結果
| 問題 |
No.1781 LCM
|
| コンテスト | |
| ユーザー |
 tko919
|
| 提出日時 | 2022-10-24 02:36:00 |
| 言語 | C++17 (gcc 13.3.0 + boost 1.87.0) |
| 結果 |
AC
|
| 実行時間 | 1,318 ms / 5,000 ms |
| コード長 | 9,785 bytes |
| コンパイル時間 | 2,284 ms |
| コンパイル使用メモリ | 207,200 KB |
| 最終ジャッジ日時 | 2025-02-08 11:59:03 |
|
ジャッジサーバーID （参考情報） |
judge5 / judge3 |
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| ファイルパターン | 結果 |
|---|---|
| sample | AC * 2 |
| other | AC * 31 |
ソースコード
#line 1 "library/Template/template.hpp"
#include <bits/stdc++.h>
using namespace std;
#define rep(i,a,b) for(int i=(int)(a);i<(int)(b);i++)
#define ALL(v) (v).begin(),(v).end()
using ll=long long int;
const int inf = 0x3fffffff;
const ll INF = 0x1fffffffffffffff;
template<typename T>inline bool chmax(T& a,T b){if(a<b){a=b;return 1;}return 0;}
template<typename T>inline bool chmin(T& a,T b){if(a>b){a=b;return 1;}return 0;}
#line 2 "library/Utility/fastio.hpp"
#include <unistd.h>
class FastIO{
static constexpr int L=1<<16;
char rdbuf[L];
int rdLeft=0,rdRight=0;
inline void reload(){
int len=rdRight-rdLeft;
memmove(rdbuf,rdbuf+rdLeft,len);
rdLeft=0,rdRight=len;
rdRight+=fread(rdbuf+len,1,L-len,stdin);
}
inline bool skip(){
for(;;){
while(rdLeft!=rdRight and rdbuf[rdLeft]<=' ')rdLeft++;
if(rdLeft==rdRight){
reload();
if(rdLeft==rdRight)return false;
}
else break;
}
return true;
}
template<typename T,enable_if_t<is_integral<T>::value,int> =0>inline bool _read(T& x){
if(!skip())return false;
if(rdLeft+20>=rdRight)reload();
bool neg=false;
if(rdbuf[rdLeft]=='-'){
neg=true;
rdLeft++;
}
x=0;
while(rdbuf[rdLeft]>='0' and rdLeft<rdRight){
x=x*10+(neg?-(rdbuf[rdLeft++]^48):(rdbuf[rdLeft++]^48));
}
return true;
}
template<typename T,enable_if_t<is_floating_point<T>::value,int> =0>inline bool _read(T& x){
if(!skip())return false;
if(rdLeft+20>=rdRight)reload();
bool neg=false;
if(rdbuf[rdLeft]=='-'){
neg=true;
rdLeft++;
}
x=0;
while(rdbuf[rdLeft]>='0' and rdbuf[rdLeft]<='9' and rdLeft<rdRight){
x=x*10+(rdbuf[rdLeft++]^48);
}
if(rdbuf[rdLeft]!='.')return true;
rdLeft++;
T base=.1;
while(rdbuf[rdLeft]>='0' and rdbuf[rdLeft]<='9' and rdLeft<rdRight){
x+=base*(rdbuf[rdLeft++]^48);
base*=.1;
}
if(neg)x=-x;
return true;
}
inline bool _read(char& x){
if(!skip())return false;
if(rdLeft+1>=rdRight)reload();
x=rdbuf[rdLeft++];
return true;
}
inline bool _read(string& x){
if(!skip())return false;
for(;;){
int pos=rdLeft;
while(pos<rdRight and rdbuf[pos]>' ')pos++;
x.append(rdbuf+rdLeft,pos-rdLeft);
if(rdLeft==pos)break;
rdLeft=pos;
if(rdLeft==rdRight)reload();
else break;
}
return true;
}
template<typename T>inline bool _read(vector<T>& v){
for(auto& x:v){
if(!_read(x))return false;
}
return true;
}
char wtbuf[L],tmp[50];
int wtRight=0;
inline void flush(){
fwrite(wtbuf,1,wtRight,stdout);
wtRight=0;
}
inline void _write(const char& x){
if(wtRight>L-32)flush();
wtbuf[wtRight++]=x;
}
inline void _write(const string& x){
for(auto& c:x)_write(c);
}
template<typename T,enable_if_t<is_integral<T>::value,int> =0>inline void _write(T x){
if(wtRight>L-32)flush();
if(x==0){
_write('0');
return;
}
else if(x<0){
_write('-');
if (__builtin_expect(x == std::numeric_limits<T>::min(), 0)) {
switch (sizeof(x)) {
case 2: _write("32768"); return;
case 4: _write("2147483648"); return;
case 8: _write("9223372036854775808"); return;
}
}
x=-x;
}
int pos=0;
while(x!=0){
tmp[pos++]=char((x%10)|48);
x/=10;
}
rep(i,0,pos)wtbuf[wtRight+i]=tmp[pos-1-i];
wtRight+=pos;
}
template<typename T>inline void _write(const vector<T>& v){
rep(i,0,v.size()){
if(i)_write(' ');
_write(v[i]);
}
}
public:
FastIO(){}
~FastIO(){flush();}
inline void read(){}
template <typename Head, typename... Tail>inline void read(Head& head,Tail&... tail){
assert(_read(head));
read(tail...);
}
template<bool ln=true,bool space=false>inline void write(){if(ln)_write('\n');}
template <bool ln=true,bool space=false,typename Head, typename... Tail>inline void write(const Head& head,const Tail&... tail){
if(space)_write(' ');
_write(head);
write<ln,true>(tail...);
}
};
/**
* @brief Fast IO
*/
#line 3 "sol.cpp"
#line 2 "library/Math/sieve.hpp"
template<int L=1010101>vector<int> sieve(int N){
bitset<L> isp;
int n,sq=ceil(sqrt(N));
for(int z=1;z<=5;z+=4){
for(int y=z;y<=sq;y+=6){
for(int x=1;x<=sq and (n=4*x*x+y*y)<=N;++x){
isp[n].flip();
}
for(int x=y+1;x<=sq and (n=3*x*x-y*y)<=N;x+=2){
isp[n].flip();
}
}
}
for(int z=2;z<=4;z+=2){
for(int y=z;y<=sq;y+=6){
for (int x=1;x<=sq and (n=3*x*x+y*y)<=N;x+=2){
isp[n].flip();
}
for(int x=y+1;x<=sq and (n=3*x*x-y*y)<=N;x+=2){
isp[n].flip();
}
}
}
for(int y=3;y<=sq;y+=6){
for(int z=1;z<=2;++z){
for(int x=z;x<=sq and (n=4*x*x+y*y)<=N;x+=3){
isp[n].flip();
}
}
}
for(int n=5;n<=sq;++n)if(isp[n]){
for(int k=n*n;k<=N;k+=n*n){
isp[k]=false;
}
}
isp[2]=isp[3]=true;
vector<int> ret;
for(int i=2;i<=N;i++)if(isp[i]){
ret.push_back(i);
}
return ret;
}
/**
* @brief Prime Sieve
*/
#line 3 "library/Math/multiplicative.hpp"
template<typename T,T (*pe)(int,int),T (*psum)(ll)>T MultiplicativeSum(ll N){
ll SQ=sqrtl(N);
auto ps=sieve(SQ);
T ret=psum(N)+1;
auto dfs=[&](auto& dfs,ll x,int i,int e,T cur,T pre)->void{
T nxt=pre*pe(ps[i],e+1);
ret+=cur*(psum(double(N)/x)-psum(ps[i]));
ret+=nxt;
ll L=sqrtl(double(N)/x);
if(ps[i]<=L)dfs(dfs,x*ps[i],i,e+1,nxt,pre);
rep(j,i+1,ps.size()){
if(ps[j]>L)break;
dfs(dfs,x*ps[j],j,1,cur*pe(ps[j],1),cur);
}
};
rep(i,0,ps.size())dfs(dfs,ps[i],i,1,pe(ps[i],1),1);
return ret;
}
/**
* @brief Multiplicative Sum
* @docs docs/multiplicative.md
*/
#line 2 "library/Math/modint.hpp"
template<int mod=1000000007>struct fp {
int v; static int get_mod(){return mod;}
int inv() const{
int tmp,a=v,b=mod,x=1,y=0;
while(b)tmp=a/b,a-=tmp*b,swap(a,b),x-=tmp*y,swap(x,y);
if(x<0){x+=mod;} return x;
}
fp(ll x=0){init(x%mod+mod);}
fp& init(int x){v=(x<mod?x:x-mod); return *this;}
fp operator-()const{return fp()-*this;}
fp pow(ll t){assert(t>=0); fp res=1,b=*this; while(t){if(t&1)res*=b;b*=b;t>>=1;} return res;}
fp& operator+=(const fp& x){return init(v+x.v);}
fp& operator-=(const fp& x){return init(v+mod-x.v);}
fp& operator*=(const fp& x){v=ll(v)*x.v%mod; return *this;}
fp& operator/=(const fp& x){v=ll(v)*x.inv()%mod; return *this;}
fp operator+(const fp& x)const{return fp(*this)+=x;}
fp operator-(const fp& x)const{return fp(*this)-=x;}
fp operator*(const fp& x)const{return fp(*this)*=x;}
fp operator/(const fp& x)const{return fp(*this)/=x;}
bool operator==(const fp& x)const{return v==x.v;}
bool operator!=(const fp& x)const{return v!=x.v;}
friend istream& operator>>(istream& is,fp& x){return is>>x.v;}
friend ostream& operator<<(ostream& os,const fp& x){return os<<x.v;}
};
template<typename T>struct factorial {
vector<T> Fact,Finv,Inv;
factorial(int maxx){
Fact.resize(maxx); Finv.resize(maxx); Inv.resize(maxx);
Fact[0]=Fact[1]=Finv[0]=Finv[1]=Inv[1]=1;
rep(i,2,maxx){Fact[i]=Fact[i-1]*i;} Finv[maxx-1]=Fact[maxx-1].inv();
for(int i=maxx-1;i>=2;i--){Finv[i-1]=Finv[i]*i; Inv[i]=Finv[i]*Fact[i-1];}
}
T fact(int n,bool inv=0){if(n<0)return 0; return (inv?Finv[n]:Fact[n]);}
T inv(int n){if(n<0)return 0; return Inv[n];}
T nPr(int n,int r,bool inv=0){if(n<0||n<r||r<0)return 0; return fact(n,inv)*fact(n-r,inv^1);}
T nCr(int n,int r,bool inv=0){if(n<0||n<r||r<0)return 0; return fact(n,inv)*fact(r,inv^1)*fact(n-r,inv^1);}
T nHr(int n,int r,bool inv=0){return nCr(n+r-1,r,inv);}
};
/**
* @brief Modint
*/
#line 3 "library/Math/primecount.hpp"
template<typename T,T (*F)(ll)>struct PrimeSum{
ll N,SQ;
vector<T> lo,hi;
PrimeSum(ll n=0):N(n),SQ(sqrtl(N)),lo(SQ+1),hi(SQ+1){
rep(i,1,SQ+1){
lo[i]=F(i)-1;
hi[i]=F(N/i)-1;
}
auto ps=sieve(SQ);
for(auto& p:ps){
ll q=ll(p)*p;
if(q>N)break;
T sub=lo[p-1],fp=lo[p]-lo[p-1];
ll L=min(SQ,N/q),M=SQ/p;
rep(i,1,M+1)hi[i]-=fp*(hi[i*p]-sub);
rep(i,M+1,L+1)hi[i]-=fp*(lo[double(N)/(i*p)]-sub);
for(int i=SQ;i>=q;i--)lo[i]-=fp*(lo[double(i)/p]-sub);
}
}
T operator[](ll x) {
return (x<=SQ?lo[x]:hi[N/x]);
}
};
/**
* @brief Prime Count
* @docs docs/primecount.md
*/
#line 7 "sol.cpp"
ll F(ll x){return x;}
PrimeSum<ll,F> buf;
using Fp=fp<998244353>;
Fp memo[50];
Fp pe(int p,int e){return memo[e];}
Fp psum(ll x){return memo[1]*buf[x];}
FastIO io;
int main(){
ll n,m;
io.read(n,m);
rep(e,0,45)memo[e]=Fp(e+1).pow(n);
buf=PrimeSum<ll,F>(m);
auto ret=MultiplicativeSum<Fp,pe,psum>(m);
io.write(ret.v);
return 0;
}