Problem Description

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.

The original statement shows some sample sequences for various values of $a$ and $b$.

:::align{center} :::

Figure: Fizz Buzz implemented in Hexagony.

Input Format

The input consists of:

• One line with two integers $c$ and $d$ ($1 \leq c \leq d \leq 10^5$), 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 $1 \leq a,b \leq 10^6$, according to the rules laid out above.

Output Format

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

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

7 11
7 8 Fizz Buzz 11

3 5

49999 50002
49999 FizzBuzz 50001 Fizz

2 125

8 11
Buzz Buzz FizzBuzz Buzz

10 1 

10 15
10 11 12 13 14 15

8 23