What's Next? (UVALive 4964, Regionals 2010 >> Africa/Middle East - Arab Contest)

///     Raihan Ruhin
///     CSE, Jahangirnagar University.
///     Dhaka-Bangladesh.
///     id: raihanruhin (topcoder / codeforces / codechef / uva / uvalive), 3235 (lightoj)
///     mail: raihanruhin@ (yahoo / gmail / facebook)
///     blog: ruhinraihan.blogspot.com

#include<bits/stdc++.h>
using namespace std;

#define SET(a) memset(a,-1,sizeof(a))
#define CLR(a) memset(a,0,sizeof(a))
#define PI acos(-1.0)

#define MOD 1000000007
#define MX 100010


int main()
{
    ios_base::sync_with_stdio(0);cin.tie(0);
    int tc, kk=1, n, m, x, y, z;
    string s;
    char ch;

    while(cin>>x>>y>>z && (x || y || z))
    {
        if((z-y)==(y-x)) cout<<"AP "<<z+z-y<<"\n";
        else             cout<<"GP "<<z*(z/y)<<"\n";
    }
return 0;
}