Gregor and Cryptography
题目描述
Gregor is learning about RSA cryptography, and although he doesn't understand how RSA works, he is now fascinated with prime numbers and factoring them.
Gregor's favorite prime number is P. Gregor wants to find two bases of P. Formally, Gregor is looking for two integers a and b which satisfy both of the following properties.
Pmoda=Pmodb, where xmody denotes the remainder when x is divided by y, and 2≤a<b≤P. Help Gregor find two bases of his favorite prime number!
输入格式
Each test contains multiple test cases. The first line contains the number of test cases t (1≤t≤1000).
Each subsequent line contains the integer P (5≤P≤10^9), with P guaranteed to be prime.
输出格式
Your output should consist of t lines. Each line should consist of two integers a and b (2≤a<b≤P). If there are multiple possible solutions, print any.
样例
2
17
5
2 16
2 4
提示
Note The first query is P=17. a=3 and b=5 are valid bases in this case, because 17mod3=17mod5=2. There are other pairs which work as well.
In the second query, with P=5, the only solution is a=2 and b=4.