BZOJ-2154 Crash的数字表格(莫比乌斯反演)

BZOJ-2154 Crash的数字表格

#include<bits/stdc++.h>
#define me(a,x) memset(a,x,sizeof(a))
#define IN freopen("in.txt","r",stdin);
#define OUT freopen("out.txt","w",stdout);
#define sc scanf
#define itn int
#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;
#define N 10000005
#define mod 20101009
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;}
inline 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;}
inline ll ksm(ll a,ll b,ll c){ll ans=1;for(;b;b>>=1,a=mul(a,a,c))if(b&1)ans=mul(ans,a,c);return ans;}
inline void exgcd(ll a,ll b,ll &x,ll &y){if(!b)x=1,y=0;else exgcd(b,a%b,y,x),y-=x*(a/b);}
int p[N],tot=0;
ll pro[N]={0};
bool vis[N]={0};
void pre(){
    pro[1]=1;
    for(int i=2;i<N;i++){
        if(!vis[i])p[++tot]=i,pro[i]=(i-1LL*i*i%mod+mod)%mod;
        for(int j=1;j<=tot&&i*p[j]<N;j++){
            vis[i*p[j]]=1;
            if(i%p[j]==0){
                pro[i*p[j]]=pro[i]*p[j]%mod;
                break;
            }else pro[i*p[j]]=pro[i]*pro[p[j]]%mod;
        }
    }
    for(int i=1;i<N;i++){
        pro[i]+=pro[i-1];
        pro[i]%=mod;
    }
}
ll n,m;
ll f(int T){return n/T*(n/T+1)/2%mod*(m/T*(m/T+1)/2%mod)%mod;}
int main(){
    pre();
    sc("%lld%lld",&n,&m);
    if(n>m)swap(n,m);
    ll ans=0;
    for(int d=1,last;d<=n;d=last+1){
        last=min(n/(n/d),m/(m/d));
        ans=(ans+f(d)*(pro[last]-pro[d-1]+mod)%mod)%mod;
    }
    printf("%lld\n",ans);
}