Description

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. Input

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. Output

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. Sample Input

143 10 143 20 667 20 667 30 2573 30 2573 40 0 0 Sample Output

GOOD BAD 11 GOOD BAD 23 GOOD BAD 31

給出兩個(gè)數(shù)S和L，S是一個(gè)非常大的數(shù)，L是一個(gè)整形數(shù)，S是由兩個(gè)素?cái)?shù)相乘得到的，求這兩個(gè)素?cái)?shù)中是否有一個(gè)小于L，如果有，輸出BAD和這個(gè)數(shù)，沒有就輸出GOOD 設(shè)S中有一個(gè)素?cái)?shù)是P，那么S%P一定等于0，并且這個(gè)P的范圍不會(huì)超過L，所以完全可以一個(gè)個(gè)試出來。剩下的問題就是如果處理大數(shù)S，我用了分段的方法，每三位就存在一個(gè)數(shù)組里