Uva 11876 - N + NOD (N)

 // Verdict :: Accepted

/// Header file begin
#include <iostream>
#include <cstdio>
#include <cstring>
#include <map>
#include <string>
#include <vector>
#include <cmath>
#include <cctype>
#include <sstream>
#include <set>
#include <list>
#include <stack>
#include<utility>
#include <queue>
#include <algorithm>
/// End
//..........
/// Macro
#define sf scanf
#define pf printf
#define sfint(a,b) scanf("%d %d",&a,&b)
#define sfl(a,b) scanf("%ld %ld",&a,&b)
#define sfll(a,b) scanf("%lld %lld",&a,&b)
#define sfd(a,b) scanf("%lf %lf",&a,&b)
#define sff(a,b) scanf("%f %f",&a,&b)
#define lp1(i,n) for(i=0;i<n;i++)
#define lp2(i,n) for(i=1;i<=n;i++)
#define mem(c,v) memset(c,v,sizeof(c))
#define cp(a) cout<<" "<<a<<" "<<endl
#define nl puts("")
#define sq(x) ((x)*(x))
#define all(x) x.begin(),x.end()
#define sz size()
#define gc getchar()
#define pb push_back
/// End.........

/// Size
#define mx7 20000100
#define mx6 1500000
#define mx5 100005
#define mx4 1000100
#define inf 1<<30                                           //infinity value
#define eps 1e-9
#define mx (65540)
#define mod 1000000007
#define pi acos(-1.0)



using namespace std;
//..................................................................................................................
typedef long long LL;
typedef long L;
typedef unsigned long long ull;
typedef unsigned long ul;
typedef unsigned int ui;
typedef pair<int, int> pii;

template<class T> T setbit(T n, T pos){n=n|(1<<pos); return n;}
template<class T> T checkbit(T n, T pos){n=n&(1<<pos); return n;}
template<class T> T gcd(T a, T b ) {return b==0?a:gcd(b,a%b);}
template<class T> T large(T a, T b ) {return a>b?a:b;}
template<class T> T small(T a, T b ) {return a<b?a:b;}

LL prime[mx4],prm[(mx4/2)+1],plen=0,sod[mx4+5],len=0;

void seieve(LL n)
{
    LL i,j,x=(long)sqrt(double(n)) + 1;

    prime[0]=setbit<LL>(prime[0],0);
    prime[0]=setbit<LL>(prime[0],1);

    for(i=4;i<=n;i+=2)prime[i>>5]=setbit<LL>(prime[i>>5],i&31);

    for(i=3;i<x;i+=2)
    {
        if(!checkbit<LL>(prime[i>>5],i&31))
        {
            for(j=i*i;j<=n;j+=i)
            {
                prime[j>>5]=setbit<LL>(prime[j>>5],j&31);
            }
        }
    }

    for(i=2;i<=n;i++)
    {
        if(!checkbit<LL>(prime[i>>5],i&31))
        {
            prm[plen++]=i;
        }
    }

    //lp1(i,plen)cp(prm[i]);
}

LL NOD(LL n)
{
    LL i,m=1;

    for(i=0;i<plen and sq(prm[i])<=n; i++)
    {
        if(!(n%prm[i]))
        {
            LL s=1;

            while(!(n%prm[i]))
            {
                s++;
                n/=prm[i];
                if(n==0 or n==1) break;
            }

            m*=s;
        }
    }

    if(n>1)
    {
        m*=2;
    }

    return m;
}

/// binary search algorithm. (Source:: Codeforces)

LL bin_search(LL target)
{
    LL lo=0,hi=len,mid;

    while(lo <= hi)
    {
        mid = lo + (hi-lo)/2;

        if(sod[mid] == target)
        {
            return mid;
        }

        else if(sod[mid] < target)
        {
            lo = mid + 1;
        }

        else
        {
            hi = mid - 1;
        }
    }

    return lo;
}

int main()
{
    seieve(mx4);

    sod[len++]=1;
    sod[len++]=2;

    for(LL i=2;i<=mx4;i++)
    {
        sod[len++] = sod[i-1] + NOD(sod[i-1]);
    }

    //for(LL i=0;i<7;i++) cp(sod[i]);
    LL t,tc=0;

    sf("%lld",&t);

    while(t--)
    {
        LL l,u,up,low;
        sf("%lld %lld",&l,&u);

        low = bin_search(l);
        up = bin_search(u);

        //cout << "loc = " << low << " to loc = " << up;

        LL result = up - low + 1;

        // check

        if(sod[up] > u)
        {
            result--;
        }

        pf("Case %lld: %lld\n",++tc,result);
    }

    return 0;
}