Interview Question

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 $a$ and $b$, and the game consists of counting up through the positive integers, replacing any number by Fizz if it is a multiple of $a$, by Buzz if it is a multiple of $b$, and by FizzBuzz if it is a multiple of both $a$ and $b$. The most common form of the game has $a=3$ and $b=5$, 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 $a$ and $b$ that could have been used to generate it.

Figure I.1 shows some sample sequences for various values of $a$ and $b$.

Figure I.1: Example sequences for Fizz Buzz.

The input consists of:

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

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

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

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