BZOJ-4407 于神之怒加强版(莫比乌斯反演)

BZOJ-4407 于神之怒加强版

#include<bits/stdc++.h>
#define me(a,x) memset(a,x,sizeof(a))
#define sc scanf
#define itn int
#define IN freopen("in.txt","r",stdin);
#define OUT freopen("out.txt","w",stdout);
#define STR clock_t startTime = clock();
#define END clock_t endTime = clock();cout << double(endTime - startTime) / CLOCKS_PER_SEC *1000<< "ms" << endl;
using namespace std;
const int N=5e6+5;
const long long mod=1e9+7;
const long long mod2=998244353;
const int oo=0x7fffffff;
const int sup=0x80000000;
typedef long long ll;
typedef unsigned long long ull;
template <typename it>void db(it *begin,it *end){while(begin!=end)cout<<(*begin++)<<" ";puts("");}
template <typename it>
string to_str(it n){string s="";while(n)s+=n%10+'0',n/=10;reverse(s.begin(),s.end());return s;}
template <typename it>int o(it a){cout<<a<<endl;return 0;}
ll mul(ll a,ll b,ll c){ll ans=0;for(;b;b>>=1,a=(a+a)%c)if(b&1)ans=(ans+a)%c;return ans;}
ll ksm(ll a,ll b,ll c){ll ans=1;for(;b;b>>=1,a=a*a%c)if(b&1)ans=ans*a%c;return ans;}
void exgcd(ll a,ll b,ll &x,ll &y){if(!b)x=1,y=0;else exgcd(b,a%b,y,x),y-=(a/b)*x;}
int prime[N],tot=0;
int n,m,k;
ll f[N]={0};
bool vis[N]={0};
void pre(){
    f[1]=1;
    for(int i=2;i<N;i++){
        if(!vis[i])prime[++tot]=i,f[i]=(ksm(i,k,mod)-1+mod)%mod;
        for(int j=1;j<=tot&&i*prime[j]<N;j++){
            vis[i*prime[j]]=1;
            if(i%prime[j]==0){
                f[i*prime[j]]=f[i]*(f[prime[j]]+1)%mod;
                break;
            }else f[i*prime[j]]=f[i]*f[prime[j]]%mod;
        }
    }
    for(int i=1;i<N;i++)f[i]=(f[i]+f[i-1])%mod;
}
int main(){
    int t,l;
    sc("%d%d",&t,&k);
    pre();
    while(t--){
        sc("%d%d",&n,&m);
        if(n>m)swap(n,m);
        ll ans=0;
        int last=0;
        for(int i=1;i<=n;i=last+1){
            last=min(n/(n/i),m/(m/i));
            ans=(ans+1ll*(n/i)*(m/i)%mod*((f[last]-f[i-1]+mod)%mod)%mod)%mod;
        }
        printf("%lld\n",(ans+mod)%mod);
    }
}