Interview Question

문제

Fizz Buzz is a party game that is often used as a programming exercise in job interviews. In the game, there are two positive integers $aa$ and $bb$, and the game consists of counting up through the positive integers, replacing any number by Fizz if it is a multiple of $aa$, by Buzz if it is a multiple of $bb$, and by FizzBuzz if it is a multiple of both $aa$ and $bb$. The most common form of the game has $a=3a=3$ and $b=5b=5$, but other parameters are allowed.

Your task here is to solve the reverse problem: given a transcript of part of the game (not necessarily starting at 1), find possible values of $aa$ and $bb$ that could have been used to generate it.

Figure I.1 shows some sample sequences for various values of $aa$ and $bb$.

Figure I.1: Example sequences for Fizz Buzz.

입력

The input consists of:

• One line with two integers $cc$ and $dd$ ($1\le c\le d\le {10}^{5}1\; \backslash le\; c\; \backslash le\; d\; \backslash le\; 10^5$), indicating that your transcript starts at $cc$ and ends at $dd$.
• One line with $d-c+1d-c+1$ integers and strings, the contents of the transcript.

It is guaranteed that the transcript is valid for some integers $aa$ and $bb$ with $1\le a,b\le {10}^{6}1\; \backslash le\; a,b\; \backslash le\; 10^6$, according to the rules laid out above.

출력

Output two positive integers $aa$ and $bb$ ($1\le a,b\le {10}^{6}1\; \backslash le\; a,b\; \backslash le\; 10^6$) that are consistent with the given transcript.

If there are multiple valid solutions, you may output any one of them.