5 s   512 MB

Description

Every weekend, dreamoon and drazil play in the park, and for each time, one of them has to
buys drinks for both. They agree to apply the following procedure to determine who is on the

1. Put n red balls and m white balls in a paper bag.
2. dreamoon and drazil draw a ball from the bag in turns. Note that once a ball is drawn,
it is removed from the bag.
3. The person who draws a red ball first has to buy drinks.

drazil lets dreamoon perform the first draw every week for dreamoon is older than him. One
day, dreamoon suddenly wonders what is the probability that he draws a red ball first. Can
you help him to calculate it? You may assume when every ball has the same probability to be
drawn.

Input

The first line contains a positive integer $T$, $T \leq 1770$, indicating the number of test cases. Each
test case has one line contains two positive integers $n$ and $m$ where $1 \leq n \leq 59$, $1 \leq m \leq 59$
and $n + m \leq 60$. $n$ is the number of red balls, and $m$ is the number of white balls.

Output

For each test case, output one line containing the answer represented by a reduced fraction.

2
1 1
1 2
1/2
2/3

Source

2015 ACM-ICPC Taiwan Online Programming Contest