[bzoj4407] Mobius inversion + Dirichlet convolution enhanced by the wrath of God

Description

Give N,M,K

Input

There are multiple groups of data in the input. The first row of the input data contains two positive integers T and K, which represent the group of T data. The meaning of K is as shown above. The second row below goes to the row T+1. Each row contains two positive integers n and m, whose meaning is as shown above.
Output

For example
Sample Input

1 2

3 3
Sample Output

20

HINT

1<=N,M,K<=5000000,1<=T<=2000

Explanation:
Orz YZH

It's the first time to do Dirichlet convolution. The convolution F (D) of two product functions is product function, which can be obtained by linear sieve.
If D is prime, F(D)=D^k-1
If D is not a prime number, it will be screened by its smallest quality factor p to f (d) = f (D / P) × p ^ k

Code

```#include<bits/stdc++.h>
#define ll long long
#define inf 1000000000
#define mod 1000000007
using namespace std;
{
int x=0,f=1;char ch=getchar();
while(ch<'0'||ch>'9'){if (ch=='-') f=-1;ch=getchar();}
while(ch>='0'&&ch<='9'){x=x*10+ch-'0';ch=getchar();}
return x*f;
}
const int N=5000001;
int F[N],f[N],flag[N],k,tot,p[N],ans;
inline int gpow(int x,int y)
{
int ans=1;
while (y)
{
if (y&1) ans=(ll)ans*x%mod;
y>>=1;x=(ll)x*x%mod;
}
return ans;
}
void preparation()
{
F[1]=1;
for (int i=2;i<N;i++)
{
if (!flag[i]){f[i]=gpow(i,k);F[i]=f[i]-1;p[++tot]=i;}
for (int j=1;j<=tot&&i*p[j]<N;j++)
{
flag[i*p[j]]=1;
if (i%p[j])F[i*p[j]]=(ll)F[i]*F[p[j]]%mod;
else{F[i*p[j]]=(ll)F[i]*f[p[j]]%mod;break;}
}
}
for (int i=1;i<N;i++) (F[i]+=F[i-1])%=mod;
}
int main()
{
preparation();
while (Case--)
{