UVA 12703 - Little Rakin

/******************************************************************
***   Problem       :                                           ***
***   Author        : Shipu Ahamed (Psycho Timekiller)          ***
***   E-mail        : shipuahamed01@gmail.com                   ***
***   University    : BUBT,Dept. of CSE                         ***
***   Team          : BUBT_Psycho                               ***
***   My Blog       : http://shipuahamed.blogspot.com           ***
***   Facebook      : http://www.facebook.com/DeesheharaShipu   ***
******************************************************************/

#include 
#include 
#include 
#include 
#include 
#include 
#include 
#include 
#include 
#include 
#include 
#include 
#include 
#include 
#include 
#include 
#include 
#include 
using namespace std;

#define pi 2*acos(0.0)
#define all(v) v.begin(),v.end()

//input
#define si(t) scanf("%d",&t)
#define sl(t) scanf("%lld",&t)
#define sf(t) scanf("%f",&t)
#define sd(t) scanf("%lf",&t)
#define sc(c) scanf("%c",&c)
#define sii(a,b) scanf("%d%d",&a,&b)
#define sll(a,b) scanf("%lld%lld",&a,&b)

//Output
#define P(a) printf("%d\n",a)
#define PL(a) printf("%lld\n",a)
#define PF(a) printf("%f\n",a)
#define PDB(a) printf("%lf\n",a)
#define PS(a) printf("%s\n",a)
#define PSN(a) printf("%s ",a)
#define PN(a) printf("%d ",a)
#define PLN(a) printf("%lld ",a)
#define PFN(a) printf("%f ",a)
#define PDBN(a) printf("%lf ",a)
#define PP(a,b) printf("%d %d\n",a,b)
#define PPN(a,b) printf("%d %d ",a,b)
#define PPL(a,b) printf("%lld %lld\n",a,b)
#define PPLN(a,b) printf("%lld %lld ",a,b)

#define CP(a) cout< pii;
typedef  pair piii;
typedef  pair pll;
typedef  pair psi;
typedef  vector vi;
typedef  vector vll;
typedef  vector vpii;
typedef  vector vs;
typedef  set si;
typedef  set ss;
typedef  map mii;
typedef  map mll;
typedef  map msi;

template string toString( T Number ){stringstream st;st << Number;return st.str();}
template  T SOD(T n) {__typeof(n) sum=0;for(__typeof(n) i=1;i*i<=n;i++)sum+=(n%i)?0:((i*i==n)?i:i+n/i);return sum;}


//For Define
#define forab(i,a,b) for(__typeof(b) i=(a);i<=(b);i++)
#define for0(i,n) forab(i,0,(n)-1)
#define for1(i,n) forab(i,1,n)
#define rforab(i,b,a) for(__typeof(b) i=(b);i>=(a);i--)
#define rfor0(i,n) rforba(i,(n)-1,0)
#define rfor1(i,n) rforba(i,n,1)
#define forstl(i,s) for(__typeof((s).end()) i=(s).begin(); i != (s).end(); i++)

//Debug
#define dbg(x) cout << #x << " -> " << (x) << endl;
#define dbgsarr(i,a) cout<<#a<<"["< "< "< "<>p ; return p;}

ll pow(ll a,ll b, ll m) { ll res = 1; while(b) { if(b & 1) { res = ( (res % m) * (a % m) ) %m ; } a= ((a%m) * (a%m)) %m; b >>= 1; } return res; }
ll modInverse(ll a, ll m){return pow(a,m-2,m);}

////============ CONSTANT ===============////
#define mx7   10000007
#define mx6   1000006
#define mx5   100005
#define inf   1<<30                                           //infinity value
#define eps   1e-9
#define mx    (10010)
#define mod   1000000007
////=====================================////

bool prime[mx];
int pd[mx];


struct factorize
{
    int prime,pow=0;
};


void seive()
{
    prime[0]=1;
    prime[0]=1;
    for(int i=2;i<=mx;i+=2)
        pd[i]=2,prime[i]=1;

    prime[2]=0;

    for(ll i=3;i<=mx;i+=2)
    {
        if(!prime[i])
        {
            pd[i]=i;
            ll mul=i<<1;
            ll j=i;
            for(j*=i;j<=mx;j+=mul)
            {
                pd[j]=i;
                prime[j]=1;
            }
        }
    }
}

vectorv[50];
void fact(int n,int pos)
{

    while(n!=1)
    {
        int s=pd[n],cnt=0;
        while(n%s==0)
        {
           n/=s,cnt++;
        }
        factorize res;
        res.pow=cnt;
        res.prime=s;
        v[pos].pb(res);
    }

}


int main()
{
    seive();
    int t;
    si(t);
    while(t--)
    {
        int n,a,b;
        sii(n,a),si(b);

        fact(a,0);
        fact(b,1);

        forab(i,2,n)
        {
            vectoradd;
            mii mp;
            for0(j,sz(v[i-1]))
            {
                mp[v[i-1][j].prime]+= v[i-1][j].pow;
            }
            for0(j,sz(v[i-2]))
            {
                mp[v[i-2][j].prime]+= v[i-2][j].pow;
            }
            forstl(it,mp)
            {
                factorize res;
                res.prime= it->ff;
                res.pow= it->se;
                add.pb(res);
            }
            v[i]=add;
        }

        int s=sz(v[n]);
        for0(i,s)
        {
            PP(v[n][i].prime,v[n][i].pow);
        }
        nl;
        for0(i,n+1)
        {
            v[i].clear();
        }

    }
    return 0;
}