I Will Win

Dumbear likes to play table tennis with his daughter – Quan. But Dumbear found that Quan played table tennis better and better recently, Dumbear wondered that Quan would defeat him someday. So he wants to know if he will win in the next match.

To simplify the problem, you can assume that the probability of Dumbear’s winning in each match is a constant number P (But Dumbear and you don’t know the number exactly). Of course 0 ≤ P ≤ 1. Dumbear had already taken N matches with Quan. And he won for M matches. He wants to know the expected probability of his winning for the next match. But Dumbear is very dumb, so he wants you to help him.

Each line of the input file contains two numbers N and M (0 ≤ M ≤ N) indicate the number of the matches Dumbear had taken and the number of matches Dumbear had won. The last line of the input file contains two numbers "0 0".

For each line, output two integers A and B indicates the expected probability of Dumbear’s winning for the next match is A / B. Make sure that gcd(A, B) = 1!

1 1
2 1
0 0

2 3
1 2

2009 Multi-University Training Contest 3 - Host by WHU

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