Owning a candy store is tough! You have to optimize all kinds of things. Lately you've been selling a very popular kind of candy called Whizboppers. These candies become rotten very quickly, which gives them the following properties:
Every day up to k people visit your store, and, starting from the first person, they will choose an integer number of cents to spend on Whizboppers: between 1 and C cents inclusive. You're going to sell Whizboppers for 1 cent per gram; so if a person wants to spend 4 cents, you will give that person exactly 4 grams of candy. You might do this by giving the person a 4gram box, or perhaps a 2gram box and two 1gram boxes.
What is the minimum number of boxes you need to order so that, no matter what amount each person orders, you can always give all of the people the mass of Whizboppers they want?
Note: When a person chooses how much candy to buy, you know what other people have already bought, but you don't know what future people will buy.
For example, if up to 2 people visit your store every day, and they spend up to 2 cents each (k=2, C=2), you could buy four 1gram boxes from your supplier. But you can do better: if you buy two 1gram boxes and one 2gram box, you can satisfy your customers. Here's how:
First Person Boxes given Second Person Boxes given  2 cents 1 x 2gram 2 cents 2 x 1gram 1 cent 1 x 1gram  1 cent 1 x 1gram 2 cents 1 x 2gram 1 cent 1 x 1gramRegardless of what the first person orders, you can give out boxes so that the second person can still get the right amount of candy. So for k=2, C=2, you can serve any sequence of orders with 3 boxes.
The first line of the input gives the number of test cases, T. T lines follow, each of which contains two integers: k and C, the maximum number of people and the maximum number of cents each person may spend.
For each test case, output one line containing "Case #x: y", where x is the case number (starting from 1) and y is the minimum number of boxes you need to order every day.
1 ≤ T ≤ 100.
1 ≤ k ≤ 20.
1 ≤ C ≤ 3.
1 ≤ k ≤ 1000.
1 ≤ C ≤ 10^{12}.
Input 
Output 
4

Case #1: 3

In the first case, you can buy one 1gram box and two 2gram boxes. In the second case, you can buy two 1gram boxes and one 2gram box.
Points  Correct  Attempted 

7pt  21  21 
20pt  12  13 