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
Sample Output
题意
已知K是两个素数的乘积,判断这两个素数中最小的一个是否小于L,若小于,输出BAD + MIN_PRIME
,否则输出GOOD
。
思路
同余定理中有这么几条定律
(a+b)%c=(a%c+b%c)%c
(a∗b)%c=(a%c∗b%c)%c
例如要验证123是否被3整除,只需求 123%3
但是,当123是一个大数时,我们不能直接对它进行模运算,只能通过同余定理对大数进行分块,然后间接运算。
具体的做法:
先求 1%3=1
再求 (1∗10+2)%3=0
再求 (0∗10+3)%3=0
于是便间接得到了 123%3=0
题目中有说明K的范围是 [4,10100]
用千进制存储主要是为了减少循环的次数,可以把原数长度缩短3倍,毕竟 1000=103
AC代码