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.</p>

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.

입력 형식

The input consists of:</p>

• 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 형식

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

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

예제 입력 1

7 11
7 8 Fizz Buzz 11

예제 출력 1

3 5

예제 입력 2

49999 50002
49999 FizzBuzz 50001 Fizz

예제 출력 2

2 125

예제 입력 3

8 11
Buzz Buzz FizzBuzz Buzz

예제 출력 3

10 1

예제 입력 4

10 15
10 11 12 13 14 15

예제 출력 4

8 23