Uva 516 - Prime Land

 /*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 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;}

int prime[mx],prm[(mx/2)+1],plen=0;

void seieve(int n)
{
    int i,j,x=(int)sqrt(double(n));

    prime[0]=setbit(prime[0],0);
    prime[0]=setbit(prime[0],1);

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

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

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

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

map<int,int>mp;

void find_factors(int n)
{
    vector<int>fctor;
    fctor.clear();
    mp.clear();

    int sp=0;

    for(int i=0;i<plen ; i++)
    {
        if(!(n%prm[i]))
        {
            fctor.push_back(prm[i]);
            sp++;

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

            fctor.push_back(mp[prm[i]]);
        }
    }

    int fctorlen=fctor.size();

    for(int i=0;i<fctorlen-1;i+=2)
    {
        cout << fctor[i] << " " << fctor[i+1];
        if(sp > 1)
        {
            cout << " ";
        }

        sp--;
    }

    nl;
}

int main()
{
    seieve(mx);
    int i;
    vector<int>in;
    string s;

    while(getline(cin,s) and s!="0")
    {
        int n,x=1;
        stringstream ss(s);
        //ss >> n;
        //cout << n;
        in.clear();
        while(ss >> n) in.push_back(n); // string to integer.
        //lp1(i,in.size())cp(in[i]);
        int inlen=in.size();

       for(i=0;i<inlen-1;i+=2)
       {
           x *= powl(in[i],in[i+1]);
       }

       x--;
       //cout << x << endl;

       find_factors(x);
    }

    return 0;
}