洛谷 P2260 [清华集训2012]模积和 || bzoj2956

https://www.lydsy.com/JudgeOnline/problem.php?id=2956

https://www.luogu.org/problemnew/show/P2260

暴力推式子即可

#include<cstdio>
#include<algorithm>
#include<cstring>
#include<vector>
using namespace std;
#define fi first
#define se second
#define mp make_pair
#define pb push_back
typedef long long ll;
typedef unsigned long long ull;
typedef pair<int,int> pii;
const ll md=19940417;
ll n,m,ans,a1,a2;
ll Mod(ll x,ll md=md)
{
    if(x>=0)    return x%md;
    else if(x%md==0)    return 0;
    else    return md+x%md;
}
ll calc(ll x)
{
    return (x)*(x+1)%md*(2*x+1)%md*3323403%md;
}
int main()
{
    ll i,j;
    scanf("%lld%lld",&n,&m);
    if(n>m)    swap(n,m);


//    {
//        ll ams=0;
//        for(ll i=1;i<=n;i++)
//            for(ll j=1;j<=m;j++)
//                if(i!=j)
//                ams=Mod(ams+(n-n/i*i)*(m-m/j*j));
//        printf("%lld",ams);
//        return 0;
//    }


    for(i=1;i<=n;i=j+1)
    {
        j=n/(n/i);
        a1=Mod(a1+Mod((i+j)*(j-i+1)/2)*(n/i));
    }
    for(i=1;i<=m;i=j+1)
    {
        j=m/(m/i);
        a2=Mod(a2+Mod((i+j)*(j-i+1)/2)*(m/i));
    }
    //printf("a%lld %lld
",a1,a2);

    ans=Mod(ans+n*n%md*m%md*m%md);
    ans=Mod(ans-n*n%md*a2%md);
    ans=Mod(ans-m*m%md*a1%md);
    ans=Mod(ans+a1*a2%md);

    ans=Mod(ans-n*n%md*m%md);
    {
        ll t=0;
        for(i=1;i<=n;i=j+1)
        {
            j=min(n,m/(m/i));
            t=Mod(t+Mod((i+j)*(j-i+1)/2)*(m/i));
        }
        ans=Mod(ans+n*t%md);
    }
    ans=Mod(ans+m*a1%md);
    {
        ll t=0;
        for(i=1;i<=n;i=j+1)
        {
            j=min(n/(n/i),m/(m/i));
            t=Mod(t+Mod(calc(j)-calc(i-1))*(n/i)%md*(m/i));
        }
        //printf("t%lld
",t);
        ans=Mod(ans-t);
    }

    printf("%lld",ans);
    return 0;
}