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 $a$ 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 $b$ .


$a=3, b=5:$	`1 2 Fizz 4 Buzz Fizz 7 8 Fizz Buzz 11 Fizz 13 14 FizzBuzz`
$a=6, b=2:$	`1 Buzz 3 Buzz 5 FizzBuzz 7 Buzz 9 Buzz 11 FizzBuzz 13`
$a=4, b=4:$	`1 2 3 FizzBuzz 5 6 7 FizzBuzz 9 10 11 FizzBuzz 13 14`

Figure I.1: Example sequences for Fizz Buzz.

입력

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.

출력

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.