The Embarrassed Cryptographer

Time Limit: 2000MS		Memory Limit: 65536K
Total Submissions: 15069		Accepted: 4132

The young and very promising cryptographer Odd Even has implemented the security module of a large system with thousands of users, which is now in use in his company. The cryptographic keys are created from the product of two primes, and are believed to be secure because there is no known method for factoring such a product effectively.
What Odd Even did not think of, was that both factors in a key
should be large, not just their product. It is now possible that some of
the users of the system have weak keys. In a desperate attempt not to
be fired, Odd Even secretly goes through all the users keys, to check if
they are strong enough. He uses his very poweful Atari, and is
especially careful when checking his boss' key.

The input consists of no more than 20 test cases. Each test case is a line with the integers 4 <= K <= 10¹⁰⁰ and 2 <= L <= 10⁶.
K is the key itself, a product of two primes. L is the wanted minimum
size of the factors in the key. The input set is terminated by a case
where K = 0 and L = 0.

For
each number K, if one of its factors are strictly less than the
required L, your program should output "BAD p", where p is the smallest
factor in K. Otherwise, it should output "GOOD". Cases should be
separated by a line-break.

143 10

143 20

667 20

667 30

2573 30

2573 40

0 0

GOOD

BAD 11

GOOD

BAD 23

GOOD

BAD 31

/*

* @Author: lyucheng

* @Date:   2017-10-17 19:03:06

* @Last Modified by:   lyucheng

* @Last Modified time: 2017-10-17 16:50:37

*/

#include <stdio.h>

#include <vector>

#include <string.h>

#define MAXN 105

#define MAXM 1000005

using namespace std;

char str[MAXN];

int k;

int p[MAXM];

bool prime[MAXM];

int tol;

int num[MAXM];

vector<int>v;

void init(){

    tol=;

    for(int i=;i<MAXM;i++){

        if(prime[i]==false)

            p[tol++]=i;

        for(int j=;j<tol&&i*p[j]<MAXM;j++){

            prime[i*p[j]]=true;

            if(i%p[j]==)

                break;

        }

    }

}

bool ok(int k){

    int s=;

    for(int i=(int)v.size()-;i>=;i--){

        s*=;

        s%=k;

        s+=v[i];

        s%=k;

    }

    if(s==)

        return true;

    else

        return false;

}

int main(){

    // freopen("in.txt","r",stdin);

    init();

    while(scanf("%s%d",str,&k)!=EOF&&(str[]-''!=&&k!=)){

        int n=strlen(str);

        v.clear();

        for(int i=n-;i>=;i-=){

            int s=;

            for(int j=max(,i-);j<=i;j++){

                s*=;

                s+=str[j]-'';

            }

            v.push_back(s);

        }

        // for(int i=0;i<(int)v.size();i++){

        //     cout<<v[i]<<" ";

        // }cout<<endl;

        bool flag=true;

        for(int i=;p[i]<k;i++){

            if(ok(p[i])==true){

                printf("BAD %d\n",p[i]);

                flag=false;

                break;

            }

        }

        if(flag==true)

            puts("GOOD");

    }

    return ;

}