}
template<typename T> void Scan_(Vec2D<T>& a){
for(auto& v:a){
for(auto& u:v){
Scan_(u);
}
}
}
void Scan(){}
template<typename T,class... Args> void Scan(T& n,Args&... args){
Scan_(n),Scan(args...);
}
template<typename T> void Print_(T a){
cout<<a;
}
template<typename T,typename U> void Print_(pair<T,U> a){
Print_(a.first),cout<<" ";Print_(a.second);
}
template<typename T> void Print(Vec<T> a){
for(size_t i=0;i<a.size();++i){
Print_(a[i]);
cout<<" \n"[i==a.size()-1];
}
}
template<typename T> void Print(Vec2D<T> a){
for(auto& v:a){
for(size_t i=0;i<v.size();++i){
Print_(v[i]);
cout<<" \n"[i==v.size()-1];
}
}
}
template<typename T> void Print(T a){
Print_(a);
cout<<"\n";
}
template<typename T,class... Args> void Print(T a,Args... args){
Print_(a),cout<<" ",Print(args...);
}
i64 Sum(vector<i64> a){
return accumulate(a.begin(),a.end(),i64(0));
}
Vec<i64> LISSize(Vec<i64> A){
int N=A.size();
Vec<i64> dp(N+1,2e18),res(N+1);
dp[0]=-1;
for(int i=0;i<N;++i){
auto j=(lower_bound(dp.begin(),dp.end(),A[i])-dp.begin())-1;
dp[j+1]=A[i];
res[i+1]=max(res[i],i64(j+1));
}
return res;
}
struct ESieve{
int n;
Vec<i64> lpf;
ESieve(int n_):n(n_),lpf(n_+1,-1){
for(i64 p=2;p<=n;++p){
if(lpf[p]!=-1){
continue;
}
for(i64 q=p;q<=n;q+=p){
if(lpf[q]==-1){
lpf[q]=p;
}
}
}
}
Vec<pair<i64,i64>> operator()(int m){
Vec<i64> v;
while(m!=1){
v.emplace_back(lpf[m]);
m/=lpf[m];
}
if(v.size()==0){
return {};
}
Vec<pair<i64,i64>> res;
res.emplace_back(v[0],1);
for(size_t i=1;i<v.size();++i){
if(v[i-1]!=v[i]){
res.emplace_back(v[i],1);
}
else{
res.back().second++;
}
}
return res;
}
};
bool CheckPrime(i64 n){
if(n<2){
return 0;
}
for(i64 i=2;i*i<=n;++i){
if(n%i==0){
return 0;
}
}
return 1;
}
Vec<pair<i64,i64>> PrimeFact(i64 n){
Vec<pair<i64,i64>> res;
for(i64 i=2;i*i<=n;++i){
if(n%i!=0){
continue;
}
i64 ex=0;
while(n%i==0){
ex++,n/=i;
}
res.emplace_back(i,ex);
}
if(n!=1){
res.emplace_back(n,1);
}
return res;
}
Vec<i64> EnumDiv(i64 n){
Vec<i64> res;
for(i64 i=1;i*i<=n;++i){
if(n%i!=0){
continue;
}
res.emplace_back(i);
if(i*i!=n){
res.emplace_back(n/i);
}
}
sort(res.begin(),res.end());
return res;
}
u64 Popcnt(u64 k){
return __builtin_popcountll(k);
}
template<typename T> Vec<pair<T,i64>> RunLenEnc(Vec<T> a){
int n=a.size();
Vec<pair<T,i64>> res;
T now=a[0];
int l=1;
for(int i=1;i<n;++i){
if(a[i-1]==a[i]){
l++;
}
else{
res.emplace_back(now,l);
now=a[i],l=1;
}
}
res.emplace_back(now,l);
return res;
}
Vec<char> StrToVec(string S){
Vec<char> res;
for(auto v:S){
res.emplace_back(v);
}
return res;
}
}
template<u64 mod> struct Modint{
u64 val;
Modint(i64 val_=0):val((val_%i64(mod)+i64(mod))%i64(mod)){}
Modint operator-(){
return (val==0)?0:mod-val;
}
Modint operator+(Modint rhs){
return Modint(*this)+=rhs;
}
Modint operator-(Modint rhs){
return Modint(*this)-=rhs;
}
Modint operator*(Modint rhs){
return Modint(*this)*=rhs;
}
Modint operator/(Modint rhs){
return Modint(*this)/=rhs;
}
Modint pow(i64 rhs){
Modint res=1,now=(*this);
while(rhs){
res*=((rhs&1)?now:1),now*=now,rhs>>=1;
}
return res;
}
Modint &operator+=(Modint rhs){
val+=rhs.val,val-=((val>=mod)?mod:0);
return (*this);
}
Modint &operator-=(Modint rhs){
val+=((val<rhs.val)?mod:0),val-=rhs.val;
return (*this);
}
Modint &operator*=(Modint rhs){
val=val*rhs.val%mod;
return (*this);
}
Modint &operator/=(Modint rhs){
return (*this)*=rhs.pow(mod-2);
}
bool operator==(Modint rhs){
return val==rhs.val;
}
bool operator!=(Modint rhs){
return val!=rhs.val;
}
friend std::ostream &operator<<(std::ostream& os,Modint x){
return os<<(x.val);
}
friend std::istream &operator>>(std::istream& is,Modint& x){
u64 t;
is>>t,x=t;
return is;
}
};
template<typename T> struct Comb{
vector<T> dat,idat;
Comb(int mx=3000000):dat(mx+1,1),idat(mx+1,1){
for(int i=1;i<=mx;++i){
dat[i]=dat[i-1]*i;
}
idat[mx]/=dat[mx];
for(int i=mx;i>0;--i){
idat[i-1]=idat[i]*i;
}
}
T operator()(int n,int k){
if(n<0||k<0||n<k){
return 0;
}
return dat[n]*idat[k]*idat[n-k];
}
};
using namespace ttl;
i64 SqrtF(i64 n){
//x*x<=n x
i64 ok=0,ng=1e9+5;
while(std::abs(ok-ng)>1){
i64 mid=(ok+ng)/2;
(mid*mid<=n?ok:ng)=mid;
}
return ok;
}
i64 FDiv(i64 a,i64 b){
if(b<0){
a*=-1,b*=-1;
}
if(a<0){
return -(-a+b-1)/b;
}
return a/b;
}
i64 CDiv(i64 a,i64 b){
if(b<0){
a*=-1,b*=-1;
}
if(a<0){
return -(-a)/b;
}
return (a+b-1)/b;
}
void solve(){
using mint=Modint<1000000007>;
i64 a,N;
Scan(a,N);
i64 T=SqrtF(a*N);
mint ans=0;
mint I2=mint(1)/2,I3=mint(1)/3;
for(i64 t=0;t<a;++t){
if(T-1-t<0){
continue;
}
i64 m=(T-1-t)/a;
i64 p=(t*t+2*t)/a-FDiv((t*t-1),a);
//sum[s=0,m] (t+as)(f(t^2+2t,a)-f(t^2-1,a)+2s))
ans+=mint(t)*(m+1)*(p+m);
ans+=mint(a)*p*m*(m+1)*I2;
ans+=mint(a)*(2*m+1)*m*(m+1)*I3;
}
ans+=mint(T)*(N-(T*T-1)/a);
Print(ans);
}
int main(){
constexpr u64 mod=998244353;
int T;
Scan(T);
while(T--){
solve();
}
}
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