SPOJ Prime Time

#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 <queue>
#include <algorithm>
#define sf scanf
#define pf printf
#define sfint scanf ("%d %d",&a,&b)
#define sfl scanf ("%ld %ld",&a,&b)
#define sfll scanf ("%lld %lld",&a,&b)
#define sfd scanf ("%lf %lf",&a,&b)
#define sff scanf ("%f %f",&a,&b)
#define loop(i,n) for(i=0;i<n;i++)
#define LL long long
#define L long
#define nl puts("")
#define MX 10100
#define N 100
#define MOD 10000000007
#define pb push_back
#define pi acos(-1.0)
#define sz size()
#define gc getchar ()
#define ps push
#define clr clear
#define bn begin()
#define ed end()

using namespace std;

int prime[(MX >> 6) + 1];

typedef vector<int>vi;
typedef vector<LL>vl;

vi prm;

#define setbit(n) (prime[n>>6] |= (1 << ((n >> 1) & 31)))
#define checkbit(n) (prime[n>>6] & (1 << ((n >> 1) & 31)))

void sieve()
{
    int i,j;

    for(i=3; i*i<=MX; i+=2)
    {
        if(!checkbit(i))
        {
            for(j=i*i; j<=MX; j+=(2*i))
            {
                setbit(j);
            }
        }
    }

    prm.push_back(2);

    for(i=3; i<=MX; i+=2)
    {
        if(!checkbit(i))
        {
            prm.push_back(i);
        }
    }

    //for(i=0; i<100; i++) cout << prm[i] << " ";
}

int ret_factors(int n, int p)
{
    int cnt=0;

    while(n)
    {
        cnt+=(n / p);
        n/=p;
    }

    return cnt;
}

int main()
{
    sieve();
    int num;
    while(~sf("%d", &num))
    {
        bool f=false;

        for(int i=0; prm[i] <= num; i++)
        {
            if(!f)
            {
                pf("%d^%d", prm[i], ret_factors(num, prm[i]));
                f=true;
            }

            else
            {
                pf(" * %d^%d", prm[i], ret_factors(num, prm[i]));
            }
        }

        pf("\n");
    }

    return 0;
}