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.

Below are examples of 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

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 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.