学步园

#pragma comment(linker, "/STACK:102400000,102400000")
#include<iostream>
#include<vector>
#include<algorithm>
#include<cstdio>
#include<queue>
#include<stack>
#include<string>
#include<map>
#include<set>
#include<cmath>
#include<cassert>
#include<cstring>
#include<iomanip>
using namespace std;
#ifdef _WIN32
#define i64 __int64
#define out64 "%I64d\n"
#define in64 "%I64d"
#else
#define i64 long long
#define out64 "%lld\n"
#define in64 "%lld"
#endif
/************ for topcoder by zz1215 *******************/
#define FOR(i,a,b)      for( int i = (a) ; i <= (b) ; i ++)
#define FF(i,a)        for( int i = 0 ; i < (a) ; i ++)
#define FFD(i,a,b)      for( int i = (a) ; i >= (b) ; i --)
#define S64(a)          scanf(in64,&a)
#define SS(a)           scanf("%d",&a)
#define LL(a)           ((a)<<1)
#define RR(a)           (((a)<<1)+1)
#define pb              push_back
#define pf              push_front
#define X               first
#define Y               second
#define CL(Q)           while(!Q.empty())Q.pop()
#define MM(name,what)   memset(name,what,sizeof(name))
#define MC(a,b)         memcpy(a,b,sizeof(b))
#define MAX(a,b)        ((a)>(b)?(a):(b))
#define MIN(a,b)        ((a)<(b)?(a):(b))
#define read            freopen("in.txt","r",stdin)
#define write           freopen("out.txt","w",stdout)

const int inf = 0x3f3f3f3f;
const i64 inf64 = 0x3f3f3f3f3f3f3f3fLL;
const double oo = 10e9;
const double eps = 10e-9;
const double pi = acos(-1.0);
const int mod = 1000000007;
const int maxn = 5000001;

i64 f[maxn];
int s[maxn];

i64 range(int l,int r)
{
	l=(l+1)&(0x7ffffffe);
	r&=(0x7ffffffe);
	return (r-l)/2+1;
}

i64 find(int x)
{
	i64 temp;
	i64 re;
	i64 l,r;
	if(x%2==0)
	{
		x/=2;
		temp = x/3;
		l = x-2;
		r = x-3*temp+1;
		re = (l+r)*temp/2;
		re += range(x+1,x+temp);
		re/=2;
	}
	else
	{
		x/=2;
		temp = (x-1)/3;
		l = x;
		r = x-3*temp;
		re = (l+r)*(temp+1)/2;
		re += range(x+1,x+temp+1);
		re/=2;
	}
	return re;
}

void start()
{
	for(int i=1;i<maxn;i++)
	{
		f[i]=find(i);
	}
	int temp;
	for(int i=3;i<maxn;i++)
	{
		temp = i;
		while(true)
		{
			temp+=i;
			if(temp<maxn)
			{
				f[temp]-=f[i];
			}
			else
			{
				break;
			}
		}
	}
	for(int i=0;i<maxn;i++)
	{
		f[i]%=mod;
	}
	s[0]=1;
	s[1]=2;
	for(int i=2;i<maxn;i++)
	{
		s[i]=2*s[i-1];
		s[i]%=mod;
	}
}

int n;
vector<int>a;

int main()
{
	int temp;
	start();
	i64 ans;
	int tt=1;
	while(cin>>n)
	{
		ans=0;
		a.clear();
		for(int i=1;i*i<n;i++)
		{
			if(n%i == 0)
			{
				a.pb(i);
				a.pb(n/i);
			}
		}
		temp = sqrt(double(n));
		if(temp*temp == n)
		{
			a.pb(temp);
		}
		for(int i=0;i<a.size();i++)
		{
			ans+=f[a[i]]*s[n/a[i]-1];
			ans%=mod;
		}
		cout<<"Case "<<tt++<<": "<<ans<<endl;
	}
	return 0;
}