2015/round1/winning_at_sports.md

In the game of _Sports_, the object is have more points than the other team
after a certain amount of time has elapsed. Scores are denoted by two hyphen-
separated integers. For example, scores may include 3-2, 4-1, or 10-0. The
first number is how many points you've scored, and the second is the number of
points scored by the opposing team. You're very good at _Sports_, and
consequently you always win. However, you don't always achieve victory the
same way every time.

The two most extreme kinds of victory are called **stress-free** and
**stressful**. In a **stress-free** victory, you score the first point and
from then on you always have more points than your opponent. In a
**stressful** victory, you never have more points than your opponent until
after their score is equal to their final score.

Given the final score of a game of _Sports_, how many ways could you arrange
the order in which the points are scored such that you secure a **stress-
free** or **stressful** win?

### Input

Input begins with an integer **T**, the number of games you'll play. For each
game, there is one line containing the final score of the game in the format
described above.

### Output

For the **i**th game, print a line containing "Case #**i**: " followed by two
space-separated integers, the number of ways you can achieve a **stress-free**
or **stressful** win, respectively. Since these numbers may be very large,
output them modulo 1,000,000,007.

### Constraints

1 ≤ **T** ≤ 100  

Since you always win, the first number in any final score will always be
larger than the second. Both scores will be non-negative integers not
exceeding 2000.

### Explanation of Sample

In the third test case, you can get a stress-free win by scoring points 1, 2,
and 4, or points 1, 2, and 3. You can get a stressful win by scoring points 2,
4, and 5, or points 3, 4, and 5.