51nod 1225 余数的和 数学

#include<iostream>
#include<cstdio>
#include<cmath>
#include<string>
#include<queue>
#include<algorithm>
#include<stack>
#include<cstring>
#include<vector>
#include<list>
#include<set>
#include<map>
using namespace std;
#define ll long long
#define mod 1000000007
#define inf 999999999
#define esp 0.00000000001
//#pragma comment(linker, "/STACK:102400000,102400000")
void extend_Euclid(ll a, ll b, ll &x, ll &y)
{
    if(b == 0)
    {
        x = 1;
        y = 0;
        return;
    }
    extend_Euclid(b, a % b, x, y);
    ll tmp = x;
    x = y;
    y = tmp - (a / b) * y;
}
ll mul(ll x,ll y)
{
    x%=mod;
    y%=mod;
    return (x*y)%mod;
}
ll divi(ll x,ll y)
{
    ll xx,yy;
    extend_Euclid(y,mod,xx,yy);
    xx=(xx%mod+mod)%mod;
    return mul(x,xx);
}
int main()
{
    ll x,y,z,i,t;
    scanf("%lld",&z);
    ll ans=0;
    for(i=2;i<=z;i++)
    {
        if(z%i!=0)
        {
            ll d=z/i;
            ll maxx=(z%i)/d+1;
            d=-d;
            ans+=mul((z%i),maxx)+divi(mul(maxx,mul((maxx-1),d)),2);
            ans=(ans%mod+mod)%mod;
            i+=maxx-1;
        }
    }
    printf("%lld\n",ans);
    return 0;
}