Chocolate Box
Input: standard input
Output: standard output
Time Limit: 1 second


Recently one of my friend Tarik became a member of the food committee of an ACM regional competition. He has been given m distinguishable boxes, he has to put n types of chocolates in the boxes. The probability that one chocolate is placed in a certain box is 1 / m. What is the probability that one or more boxes are empty? At first he thought it as an easy task. But soon he found that it was much harder. So, he falls into a great trouble and asked you to help him in this task.

 

Input

 

Each line of the input contains two integers n indicating total number of distinguishable types of chocolate and m indicating total number of distinguishable boxes ( m <= n < 100 ). A single line containing -1 denotes the end.


Output

 

For each of the cases you should calculate the probability corrected to seven decimal places. The output format is shown below.

 

Sample Input

50 12

50 12
-1

Sample Output

Case 1: 0.1476651

Case 2: 0.1476651

 

Problem Setter: A. K. M. Saifun Nabi (Shabuj) ( BUET PESSIMISTIC )
Thanks to Anupam Bhattacharjee for his alternate solution and data.