Time Limit: 5000/1000 MS (Java/Others)

Memory Limit: 32768/32768 K (Java/Others)

## Description

Xiaoming has just come up with a new way for encryption, by calculating the key from a publicly viewable number in the following way:
Let the public key N = AB, where 1 <= A, B <= 1000000, and a0, a1, a2, …, ak-1 be the factors of N, then the private key M is calculated by summing the cube of number of factors of all ais. For example, if A is 2 and B is 3, then N = AB = 8, a0 = 1, a1 = 2, a2 = 4, a3 = 8, so the value of M is 1 + 8 + 27 + 64 = 100.
However, contrary to what Xiaoming believes, this encryption scheme is extremely vulnerable. Can you write a program to prove it?

## Input

There are multiple test cases in the input file. Each test case starts with two integers A, and B. (1 <= A, B <= 1000000). Input ends with End-of-File.
Note: There are about 50000 test cases in the input file. Please optimize your algorithm to ensure that it can finish within the given time limit.

## Output

For each test case, output the value of M (mod 10007) in the format as indicated in the sample output.

## Sample Input

2 2
1 1
4 7

## Sample Output

Case 1: 36
Case 2: 1
Case 3: 4393

lcy

## Source

2008 Asia Hangzhou Regional Contest Online