# 题目链接

https://lydsy.com/JudgeOnline/problem.php?id=3512

# 题解

$g(n,m)=\sum_{i=1}^m \varphi(in)$

$n=\prod_{k}p_k^{a_k}$

$n'=\prod_{k}p_k\\ r=\prod_{k}p_k^{a_k-1}$

$g(n,m)=r\sum_{i=1}^m \varphi(in)$

$g(n,m)=r\sum_{d|n'}\varphi(\frac{n'}{d})g(d,\lfloor\frac{m}{d}\rfloor)$

# 代码

#include <map>
#include <cstdio>

int read()
{
int x=0,f=1;
char ch=getchar();
while((ch<'0')||(ch>'9'))
{
if(ch=='-')
{
f=-f;
}
ch=getchar();
}
while((ch>='0')&&(ch<='9'))
{
x=x*10+ch-'0';
ch=getchar();
}
return x*f;
}

const int maxn=1000000;
const int maxm=100000;
const int mod=1000000007;

int p[maxn+10],prime[maxn+10],cnt,mu[maxn+10],phi[maxn+10],last[maxm+10],sum[maxn+10];

int getprime()
{
p[1]=phi[1]=mu[1]=1;
for(int i=2; i<=maxn; ++i)
{
if(!p[i])
{
prime[++cnt]=i;
phi[i]=i-1;
mu[i]=-1;
}
for(int j=1; (j<=cnt)&&(i*prime[j]<=maxn); ++j)
{
int x=i*prime[j];
p[x]=1;
if(i%prime[j]==0)
{
mu[x]=0;
phi[x]=phi[i]*prime[j];
break;
}
mu[x]=-mu[i];
phi[x]=phi[i]*(prime[j]-1);
}
}
for(int i=1; i<=maxm; ++i)
{
if(mu[i])
{
for(int j=i; j<=maxm; j+=i)
{
last[j]=i;
}
}
}
for(int i=1; i<=maxn; ++i)
{
sum[i]=sum[i-1]+phi[i];
if(sum[i]>=mod)
{
sum[i]-=mod;
}
}
return 0;
}

std::map<int,int> mp;

int getphi(int n)
{
if(n<=maxn)
{
return sum[n];
}
if(mp.count(n))
{
return mp[n];
}
int res=(1ll*n*(n+1)/2)%mod;
for(int l=2,r; l<=n; l=r+1)
{
r=n/(n/l);
res=(res-1ll*(r-l+1)*getphi(n/l))%mod;
}
if(res<0)
{
res+=mod;
}
return mp[n]=res;
}

struct data
{
int n,m;

data(int _n=0,int _m=0):n(_n),m(_m){}

bool operator <(const data &oth) const
{
return (n==oth.n)?(m<oth.m):(n<oth.n);
}
};

std::map<data,int> mf;

int F(int n,int m)
{
if(m==0)
{
return 0;
}
if(n==1)
{
return getphi(m);
}
data d(n,m);
if(mf.count(d))
{
return mf[d];
}
int ans=0;
for(int i=1; i*i<=n; ++i)
{
if(n%i!=0)
{
continue;
}
ans=(ans+1ll*phi[n/i]*F(i,m/i))%mod;
if(i*i!=n)
{
ans=(ans+1ll*phi[i]*F(n/i,m/(n/i)))%mod;
}
}
return mf[d]=ans;
}

int n,m;

int main()
{
getprime();
n=read();
m=read();
int ans=0;
for(int i=1; i<=n; ++i)
{
ans=(ans+1ll*(i/last[i])*F(last[i],m))%mod;
}
printf("%d\n",ans);
return 0;
}