数论+乱搞——cf181B

/*
2-type B|D^k
3-type B|D-1
11-type B|D+1 
6-type B质因子分解， 
7-type 其他情况 
 
3-type:
    (a*(D^4-1)+b*(D^3-1)+...+d*(D-1)) % B = 0
    B|(D-1)  
11-type:
    (a*(D^4-1)+b*(D^3+1)+c*(D^2-1)+d*(D^1+1)) % B=0
    B|(D^k+(-1)^k)
    k为奇数时，D^k-1因式分解后必然有B|(D+1) 
    k为偶数时，(D+1)(D^(k-1)-D^(k-2)+D^(k-3)...+1),也必有B|(D+1)
    且对于任意的k，(D^k+(-1)^k)只有(D+1)这个公因子

*/
#include<bits/stdc++.h>
using namespace std;
#define ll long long 

int prime[200],vis[200],m;
void init(){
    for(int i=2;i<=100;i++){
        if(!vis[i])prime[++m]=i;
        for(int j=i;j<=100;j+=i)
            vis[j]=1;
    }
}

ll D,B;//D进制下，除数是B 

int k;
int calc(ll B){
    if((D-1)%B==0)return 3;
    if((D+1)%B==0)return 11;
    ll tmp=D;
    k=0;
    for(;tmp<=1e16;tmp*=D){//2^7
        ++k;
        if(tmp%B==0)return 2;
    }
    
    return -1;
}

int main(){
    init();
    cin>>D>>B;
    int res=calc(B); 
    if(res!=-1){
        if(res==2){
            cout<<"2-type"<<'\n';
            cout<<k<<'\n';
            return 0;
        }
        else if(res==3){
            cout<<"3-type"<<'\n';
            return 0;
        }
        else if(res==11){
            cout<<"11-type"<<'\n';
            return 0;
        }
        return 0;
    }
    
    for(int i=1;i<=m;i++)
        if(B%prime[i]==0){//每个质因子都要符合要求 
            ll tmp=1;
            while(B%prime[i]==0)
                B/=prime[i],tmp*=prime[i];
            int res=calc(tmp);
            if(res==-1){
                cout<<"7-type"<<'\n';
                return 0;
            }
        }

    cout<<"6-type"<<'\n';
}